AMBIGUITIES RESOLUTION WITH GPS AND GLONASS ......Leslie, Cyril my desk neighbour, Nicola, Martine, Melania, Anshu for the many discus-sions and advices that have enriched my stay

AMBIGUITIES RESOLUTION WITH GPS AND GLONASS MEASUREMENTS

IN OBSTRUCTED ENVIRONMENT

MASTER THESIS

Submitted for the degree in Master of Science in Sciences and Environmental Engineering

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

Geodetic Engineering Laboratory

By

Leïla KLEINER

June 2010

PLAN GROUP– Master Project Leïla Kleiner June 2010

Final report_23June2010 -3-

Table of contents

I ABSTRACT ........................................................................................................................... 6

II RÉSUMÉ ............................................................................................................................... 6

III AKNOWLEGMENTS ............................................................................................................. 7

IV INTRODUCTION ............................................................................................................... 8

IV.1 CONTEXT ................................................................................................................................ 8

IV.2 PROJECT OBJECTIVES ......................................................................................................... 9

IV.3 THESIS OUTLINE ...................................................................................................................... 9

V STAT OF THE ART ............................................................................................................... 11

VI PROCESSING ................................................................................................................. 12

VI.1 SATELLITE DATA ................................................................................................................... 12

VI.1.1 GLOBAL SATELLITES SYSTEMS .................................................................................... 14

VI.1.2 GNSS ERRORS .............................................................................................................. 16

VI.1.3 GPS SPECIAL FEATURES ............................................................................................. 17

VI.1.4 GLONASS SPECIAL FEATURES................................................................................... 17

VI.2 PLANSOFTTM PROCESSING................................................................................................ 19

VI.2.1 THE OBSERVATIONS .................................................................................................... 19

VI.2.2 ENTIRE PROCESS OVERVIEW .................................................................................... 20

VI.2.3 INITIALIZATION OF REQUIRED PARAMETERS WITH CODE MEASUREMENTS ... 21

VI.2.4 PARAMETERS INITIALIZATION AND VELOCITY DETERMINATION WITH DOPPLER MEASURMENTS ........................................................................................................ 22

VI.2.5 POSITION DETERMINATION WITH CARRIER PHASE MEASURMENT ................... 23 VI.2.5.1 OBSERVATION PREPARATION ............................................................................................................ 24 VI.2.5.2 INTER-STATION SINGLE-DIFFERENCE STEP ........................................................................................ 25 VI.2.5.3 INTER SATELLITE DOUBLE-DIFFERENCE STEP ..................................................................................... 26 VI.2.5.4 AMBIGUITIES RESOLUTION ................................................................................................................... 28 VI.2.5.5 RELIABILITY OF THE FIXED AMBIGUITIES FOUND .............................................................................. 33

VI.2.6 CYCLE SLIP DETECTION ............................................................................................. 36

VI.3 ANALYSIS TOOLS ................................................................................................................. 36

VI.3.1 REQUIREMENTS DEFINED BY THE APPLICATION ................................................... 36

VI.3.2 STATISTICS TOOLS ........................................................................................................ 38 VI.3.2.1 A PRIORI QUALITY OF COMPUTED SOLUTION ................................................................................ 38 VI.3.2.2 CRITERIONS TO ASSESS ACCURACY AND PRECISION ................................................................. 40 VI.3.2.3 INTEGRITY, CONTINUITY AND AVAILABILITY OF MEASURMENTS ................................................. 43

VII DATA ANALYSIS ............................................................................................................ 45

VII.1 DATA ANALYSED ............................................................................................................. 45

VII.1.1 GNSS-INS REFERENCE................................................................................................. 45

VII.1.2 GNSS PLANSOFT DATA .............................................................................................. 46

VII.2 DATA SET UNDER TREES CLOSE TO THE BOW RIVER ................................................. 49

VII.2.1 TEST DESCRIPTION ....................................................................................................... 49

VII.2.2 GNSS-INS REFERENCE FOR THE BOW RIVER DATA SET ....................................... 51

VII.2.3 GNSS PLANSOFT SOLUTION FOR THE BOW RIVER DATA SET ............................ 54 VII.2.3.1 GLOBAL QUALITY OF THE COMPUTATIONS 5 AND 6 FOR THE GLOBAL DATA SET............ 55

VII.2.4 DATA ANALYSIS ........................................................................................................... 56 VII.2.4.1 INTERNAL QUALITY OF GNSS PLANSOFT DATA .......................................................................... 56 VII.2.4.2 IMPACT OF THE AMBIGUITIES RESOLUTION ................................................................................ 62 VII.2.4.3 COMPARISON OF DIFFERENTS ENVIRONMENTS ....................................................................... 65 VII.2.4.4 GAIN OF GNSS VERSUS GPS ALONE ............................................................................................ 74



VII.3 ANALYSIS OF THE INFLUENCE OF THE NATURE OF OBSTACLES OVER THE

SOLUTION ........................................................................................................................................ 79

VII.3.1 TEST DESCRIPTION ....................................................................................................... 79 VII.3.1.1 GNSS_INS REFERENCE FOR THE TREES AND BUILDING DATA SET .......................................... 80

VII.3.2 GNSS PLANSOFTTM SOLUTION FOR THE TREES AND BUILDING DATA SET ....... 80

VII.3.3 DATA ANALYSIS ........................................................................................................... 81

VIII CONCLUSION AND PERSPECTIVES.............................................................................. 84

IX TABLES DES ILLUSTRATIONS .......................................................................................... 87

IX.1 TABLE OF FIGURES: ............................................................................................................. 87

REFERENCES ....................................................................................................................................... 89

X ANNEXES OF COMPUTATIONS: ...................................................................................... 93



ACRONYM LIST

Compass: Global navigation system of China

DD: double difference / double differencing / double differenced

DOP: Dilution of Precision

ECEF: Earth-Centred Earth-Fixed Coordinate System

EGNOS: European Geostationary Overlay Service, augmentation System in Europe

Galileo: Global navigation system developed by Europe

GDOP: Geometric Dilution of Precision

GLONASS: GLObal Navigation Satellite System of the Russian Federation

GLONASST: GLONASS clocks time

GNSS: Global Navigation Satellite System

GNSS-INS: Relative to GPS and GLONASS coupled to inertial data

GPS: Global Positioning System developed by the United States

HDOP: Horizontal Dilution of Precision

IMU: Inertial Measurement Unit

INS: Inertial Navigation System

IRNSS: India Regional Navigational Satellite System

MSAS: Satellite-based Augmentation System in Japan

PDOP: Position Dilution of Precision

QZSS : Quasi-Zenith Satellite System in Japan

SBAS: Satellite based augmentation system

SD: single difference / single differencing / single differenced

UTC_SU: Universal Coordinated Time of Soviet Union time standard

VDOP: Vertical Dilution of Precision

WAAS: Wide Area Augmentation System in USA

LIST OF OPERATORS

a vectors are in bold and lower-case

A matrices are in bold and upper-case

is the between-receiver differencing of quantity a

is the between-satellite differencing of quantity a

δa is the between-epoch differencing of quantity a

is the between-satellite between-receiver double differencing of a

A-1 is the inverse of A

AT is the transpose of A

is the estimated value for a

is the solution corresponding to a

is the rate of change of a

is the absolute value of quantity a

is the nearest integer operation on quantity a



I ABSTRACT

The localization of a moving-sensor like laser-scanner or a camera ordinary is ordinar-

ily done with a combination of satellite and inertial data. This measurements combi-

nation allows reaching a sufficient continuity and integrity of the position whatever

the environment crossed. The satellite measurements are used to correct the bias of

the inertial location. They need to be accurate enough, even in closed environment

such as under trees or in urban areas. The highly precise relative dynamic positioning

is based on precise dual frequency carrier phase observations, and usually com-

puted with double differencing process. A prerequisite for carrier phase positioning is

the ambiguity resolution. Once the integer carrier-phase ambiguities are fixed cor-

rectly, the positioning reaches a sub-centimetre precision. This resolution of the am-

biguities is complicated in obstructed environments because cycle slips affect the

continuity of the satellite signal. By using other satellite systems, the measurement

redundancy as well as the accuracy, availability and reliability of the final position

are increased. The GLONASS Russian satellite system completes well the commonly

used Global Satellite System (GPS) and can be used to augment GPS data. Again

since 2009, this system offers 21 available satellites over the 24 satellites composing

the full operational GLONASS constellation. As demonstrated in this project, this

measurement augmentation using GPS and GLONASS data is especially relevant for

obstructed environments. The computation of the final solution presents difficulties

linked especially with the differences in signal structure between the two satellite

systems. This project presents the main steps of the software PLANSoftTM built by the

PLAN research group of the University of Calgary. This software computes precise

positions using GPS and GLONASS dual frequency carrier phases. Tests in obstructed

environment were conducted to analyse different kinds of computation parameters,

the ambiguity resolution and the gain obtained with GLONASS.

II RÉSUMÉ

La localisation d‟un capteur mobile tel qu'un laser scanner ou un appareil photo-

graphique est usuellement réalisée grâce à une combinaison de mesures satellitai-

res et inertielles. Cette combinaison de mesures permet d‟atteindre une continuité

et une intégrité suffisante quelque soit le milieu traversé. Les mesures satellitaires seu-

les sont souvent suffisantes en zones non obstruées. Les mesures satellitaires sont utili-

sées pour corriger la dérivée de la localisation inertielle.

Elles ont donc besoin d‟être spécialement précises, même dans des environnements

fermés comme sous des arbres ou en milieu urbain. Une position précise en mouve-

ment est basée sur des observations de phase double fréquences, généralement

calculées par un processus de double différence.

Une condition préalable pour le positionnement grâce à des mesures de phase est

la résolution des ambiguïtés de la phase porteuse. Une fois les ambiguïtés fixées, le

positionnement atteint une précision sub-centimétrique. Cette résolution

d‟ambiguïtés est complexe, particulièrement en environnement obstrué, où des

sauts de cycles affectent la continuité du signal satellite. L‟augmentation des mesu-

res par l‟utilisation de satellites d‟autres systèmes améliore la précision, la disponibilité

et la fiabilité de la position. Le système de satellites russe GLONASS complète effica-

cement le Global Positioning System (GPS) américain couramment utilisé mondia-

lement, et peut être utilisé pour enrichir les données GPS. Depuis 2009, le système

GLONASS offre à nouveau 21 satellites sur les 24 de la constellation opérationnelle



complète. Comme démontré dans ce projet, l‟augmentation des mesures GPS par

des mesures GLONASS est particulièrement pertinente pour des environnements obs-

trués. Le calcul de la solution finale présente des difficultés liées notamment à des

différences de structure du signal des deux systèmes de satellites. Ce projet présente

les principales étapes du calcul réalisé par le logiciel PLANSoftTM développé dans le

groupe de recherche PLAN à l‟Université de Calgary. Ce logiciel calcule une posi-

tion précise utilisant des mesures de phase double fréquence GPS et GLONASS. Des

tests en environnement obstrué, très densément végétalisé, permettent d‟analyser

différents paramétrages de calcul, la résolution des ambiguïtés et le gain obtenu

avec GLONASS.

III AKNOWLEGMENTS

I would like to thank Dr. Gérard Lachapelle, director of the research Group PLAN for

his excellent supervision and financial support during my Master Project done at the

University of Calgary. His advices during the presentations and discussions have

been very precious to improve my work. Having had the opportunity to realise my

Master Project in a research group at the forefront of the navigation technology was

an exceptional experience not possible without him.

Deep gratitude and appreciation are extended to the professor Bertrand Merminod,

head of the Geodetic Engineering Laboratory of EPFL for his supervision, precious

advices and numerous readings and feedbacks. His encouragements have marked

my career and allowed me to progress. His many teachings during my studies in EPFL

provide me with the basis of my knowledge in satellite navigation and the mean to

progress.

I want to give specials thanks to Dr. Valérie Renaudin for the energy and for advising

me, reading my work and giving me numerous feedbacks during my Master project.

Her qualifications in human contacts, her technical support, her perspicacity, her

enthusiasm and her patience have been particularly beneficial for my progression.

The many discussions we had together were really rich and successful.

Thank also to Richard Ong for the technical support and advices on the operation of

the software used. His technical skills were always targeted and effective.

Thanks again to my colleagues of the PLAN research Group, without whom the

working days would not have been so pleasant and rewarding. Discover Calgary

and the Rockies with them was an unforgettable experience. A special thought for

Leslie, Cyril my desk neighbour, Nicola, Martine, Melania, Anshu for the many discus-

sions and advices that have enriched my stay and work.

Last but not least, I would like to thank my family for their unfailing support and en-

couragements. Finally my future husband and best partner in all my projects is infi-

nitely thanked for his love, understanding and patience. This work would not have

been conceivable without his support.



IV INTRODUCTION

Numerous topometric applications dedicated to dynamic motion, e.g. laser-

scanning or photogrammetry, need a precise location of the sensor to process data.

The precise positioning is ordinary reached by coupling satellite positioning signals

and Inertial Navigation System (INS) data. The quality of the INS data depends

strongly on the type of onboard gyroscope and accelerometer sensors. The relation

between the quality of these sensors and their cost is exponential.

The satellite positioning quality influences too the quality of the final combined posi-

tion and the improvement of his quality can be cheaper. Therefore precise satellite

positioning is investigated in this project.

Firstly, the project context is presented with the applications that motivate this work.

Then the project objectives are explained and finally the thesis outline is given.

IV.1 CONTEXT

The Positioning, Location and Navigation research group (the PLAN) from the Geo-

matics Engineering Department in the University of Calgary has developed the

PLANSoftTM software to compute precise positioning in static and dynamic motion.

Tests have already been done to assess the PLANSoftTM within the framework of skiing

applications to increase sportive performance and for vehicle to vehicle positioning

to improve the security. Relative vehicle positioning in hard conditions like in moun-

tains, urban canyon or road with overhead foliage have already been tested.

During this project the PLANSoftTM software was tested for pedestrian topometric ap-

plications. Precise positioning of pedestrians is necessary for applications such as

footpaths cartography, the creation of rapid urban maps or the localisation of pic-

tures taken by a pedestrian. For this last application, i.e. the representation of views

adapted for pedestrianized needs requests the trajectory localisation of a camera

placed on a pedestrian. By this way, views of trails observed by pedestrians could

be directly geolocated and made available in Google Street View. Indeed nowa-

days Google Map with Street View integrates only view shot from roads. From the

user point of view, it could also be interesting to dispose of views from exclusively

pedestrian passages, located in parks or in paths closed to the road traffic. The

creation of these views involves the localization of the pictures taken by pedestrians,

so the precise positioning of pedestrian‟s trajectories is required. These pedestrian

trajectories may occur in obstructed environments, where the best possible position-

ing quality should be reached.

High precise relative dynamic positioning is based on precise carrier phase observa-

tions and usually computed with double differencing process. A prerequisite for car-

rier phase positioning is the ambiguity resolution. Once the integer carrier-phase

ambiguities are fixed correctly, the carrier-phase observations are conceptually

turned into half of the phase wavelength namely sub-centimetres level of positioning

precision [Kim & Langley 2000]. This can be achieved in open sky environments using

the current GPS constellation and with low receiver dynamic motion [Ong et al

2009].

The positioning accuracy, availability and reliability depend on available satellites.

To improve the positioning quality, another satellites system, like GLONASS, can be

used by integrating GPS and GLONASS observations together. Nowadays GLONASS



system is rebuilt thanks to important investments of the Russian government. There-

fore it becomes again relevant to investigate the use of combined GPS and GLON-

ASS systems. In May 2010, the GLONASS system offered 21 satellites available over 24

satellites composing the full operational constellation [2]. In the future, other systems,

i.e. Galileo or Compass, will provide even more satellites, which will be used to aug-

ment GPS positioning. Exploring the gain of GLONASS, particularly in congested en-

vironment, is one of the goals of this project.

IV.2 PROJECT OBJECTIVES

This project involves analysing the use of combined GPS and GLONASS signals for

precise positioning in obstructed environment.

The first goal is the understanding of the computations necessary to produce precise

positioning. The understanding of the PLANSoftTM software, in order to to relate the

post-processing performances with the different environments crossed, was first tar-

geted. A detailed study of the different parametrization of the computation and the

associated main equations is necessary. Particularly the different combinations ap-

plied to the observations used in the final computation are studied to foresee their

eventual impact on the post-processing results. Understanding the process of ambi-

guities resolution was done in details in order to assess the gain of adding GLONASS

and the impact of difficult environments. This first theoretical analysis was done in-

dependently without accessing to the PLANSoftTM code processing.

The second objective is the comprehension of the difficulties inherited from the addi-

tion of GLONASS to GPS data. The gain of combined GPS and GLONASS measure-

ments compared to GPS only in different environments is also analyzed through dif-

ferent tests conducted in real conditions.

The third goal is to study the position‟s quality reached in difficult environments, e.g.

under trees or man-made constructions like roofs. This last objective was also proc-

essed through different data sets.

The study is based on the equations used for post-processing and the analysis of ex-

perimental data. The tests were conducted in congested environments for analysing

the impact of cycle slips on ambiguities‟ resolution. The purpose of these tests is to

analyze PLANSoftTM processing performances in extreme conditions and more spe-

cifically the ambiguities resolution part. Pedestrian trajectories are less smoothed

than vehicle ones. Therefore the smoothing process of the PLANSoftTM was tested to

observe if the last is adapted to pedestrian motion. All tests have been designed in

order to experiment these project‟s objectives.

IV.3 THESIS OUTLINE

The report begins with a review of the state of the art of precise positioning with GPS

and GLONASS measurements in the chapter V STAT OF THE ART. Then the satellites

systems are presented in the first part of chapter VI PROCESSING. The global process

of the PLANSoftTM is explained in the chapter VI.2 PLANSOFTTM PROCESSING. The cor-

responding main equations are presented in this chapter VI.2.5.4 AMBIGUITIES RESO-

LUTION, including more details about the ambiguities resolution Lambda method, a

key process to reach high precision positioning. The difficulties encountered while to



estimate a combined GPS-GLONASS solution and particularly to fix the ambiguities is

detailed in this chapter.

To compare the results and analyze them, the study and the development of statis-

tics tools are involved. They are presented in the chapter VI.3 ANALYSIS TOOLS.

Chapter VII DATA ANALYSIS presents pedestrian tests that took place in congested

environments with trees and building. Different parametrizations of the post-

processing are tested trying to highlight optimal solutions as a function of the envi-

ronment. The different computations are presented in chapter VII.1.2 GNSS PLAN-

SOFTTM DATA. Two data sets are analysed in this report. The first one contains essen-

tially parts covered by trees and is detailed in chapter VII.2 DATA SET UNDER TREES

CLOSE TO THE BOW RIVER. The second data set compare the impact of two different

obstructions: one with trees and the other one with buildings. It is detailed in chapter

VII.3 ANALYSIS OF THE INFLUENCE OF THE NATURE OF OBSTACLES OVER THE SOLUTION.

A conclusion summarizing the main results and perspectives ends the report in chap-

ter VIII CONCLUSION AND PERSPECTIVES.



V STAT OF THE ART

During this project three main elements are addressed. The first topic is the possibility

to augment GPS measurements with GLONASS data, especially to improve the am-

biguities resolution. The second element is the ability of PLANSoftTM to compute pre-

cise positions with GPS and GLONASS signals. The third one is the quality of position-

ing in obstructed environment. For each element, it sounds useful to do a short re-

view of the previous studies.

Several works have already been done on augmenting GPS measurements with

GLONASS. These researches have been undertaken especially before the year 2000,

when the potential of GLONASS was obvious and before its degradation. Comput-

ing positions with GPS and GLONASS comprises some difficulties, especially because

of the differences in signal structures between GPS and GLONASS waves. The main

difficulties in ambiguities resolution is the procedure of the ambiguity search and the

performance of the choice of the good integer ambiguities set from another candi-

date [Kim & Langley 2000]. To improve these elements different algorithms for solving

ambiguities were developed by scientists. A first and simplest technique solves am-

biguities using C/A or P code pseudoranges generally improved by a smoothing

process [Kim & Langley 2000]. A second solution uses the Ambiguity Function

Method (AFM). This algorithm is applied on only the fractional value of the instanta-

neous carrier-phase measurements to avoid degradation of the solution‟s quality

induced by cycle slips or a whole-cycle change of the carrier phase [Kim & Langley

2000]. A third class of ambiguities resolution algorithms is based on the integer least-

squares developed by Teunissen in 1993 [Kim & Langley 2000]. This last technique is

popular and is used in the PLANSoftTM processing. With GPS and GLONASS data, the

ambiguities resolution process is complicated by the frequency division multiple ac-

cess (FDMA) structure of GLONASS. A parametrization of the double differencing

equation is necessary to eliminate the GLONASS clock offset. It can‟t be eliminating

using a normal double differencing process as the phase wavelengths between di-

verse GLONASS satellites are different. The FDMA structure induces some frequency-

dependent biases resulting from inter-frequency interferences. These frequency de-

pendant biases are caused by differences in the signal acquisition between one

receiver and another. They are related to the hardware or signal processing archi-

tecture of the receiver or from temperature‟s variations [Takac & Petovello 2009].

Contrary to GPS, for GLONASS measurements these biases are different from one

satellite to another and cannot be eliminated by the double differencing process.

Because these biases are absorbed by the ambiguities resolution, they complicate

the ambiguities resolution process [Takac & Petovello 2009].

Several PLAN‟s group works have preceded the design of PLANSoftTM. One of them is

the development of a software to determine heading, pitch, and roll combining GPS

and GLONASS carrier phase and using a single differencing technique [Keong 1999].

These parameters are part of a combined GPS, GLONASS and inertial (GNSS-INS)

final solution. This work was taken over by R. Ong and implemented in the PLAN-

SoftTM. A double difference equation parametrization using dual carrier phase dou-

ble differencing is implemented in this new software. A float estimated solution is

computed using single difference between the receivers with pseudorange, phase

and Doppler measurements. The solution is then double differenced between satel-

lites to resolve the ambiguities.



As said in the introduction, these PLANSoftTM solutions have already been tested for

assessing skiing performances and for vehicle to vehicle positioning. Road tests with

receivers placed on two cars have been achieved in harsh conditions like in moun-

tains, urban canyon or road with overhead foliage. These tests have shown an ac-

curacy and availability improvement when GLONASS are added [Ong et al 2009]. In

the mountain highway, the accuracy obtained is around a horizontal Root mean

square (RMS) of 1 centimetre for a GPS-GLONASS single frequency solution [Ong et

al 2009]. In heavy overhead foliage, the solution using GPS-GLONASS dual frequency

with a L1 and L2 widelane combination provide 65% of the time sub-decimetre hori-

zontal accuracy [Ong et al 2009]. In urban canyons, the ambiguities can be re-

solved but high precision isn‟t reached. In this challenging environment, the horizon-

tal RMS of the GPS-GLONASS solution is around 10 metres with an availability of 58%

[Ong et al 2009].

In light of the tests that had already been done and of the interest in topometric

applications for tracking pedestrian, it was decided to test the quality of the PLAN-

SoftTM positioning for pedestrian applications with dynamic motion in obstructed en-

vironments.

VI PROCESSING

This chapter gives information about the satellite data used, the process of position

computation and the statistics tools employed to analyze the results‟ quality.

VI.1 SATELLITE DATA

The satellite positioning system operates with radio navigation signals emitted by

satellites. To determine a position several information are required: a time and space

reference system, measurements, correction of measurements to account for errors,

a mathematical model to estimate the final position and transformation of results to

the final geographical reference system. The GPS reference time is the Coordinated

Universal Time (UTC), time with the stability and the precision of International Atomic

Time (TAI). The geodetic reference frame is the World Geodetic System - 1984

(WGS84), a global reference ellipsoid centered in the Earth center of mass. The

WGS84 ellipsoid is described in the Earth-Centered Earth-Fixed (ECEF) Cartesian ro-

tating reference coordinate system [Kaplan & Hegarty, 2006]. The WGS84 is the

standard physical model of the Earth used for GPS applications. This Earth ellipsoid is

described by his shape, his angular velocity and the Earth mass included in it. WGS84

is also based on a detailed gravity model of the earth established thanks to multiple

measurements around the world [11]. Specific properties of the WGS84 model are

here circular cross-sections parallel to the equatorial plan with a radius equivalent of

the mean equatorial radius of the earth, and here ellipsoidal cross-sections normal to

the equator plane [Kaplan & Hegarty, 2006]. The semi major axis of this ellipsoid co-

incides with the hearth equator line, and the semi minor axis corresponds to the po-

lar diameter of the Earth. In this global geodetic reference system, the position is de-

scribed by the longitude, the latitude and the height. The position is computed by

spatial trilateration of distance between satellites and the receiver. These distances

are measured in real time thanks to the trip time of the signal. This method requires a

very precise time computation and the addition of small correction. For this purpose,

each satellite is equipped with precise atomic clock. The receiver time measure-



ment is realized by electronic clock controlled by quartz. Each satellite transmits over

carrier wave at a specific frequency the Broadcast Ephemeris, a message contain-

ing information on satellite orbital parameters, on satellite health and clock. This sat-

ellite navigation message is decoded by the receiver. The high frequency signal

generated by the satellite as pure sinusoidal waves is modulated by a digital modu-

lation technique to carry information [Keong 1999]. The unknowns required to com-

pute the position are the receiver coordinates (longitude, latitude and height) and

the receiver clock error. This delay between receiver clock and GPS time biases is

equivalent for all measured distances, so only one receiver clock error is added. The

delay between satellite clock time and GPS time is already corrected in the naviga-

tion message. To resolve this linear and independent equations system of four un-

knowns at least four satellites are required. Depending on computation mode of the

difference, i.e static or dynamic, different combination of equations may be used,

but the basis equation used sill remains the same. In general the positioning can be

achieved using code, carrier-phase or Doppler shifts measurements [Eissfeller et al

2007]. The different types of observations and processing models are summarized in

the following:

Single point positioning applies to single receiver. The absolute positioning

contains errors like orbit errors, satellite and receiver clock errors, atmospheric

(ionospheric and tropospheric) errors, multipath and receiver noise. Different

observations can be used:

o Code phase measurements measure pseudoranges, i.e. the apparent

ranges between satellites and a receiver.

o Carrier phase measurements in unit of cycle are computed by differ-

entiating the phase of the signal generated at the receiver and the

carrier phase received from a satellite at the instant of the measure-

ment. The number of cycles (ambiguities) must be known to compute

the distance travelled by the signal between the receiver and the sat-

ellite. The precision is a few centimetres for dynamic positioning and a

few millimeters for static positioning. This method represents the most

precise solution when ambiguities are solved because carrier phase

measurements have a significantly lower noise level than the code

pseudoranges [Keong 1999].

o Carrier phase smoothed pseudoranges computes a position weighting

pseudorange and carrier phase measurements. It is based on the as-

sumption that pseudorange is robust but noisy and carrier phase is less

robust but ambiguous due to the ambiguity resolution step. The best

result is obtained by merging “absolute” pseudorange and “relative”

carrier phase. The bias between them approximates the value of the

ambiguity [Lachapelle and all, 2009]. But the problem of ambiguities

resolution remains. At the beginning of signal acquisition more weight is

given to pseudorange measurements and after some time, to the car-

rier phase measurement. If a cycle slip is detected, the weight on the

carrier phase is reset to zero. This recursive filter could be interesting for

the float ambiguity estimation phase. When ambiguities are resolved,

the carrier phase measurement is improved. This smoothing method



leads to an horizontal error smaller than 50 centimeters [Lachapelle

and all, 2009].

Differential measurements apply to two receivers tracking satellites signals at

the same time. Assuming that errors like atmosphere, orbit errors and satellite

clock have the same effect on both receiver observations, these errors can

be removed by differentiating the observations from the two receivers. Ob-

servations used for differential positioning are code or carrier phase meas-

urements. Differential pseudorange positioning assisted with pseudorange

corrections (DGPS) reduces the horizontal error to 1 to 5 metres.

Positioning with Doppler shifts measurements is also possible. The position can

be integrated from receiver velocity computed with Doppler shift. This tech-

nique has the advantage to give a measure with low bias because it uses

relative velocities [HOW et al. 2002]. All recognized signals, even if they are

very noisy, could be used for Doppler computation, which constitutes a seri-

ous advantage compared to code positioning [Lehtinen 2001]. The problem

of this method is that achieving a continuous estimation is not possible if GPS

signal is blocked. The Doppler position computed with signal frequency shifts

and without pseudorange measurements is clearly less precise than the

pseudorange positioning [Lehtinen 2001]. Finally the Doppler positioning

could be foreseen as a considerable option for a rough positioning estimate if

the standard GPS positioning fails [Lehtinen 2001].

This computation may be done either in real-time or in post-processing mode. In or-

der to provide very precise positioning previously described observation and proc-

essing models could be combined. Different filtering techniques can also be ap-

plied, e.g. Kalman filter or least square. The quality of the measures depends on the

type of receiver, the number of tracked satellites and their geometry. The satellite

availability is the most important element to achieve good quality of positioning.

Different global satellites systems exist worldwide that can used to collect these

measurements.

VI.1.1 GLOBAL SATELLITES SYSTEMS

Global Navigation Satellites Systems (GNSS) have been developed by different

countries. The well known Global Positioning System (GPS) was the first radio-based

navigation systems providing timing and positioning services continuously. At the

time of writing, this system counts 31 satellites distributed in 6 orbits. Information

about precise satellite orbital parameters, satellite health and satellite clock are

emitted by each satellite on 2 modulations codes and soon on 4 modulations codes

transmitted on the two carrier frequencies L1 and L2 and in the future on the fre-

quency L5 too. In October 1982, the GLObal Navigation Satellite System (GLONASS)

was launched by the Russian federation. In early 1995, the system counted 24 satel-

lites. After its completion, the number of satellites in orbit decreased mainly due to

the collapse of the Russian economy, the Russian government wasn‟t able to invest

further in this technology. But at the 2005 European Navigation Conference in Mu-

nich, the Russian Federation has announced a new funding plan and the restoration



of satellite system [Hewitson & Wang 2005]. At the time of writing 21 satellites are

available over the 24 satellites composing the full operational GLONASS constella-

tion [2]. Europe is working on Galileo, a new system comprising a constellation of 30

satellites. This development is pursued by the European Commission (EC) and the

European Space Agency (ESA). The Galileo Open service, the Public Regulated Ser-

vice and the Search and Rescue Service will be provided as of early 2014 [4]. This

system will be inter-operable with GPS and GLONASS [5]. GPS and Galileo use similar

signals and signal structures, so receiver development can be carried out similarly for

both systems [Eissfeller and all, 2008]. The arriving of the future system Galileo is par-

ticularly waited. The orbit inclination angle of GALILEO of 56° is not so different than

the GPS one to complete the constellation as GLONASS do it, but the adding of 30

satellites will efficiently improve the worldwide coverage. China has also invested in

an independent global satellite positioning system with a constellation of 25 to 35

satellites including 4 geostationary satellites named COMPASS [3]. Its CDMA signal

structure, similar to Galileo and modernized GPS, could allow interoperability be-

tween systems. COMPASS frequencies overlap Galileo‟s ones. This overlapping could

be convenient for receiver design purposes but causes problems in the case of

emergency because Europe couldn‟t jam the Chinese signal without jamming the

Galileo encrypted one [Cameron 2008]. At the current time, only 2 COMPASS satel-

lites have been launched for testing reasons [3]. While Compass would cover the

entire China and adjacent region by the end of 2010 or early 2011, its completion is

expected for 2020 [ASM, 2009]. Other systems exist like Quasi-Zenith Satellite System

(QZSS) in Japan. QZSS will be constituted by 3 geostationary satellites and will be

used as GPS system augmentation. Finally India want to develop a regionally

autonomous system named India Regional Navigational Satellite System (IRNSS). The

project, approved in 2006, is expected to be fully operational in 2012 or 2013. The

future is looking forward to a common use of the global satellites systems. In addition

to GPS signals, other GNSS information could be added to improve the final position-

ing quality. The satellite geometry and availability will be improved, especially in ob-

structed environments like urban canyons.

To improve the quality of positioning it is possible to use Satellites Based Augmenta-

tion Systems (SBAS) in a differential mode. Augmentation systems consist of a net-

work of fixed receivers located at known positions on Earth and geostationary satel-

lites. By providing additional information, this system is able to enhance the reliability

and accuracy of GNSS position estimates and corrects some errors. Depending on

the world region different official SBAS are proposed. In United States the Wide Area

Augmentation System (WAAS) is proposed. This system is expected to augment GPS

measurements, and was originally developed for civil aviation. With 38 ground sta-

tions, the goal of WAAS is to obtain at least a 7 meters horizontal and vertical accu-

racy [6]. A similar system, named European Geostationary Navigation Overlay Ser-

vice (EGNOS), was developed in Europe. Nowadays this SBAS broadcasts messages

that can enhance the accuracy, availability and integrity of GPS and GLONASS po-

sitioning and in the future Galileo. EGNOS is constituted by 34 ground stations [7].

India has developed his own SBAS too, i.e. the Indian GPS Aided Geo Augmented

Navigation (GAGAN). Finally the Japanese Multi-functional Satellite Augmentation

System (MSAS) exists for Japan.

All experiment in this research have been conducted without using an augmenta-

tion system, as the analysis focuses on the use of GLONASS and GPS signal only.



VI.1.2 GNSS ERRORS

GNSS signal is degraded at his creation by the satellite antenna, during its transmis-

sion in space and at his acquisition by the receiver.

Generating the signal generation can introduce errors in the signal due to the satel-

lite payload distortions or the antenna gain.

Then, the wave propagation in free space and in the atmosphere attenuates the

signal. The ionosphere induces a dispersive reaction in the GNSS electromagnetic

wave, that delays the propagation time of the code and pushes forward the phase

with the same amplitude. Because the induced delay is a function of the frequency

and the relation between ionospheric delay and carrier frequency is known, dual

frequencies measurements taken at different epochs allow the removal of this iono-

spheric delay by double differencing. The troposphere induces delays too. But the

troposphere environment is non dispersive and affects the different carrier frequency

equally, so double frequency method couldn‟t remove it. This delay essentially de-

pends on the troposphere pressure, relative humidity and temperature.

The local environment around the receiver can cause multipath errors due to signal

reflection or diffraction over surrounding objects like buildings, ground. This always

cause delay on the signal. A 10° elevation mask could reduce multipath effect

[Keong 1999]. The signal can also be absorbed by local obstacles like foliage.

Finally when the signal is acquired by the antenna, some interferences could cause

errors in the signal tracked. A huge variety of interferences could be received at the

same time as useful signals. Doppler effect induces errors in the measurements too.

A variation of the propagation time results from the relative motions of the satellite

and the receiver. This Doppler effect differs with code or phase measurements. To

conclude, the receiver measurement‟s noise is generated by the receiver in the

tracking loop process. It is interesting to notice that GLONASS receiver‟s noise can

be two times more important than the GPS one [Keong 1999].

To assess the quality of measurements not only accuracy and precision should be

addressed. The continuity could be affected by errors too. This continuity of the posi-

tion calculation remains fragile and can be interrupted by external causes, for ex-

ample poor reception due to parasite, storm, high humidity or ionospheric scintilla-

tions. The continuity could as well be interrupted by a change in the orientation of

the antenna causing cycle slips, a poor satellites geometry or a failure in a satellite.

To summarize, the position accuracy depends on the satellites geometry, the at-

mosphere crossed, and the local environment. Systematic errors like orbital shifts or

delays in the atomic clock, poor calibration of the receiver (or other electronic sys-

tem) could alter the measurements too.

One way to reduce some of these errors is to apply double differences on the

measurements. This step is explained in chapter III.2.5.2 INTER-STATION SINGLE-

DIFFERENCE STEP and chapter III.2.5.3 INTER SATELLITE DOUBLE-DIFFERENCE STEP.

Once a specific processing model is applied, the type of receiver and antenna has

to be considered to reduce the error. For example, antenna gain pattern has a fixed

radiation pattern shaped to reduce low elevation angle signals and decrease errors

associated with RFI and multipath [Cannon & Lachapelle 2009].



VI.1.3 GPS SPECIAL FEATURES

The GPS Navigation message is diffused by each satellite over 2 modulations codes,

C/A and P codes, and the new “C” and military codes on newer satellites. These

codes are currently transmitted on two carrier frequencies: L1 (1575.42 MHz) and L2

(1227.60 MHz), and in the future on the frequency L5 (1176.45 MHz). To differentiate

signals, each GPS satellite transmits on the same frequencies but with different rang-

ing codes from one satellite to another. These codes were selected because they

have low cross-correlation properties [Kaplan & Hegarty, 2006]. This specificity of the

signal‟s structure is called the Code Division Multiple Access (CDMA) technique. It is

used to send different signals on the same radio frequency. The modulation method

used for these basic GPS signals is the Binary Shift Phase Keying (BPSK) [Eissfeller and

all, 2008]. So each GPS satellite can be recognized thanks to its unique pseudoran-

dom noise (PRN) code transmitted with the navigation message [Takac & Petovello

2009].

GPS is first of all a military navigation system, with the risk to have a jamming signal in

crisis time, making the GPS positioning non usable. The "Selective Availability" applied

to the signal in the past was discontinued on May 2000, allowing users to receive a

non-degraded signal.

VI.1.4 GLONASS SPECIAL FEATURES

GLONASS and GPS have strong similarities in their functioning and positioning proc-

esses [Seeber 2003]. GLONASS is, like GPS, a one-way ranging system. The radio-

signal structure of both systems is very similar: two carrier signals in the L-Band, signals

modulated by two binary codes and the message. The first GLONASS satellite was

launched in 1982, several years after the first GPS satellites. Since 2001, the Russian

government has approved a long-term plan to offer again a constellation of 24 sat-

ellites [Cai & Gao 2007]. Between 2003 and 2006, 4 GLONASS-M satellites were

launched. This „Modified‟ generation supports a number of new features, such as the

satellite lifetime increased to 7 years, an improved clock stability, and a second civil

modulation on L2 signal [Cai & Gao 2007]. Operational in 2010, GLONASS-K satellites

were launched in orbits. This third generation of satellites has an increased life-time

of 10 to 12 years, and contains a third civil signal frequency [Cai & Gao 2007]. After

a latency period, the GLONASS full operational capability is planned for early 2010-

2011 [Cannon & Lachapelle 2009].

The decisive differences with GPS are the signal multiplexing technique, the different

orbital inclination angle, the time reference system and the coordinate reference

system. Another point to consider is the lack of global coverage of ground stations.

The last could cause delays in the identification of a faulty satellite and the update

of satellite data [Eissfeller et al 2007].

The GLONASS coordinate system is called Parameters of the Earth 1990 System

(PZ90). Similarly to WGS84, the PZ90 is a Earth-Centered Earth-Fixed (ECEF) terrestrial

frame, but with different parameters [Keong 1999]. GLONASS data conversions are

necessary to combine GPS and GLONASs measurements.

The GLONASS time standard is the Universal Coordinated Time of Soviet Union

(UTC_SU). UTC_SU is synchronized with the international standard of UTC within one



microsecond. The GLONASS time (GLONASST) is based on UTC_SU standard. Due to

the location of Moscow, GLONASS has an exact offset of three hours with the

UTC_SU [Keong 1999]. This total offset of three hours must be removed from the

GLONASS time measurements to get them compatible with GPS measurements.

Due to the different orbital inclination angle (64.8 degrees for GLONASS compared

to 55 degrees for GPS), the dilution of precision (DOP) derived for GLONASS is better

in higher latitude geographical areas, such as in Canada, as illustrated in Figure 1.

Because of this high inclination angle, the position of the “shadow area” is slightly

different and leads to a better overall coverage worldwide [Seeber 2003].

Figure 1: PDOP value on the 17

th March 2010 around 6:30 pm given by the Russian Space

Agency [2].

GLONASS uses a frequency multiplex division access (FDMA) technique, which

means that each GLONASS satellite broadcasts its signals in slightly different fre-

quencies in the L1 and L2 frequency bands. While in GPS system, the carrier signal is

always transmitted at same frequency, the GLONASS carrier signal frequency is dis-

tributed between each satellites as follows [Seeber 2003].

The L1 frequencies are:

, (1)

where =0,…, 24 is the frequency number of satellite, has the value of 1.602 [MHz],

and worths 0.5625 [MHz].

L1 and L2 frequencies are related by

. (2)

This signal structure complicates the double frequencies computation, as we will see

in chapter III.2.5.2 INTER-STATION SINGLE-DIFFERENCE STEP in chapter III.2.5.3 INTER-

SATELLITE DOUBLE DIFFERENCE STEP. This is true especially to solve ambiguities, which



is a key to obtain a precise positioning at the centimeter level with GPS and GLON-

ASS dynamic data [Takac & Petovello 2009]. Furthermore the FDMA structure causes

some errors in the GLONASS Receiver which dependent biases are more difficult to

remove. These biases can result from inter-frequency interferences caused by differ-

ences in signal acquisition between one receiver and another, related to the hard-

ware or signal processing architecture of the receiver or from temperature‟s varia-

tions [Takac & Petovello 2009]. For GPS measurements this frequency-dependent

biases are identical and are removed in the double-difference equation. But for

GLONASS measurements, the biases are different from one satellite to another and

cannot be canceled. The use of similar receiver type could limit the error‟s part re-

lated to the receivers. However they still have residuals receiver dependent biases

that cannot be removed, especially for real time measurements and for different

receiver brands. They cause a significant bias in the float ambiguity solution [Takac

& Petovello 2009]. Other biases could come from variations in the GLONASS phase

measurements due to FDMA structure of the receiver [Takac & Petovello 2009]. In

order to remove the error induced in the signal, special receiver calibrations could

be apply on the signal tracked time. These calibrations enable to control errors like

inter-frequency bias, atmospheric errors, and multipath. Each receiver type has its

own calibration type [Takac & Petovello 2009].

VI.2 PLANSOFTTM PROCESSING

The PLAN Group‟s PLANSoft™ processing software used for this project estimates the

receiver position and velocity by a post processing of GPS and GLONASS measure-

ments. This software processes using a double-difference method well adapted for

GPS/GLONASS real time kinematic data.

VI.2.1 THE OBSERVATIONS

The data processed are GPS and GLONASS dual frequencies measurements. Two

types of data are required: the rover data and the basis data. Using a reference

station with known coordinates, the precision of observations at the “rover points”

could be improved [Eissfeller et al 2007]. So the basis data collection was systemati-

cally done on CCIT building, which has a well known station location. For this project

tests, reference data are acquired in static for more precise positioning. Rover data

are dynamic dual frequencies measurements. For both reference and rover receiv-

ers, code pseudorange, carrier phase and Doppler measurements are acquired.

The data were collected with a NovAtel OEMV2-G GPS and GLONASS receiver and

a NovAtel GPS-702 GNSS antenna. The recording frequency was chosen to be 2

Herz. An elevation mask of 10° was systematically applied to prevent multipath er-

rors.



VI.2.2 ENTIRE PROCESS OVERVIEW

The PLANSoftTM process applies a geometry based model that uses the satellite and

receiver position in its parametrization. The double-difference method applied is

summarized in Figure 2. This methodology uses single-difference of code pseudo-

range, carrier phase and Doppler measurements to estimate the position. A float

solution is first estimated using these single-difference measurements for the position,

the velocity, the receiver clock offsets, the zenith delay (long baseline only) and the

ambiguities. The ambiguities are then estimated with the double-difference solution.

Double-difference is also applied to other float parameters. The proposed method-

ology uses a phase parametrization to solve the GLONASS ambiguities with the dou-

ble difference solution. This methodology maintains almost a complete separation

between the float and the fixed solutions [Ong et al 2010]. As used by most GNSS

receiver, the parameters are estimated by a Kalman filter with the velocity modeled

as a random walk [Lachapelle et al 2009]. Compared with least squares process, the

Kalman filter leads to smoother and better positions. But it is also proved that it in-

creases the correlation of the errors between each other [Van Diggelen 2007]. In-

deed this estimation method can reduce the success rate of the decorrelation

process of ambiguities resolution within the LAMBDA method.

A forward and reverse processing and a combination of both solutions could op-

tionally be applied. The PLANSoft™ also implements an automatic calculation of the

base station position with a single point accuracy of a few metres, it implements a

misclosure-based ambiguity validation too and an innovation-based fault detection

[Lachapelle et al 2009]. The double differencing process help to remove errors like

stratospheric on from the measurements. In addition a tropospheric correction is

applied to remove these dispersive errors. In an unbroken sequence of the satellite‟s

carrier phase observation, the carrier phase ambiguity biases all measurements [Kim

& Langley 2000]. Once the integer ambiguities are fixed correctly, the carrier phase

observations reach millimeter-level hight-precision for range measurement [Kim &

Langley 2000]. Hence the sub-centimeter-level positioning solution can theoretically

be attained [Kim & Langley 2000]. Test over the PLANSoft demonstrates that satellite-

based positioning can be achieved with sub-decimeter accuracy using fixed differ-

ential carrier phase ambiguity resolution [Ong et al 2010]. To compute coordinates

with a precision in the range of centimeter to millimeter level, sufficient changes in

the receiver-satellite geometry are necessary, e.g. one hour of data collection [Te-

unissen 2002]. Once the integer ambiguities are fixed, and no cycle slip appears, the

measurements become very precise and short observation times may be used too.



Lambda Method to estimate integer

ambiguities

Single - difference

GPS double-difference

ambiguities

PLANSoftTM Working Flowchart :

Yes

ReferenceStatic dual frequency

data

RoverStatic or

dynamic dual frequency data

Data synchronisation

Inter-station single-difference STEP

Proces

Légende

Final solution[ (x,y,z),

velocity ]

Link between stepsData

Inter-satellite double-difference STEP

“Float“ estimated Parameters

“Fixed“ solution

Least square

Kalman filter

Choice

GLONASS double-

difference ambiguities

Double - difference

Extract position

and

velocity

No

Parameters estimation

Preparation process

Choice between options

Correleted ambiguities

?

Figure 2: PLANSoft flowchart

VI.2.3 INITIALIZATION OF REQUIRED PARAMETERS WITH CODE MEASUREMENTS

Although the carrier phase is more precise, the code solution has still a role to play

[Keong 1999]. The code solution is used to determine the base station coordinate

with single point accuracy of a few meters. It is as well exploits in the integer ambigu-

ity resolution process to compute the size of the search space [Keong 1999].



The receiver position vector and receiver clock offset can be estimated with pseu-

dorange measurements. The pseudorange observation equation is [Cannon & La-

chapelle 2009]:

(3)

where is the measured pseudorange,

the geometric range ( with rs the satellite position and Rr the receive

position both in ECEF frame),

is the orbital errors,

is the speed of light,

are the satellite and receiver clock errors respectively,

is the ionospheric delay,

is the tropospheric delay,

is the error term which includes noise, multipath, ect.

The pseudorange code measurements used in the data process of this project are

from the code C/A carried on the L1 wavelength.

VI.2.4 PARAMETERS INITIALIZATION AND VELOCITY DETERMINATION WITH DOPPLER

MEASURMENTS

The satellite-receiver relative motion induces a shift in the carrier frequency received

by the receiver as its motion changes. This so called Doppler shift must be removed

from the raw measured carrier phase, to obtain correct carrier phase measurements

[Keong 1999]. The Doppler effect is used as well to compute the receiver velocity.

Beside on the use of estimating the velocity, the Doppler measurements are used to

detect cycle slip as we will see it in the chapter VI.2.5.4 AMBIGUITIES RESOLUTION.

The Doppler observation equation is [Cannon & Lachapelle 2009]:

(4)

where is the measured Doppler,

is the geometric range rate, the change in the satellite-receiver range over an in-

terval of time divided by the interval ( with the satellite velocity

and the receiver velocity both in ECEF frame),

is the orbital errors drift, is the speed of light,

are the satellite and receiver clock errors drifts respectively,

is the ionospheric delay drift,

is the tropospheric delay drift,

is the error term which includes noise, multipath, ect.

The Doppler shift is produced by the motion of the satellite with respect to the user

[Kaplan & Hegarty, 2006].

The satellite velocity computation is based on ephemeris information and an orbital

model [Kaplan & Hegarty, 2006].



At first by knowledge of the satellite position, the satellite velocity and the receiver

position from the values of the Doppler shift we can obtain the velocity of the re-

ceiver. By this velocity integration, we can reach the position of the receiver.

VI.2.5 POSITION DETERMINATION WITH CARRIER PHASE MEASURMENT

The carrier phase measurements corrected for Doppler drift are collected with the

same sampling. One carrier phase observation corresponds to the number of full

integer carrier cycles plus the fractional cycle between the satellite and the receiver

for one particular receiver at any time. This decimal number of cycles multiplied by

the wavelength of the carrier represents the spatial distance between the satellite

and the receiver. The integer number of whole cycles in the carrier transmitted from

the satellite to the receiver, named carrier phase ambiguity term, cannot be known

directly because it is impossible to distinguish between cycles. So this ambiguity term

must be estimated in a dedicated process, as we will see it in chapter VI.2.5.4 AMBI-

GUITIES RESOLUTION. Additional to the carrier phase ambiguity, the receiver coordi-

nates, and the receiver clock error must be estimated to compute a rover position

with carrier phase measurements. The carrier phase observation equation, in units of

meters, is given by [Cannon & Lachapelle 2009]:

(5)

with is the measured carrier phase,

is the geometric range ( with rs the satellite position and Rr the receiver

position both in ECEF frame),

are the orbital errors,

is the speed of light,

are the satellite and receiver clock errors respectively,

is the cycle ambiguity (integer number),

is the ionospheric delay,

is the tropospheric delay,

is the Error term which includes noise, multipath, ect.

The ionospheric delay is subtracted because the dispersive nature of the ionosphere

increases the propagation speed of the carrier [Keong 1999].



VI.2.5.1 OBSERVATION PREPARATION

Different solution types can be used in the PLANSoft process. This solution combines

the carrier phase of dual frequency observations.

For GPS and GLONASS, L1 and L2 measurements can be linearly combined to gen-

erate a new measurement [Cannon & Lachapelle 2009].

(6)

where is the new carrier phases measured,

and are the L1 and L2 carrier phase data, and are factors depending on solution‟s type.

The wave length of the new phase measurement could be computed as [Cannon &

Lachapelle 2009]:

(7)

where is the new carrier phases wave length,

is the speed of light, is the new carrier phases frequency.

The ambiguity is then combined. The combined solutions used in the PLANSoft proc-

ess are [Cannon & Lachapelle 2009]:

For L1 only, the is 1 and is 0, is 0.1903 [m] for GPS and

[m] for GLONASS (with the frequency

number of satellite), and the ambiguity is . Only L1 C/A code is used for

data processing.

For L1 and L2 ionospheric free (IF), the L1 and L2 phase solution are not com-

bined, but used separately, and a ionosphere-free strategy is applied. For L1,

the is 1 and is

, [m] for GPS, and the ambiguity is

. The L1 C/A and L2 C/A code are used for data process-

ing.

For Widelane (WL), the is 1 and is -1, is 0.8619 [m] for GPS and is

0.84 [m] for GLONASS. The ambiguity is . The L1 C/A code

only and the widelane phase are used to estimate the relative position and

widelane ambiguities.

For L1 and Widelane, the is 1 and is -1, is 0.8619 [m] for GPS and

is 0.84 [m] for GLONASS. The ambiguity estimated are and

as well.

The wideline, with its longer combined wavelength, eases the process of ambiguity

resolution. However wideline‟s errors, like ionosphere bias, multipath and noise, are

amplified [Lachapelle 2008]. The ionospheric free strategy removes ionospheric er-



rors, and multipath and noise are less important than for widelane strategy. But the

ionospheric free (IF) ambiguities aren‟t integer. The specific combination must

be used to estimate the better integer ambiguities solution. This ionosphere free solu-

tion is efficient in the case of important difference of ionosphere errors on each fre-

quency and when integer ambiguity couldn‟t be determined [Lachapelle 2008].

VI.2.5.2 INTER-STATION SINGLE-DIFFERENCE STEP

In order to reduce the phase observations errors, double-differences technique can

be applied. The double difference carrier phase observation allows mitigating

common satellite and receiver errors like receiver and satellite clock errors [Takac &

Petovello 2009]. This technique is based on the similarity in time of errors related to

the same satellite/ receiver measurements. If we subtract instantaneous measure-

ments coming from the same satellite but tracked by two different receivers, the

satellite clock offset will be removed, as they are identical for both measurements.

The specially correlated orbital and atmospheric errors are also greatly reduced,

especially for small baseline lengths [Keong 1999]. This subtraction is called the inter-

station single difference (SD) method, see Figure 3. The same principle could be ap-

plied for instantaneous measurements from the same receiver but transmitted by

two different satellites. In this case, the receiver clock offsets are removed because

they are identical for both measurements. This method is known as the inter-satellite

double-difference (DD) (see Figure 3), because the SD results are used to apply it. As

usually known, the DD process increases errors like multipath and noise by a factor of

two [Cannon & Lachapelle 2009].

Figure 3: Double difference schema

Because of the structure‟s difference between GPS and GLONASS, the double-

difference equations are different each system.

As explained previously, all GPS carrier phase observations are transmitted over the

same carrier frequencies fL1 or fL2. First, phase measurements are used and the inter-

station single difference is applied, subtracting the measurements transmitted by the

same satellite recorded simultaneously from two different receivers [Takac & Pe-



tovello 2009]. The single-difference can be applied to obtain float estimated pa-

rameters of the position coordinates, the velocity, the offset, the drift and the ambi-

guities. Differences between GPS and GLONASS signals complicate the ambiguity‟s

estimation step. This will be explained in the chapter VI.2.5.4 AMBIGUITIES RESOLU-

TION. Using the carrier phase with the equation (5), the DD method can be applied

on GPS data using the following equation of single difference in unit of meters [Can-

non & Lachapelle 2009]:

(8)

where is the between-receiver differencing operator.

VI.2.5.3 INTER SATELLITE DOUBLE-DIFFERENCE STEP

Then the double difference observations are computed by subtracting two inter-

station single differences for two satellites [Takac & Petovello 2009]. The following

equation is currently applied to GPS data in unit of meters [Cannon & Lachapelle

2009]:

(9)

where the between-receiver differencing operator,

the between-satellite differencing operator.

For GLONASS data, the FDMA structure (described in previous chapter) prevents

from applying equation (9) as it is. The observation equations of the double differ-

enced GPS/GLONASS carrier phase for a short baseline can be written in unit of cy-

cles as [Lachapelle and all, 2009]:

(10)

where is the double difference (DD) phase measurement, in units of cycle,

is the single-differenced (SD) range to the ith satellite,

is the wavelength of the signal from the ith satellite,

is the SD clock offset in units of distance,

is the DD ambiguity,

is the phase error term.

Because the GPS signal frequency is identical for all satellites, the term

is

null and the clock offset is eliminated. For GLONASS, the carrier signal is transmitted

at different frequencies from one satellite to another. So the GLONASS clock cannot

be removed using this equation. The phase parametrization equation can be rear-

ranged and converted to units of distance [Wang 2000].



(11)

where is the DD phase measurement [m], is the DD phase ambiguity,

is the SD phase ambiguity of the reference satellite.

The above parametrization applied to GLONASS data contains the DD range, the

DD ambiguity and the SD ambiguity of the reference satellite. The latter terms

and must be estimated separately, as it is not observable with DD measure-

ments, see the following chapter VI.2.5.4 AMBIGUITIES RESOLUTION. A double-

difference equations system is created with each phase observation, always using

the same reference satellite.

The final observation equations system must be linearized with respect to its parame-

ters. Then the unknown integer double difference ambiguities and the increments of

the unknown range component must be resolved. This system is solved by means of

a conditional compensation with a constraint on the values of the ambiguities that

should be integer values [Teunissen 1995]. The measurement model to solve appears

to be [Teunissen 1995]:

(12)

Where is the double difference observations vector, is the increments of the range components, as well named baseline components,

is the integer double difference ambiguities, is the design matrix of range components,

is the design matrix of ambiguities terms, is the non modeled error term.

This integer least-squares problem can be solved in two consecutive steps. The first

one is the resolution of the observation equations linearized removing the integer

constraint. This computation can be seen as a classical least squares compensation

to obtain the float solution

using the covariance matrix of estimated parame-

ters

[Teunissen 1995].

This float solution is then used in the second step, called the isolated ambiguities

resolution, that is detailed in chapter VI.2.5.4 AMBIGUITIES RESOLUTION.

The final fixed solution is indeed computed integrating the estimated fixed ambigui-

ties according to the following equation [Teunissen 1995]:

(13)

where is the fixed solution of range components .



VI.2.5.4 AMBIGUITIES RESOLUTION

This step belongs to the position‟s estimation algorithm but it is more convenient to

isolate its explanation, especially because the process is different for GPS and

GLONASS.

In general the ambiguity resolution strategy involves three steps [Keong 1999, Kim &

Langley 2000]:

The ambiguity search space determination,

The integer ambiguity selection involving in two steps, the float solution and

the integer ambiguity estimation,

And finally the correct ambiguity distinction to find the fixed solution

The ambiguities resolution is based on DD carrier phase and code pseudorange

data. The goal of this step is to estimate integer phase ambiguity. The ambiguities

resolution contains two distinct steps: the inter-station single-difference (SD) and the

inter-satellite double difference (DD). In PLANSoftTM and its geometry-based observa-

tion model, a LAMBDA method followed by bootstrapping is employed to estimate

the correlated ambiguities [Ong et al 2010], see Figure 5 The positioning quality is

improved by the LAMBDA method and by searching in the m-dimensionnal ambigu-

ity space based on a geometry model [Teunissen 2002]. The LAMBDA method is fol-

lowed by a sequential search in the ambiguity space based on Ellipsoid space after

ambiguities decorrelation, and by an efficient and optimal estimator developed by

Teunissen in 1993 [Teunissen 2002].

The first step of double difference ambiguities resolution, the Inter-station single-

difference ambiguities can be summarized for two GPS satellites and two receivers

as follows [Takac & Petovello 2009]:

(14) For Satellite I,

(15) For Satellite j,

where

the ith satellite integer ambiguity for the receiver p,

is the between-receiver differencing operator.

The double-difference ambiguity cannot be estimated only with carrier phase

measurements, because the number of unknowns would be bigger than observa-

tions. [Takac & Petovello 2009]. In order to reduce the unknown number, we could

estimate the satellite reference ambiguity using pseudorange measurement. The

single-difference ambiguity of the reference satellite can be estimated by means of

the following equation [Takac & Petovello 2009]:

(16)

where ∆n is the single-difference ambiguity for the reference satellite,

∆P is the single-difference pseudorange,

∆ϕ is the single-difference phase observations.



The second step involves the Inter-satellite double-difference ambiguities involving

the following equation [Takac & Petovello 2009]:

(17)

where λ is the carrier signal wavelength.

The satellite i is the reference satellite common to all other double difference obser-

vations.

The GLONASS double-difference ambiguities resolution is more complicated be-

cause of the FDMA structure and the different λ wave lengths for all satellites. Similar

to double-difference positioning, a double difference parametrization equation is

required as follow [Takac & Petovello 2009]:

, (18)

where λ is the carrier signal wavelength,

(19).

To resolve the double-difference ambiguities, two different processes are employed

regardless of GPS or GLONASS data, but depending on their correlation nature. The

integer ambiguities search is based on sequential conditional least-squares adjusted

over the estimated ambiguities [Teunissen 1998]. The ambiguities must be resolved

by the minimization of the quadratic form of the residuals as shown on the following

equation [Teunissen 1998]:

(20)

where is the „float‟ estimated ambiguities (real-valued),

are the unknown integer ambiguities,

is the covariance matrix of estimated ambiguities .

The minimization problem is solved by searching over a smaller subset of the space

of integers Zn. In other words, we must find the vector of real integer which mini-

mizes distance to the float ambiguities estimated in metric of covariance . This

space must be centered at , and his shape and orientation is governed by [Teunissen 1997].

, (21)

where represents the search space.

This search space should be set such that it contains at least one integer vector.

This smaller subset of the integers‟ space is found using the equation (20). Once de-

veloped, this equation introduces an ellipsoidal region in Rn on which the search can

be performed. When the ambiguities are uncorrelated, is a diagonal matrix and

the ambiguity search is trivial. The minimization problem is derived as follows [Teunis-

sen 1995]:



(22)

where

is the variance of the ith least-squares ambiguity.

By this way, the problem is reduced to resolving m separate scalar integer least-

squares problems. But when the ambiguities are correlated, it results in an inefficient

search. The ambiguity search space is very elongated. The remedy is the reduction

of the search space by transforming the original ambiguity sets into the correspond-

ing ones in a transformed space and by defining conditional search ranges in multi-

level searches [Kim & Langley 2000]. This is done by an ambiguity decorrelation with

the Least Squares AMBiguity Decorrelation Adjustment (LAMBDA) method. This inte-

ger least squares is implemented to estimate the integer ambiguity by applying an

ambiguities decorrelation and find the integer ambiguity that minimizes the distance

between this new decorreleted estimated ambiguity and the real ambiguity value.

The first step involved is a transformation of the ambiguities by decorrelation. The

ambiguities are decorrelated to obtain homogeneous spectrum of conditional

standard deviation [Teunissen 1995]. The i transformations, depending of the dimen-

sion i of the search space, modify the tangents‟ lengths of the ellipse of the search

space. For a two dimensions search space, first the horizontal tangents of the ellipse

are pushed from level toward the

level, where is the es-

timation of the conditional decorreleted ambiguities for the second dimension, and

is its corresponding standard deviation [Teunissen 1995]. Then the vertical tan-

gents of the ellipse are

pushed from from

level toward the

level,

where is the

estimation of the conditional

decorreleted ambiguities for

the vertical dimension, and

, is its corre-

sponding standard

deviation [Teunissen

1995]. The volume of

the ellipse remains fix

during this process

and the shape of

the ellipse tends to

become a sphere

shape, as illustrated in

Figure 4.

Figure 4: Diagram of ambiguities decorrelation by pusing tangents method.



This process is continued until the next transformation is reduced to the trivial identity

transformation [Teunissen 1995].

By decreasing the variance between each set of conditional least-squares of esti-

mated ambiguities, the correlations between them are automatically decreased

[Teunissen 1995]. For two-dimensional case, the full decorrelation equation is given

by [Teunissen 1995]:

(23)

and , (24)

where is the estimation of the conditional ambiguities decoreleted,

is the unknown integer ambiguities,

is the „float‟ estimated ambiguities (real-valued),

is the decorrelation matrix,

is the covariance matrix of decorreleted ambiguities,


When a full decorrelation is not possible, because transformed ambiguities are not

integer, an approximate transformation with Gauss transformation is used to pre-

serve the integer nature of the ambiguities. For two-dimensional case, this decorrela-

tion equation is the following [Teunissen 1995]:

(25)

and , (26)

where is the decorrelated estimate ambiguities,

is the unknown decorrelated integer ambiguities,

is the decorrelation matrix with the

term round to the nearest integer,

is the covariance matrix of decorreleted ambiguities,


Following this transformation, the spectrum of conditional standard deviation be-

comes flattened and precise and decorreleted ambiguities are returned. Thereby

the search for transformed integer ambiguity becomes easier and is performed in a

more efficient manner [Teunissen 1995].



The search space area of original and decorrelated ellipse remains the same, and

the integer nature of ambiguities is preserved.

Finally, a new integer ambiguity search is done. The fixed ambiguities can now be

estimated by the decorreleted and simplified ambiguities minimization equation as

follow [Teunissen 1995]:

(27)

where (28) is the integer bootstrapped solution estimated,

and (29),

is the integer bootstrapped solution,

is the integer ambiguity solution related to .

The ambiguities resolution is done using a minimum time to fix the ambiguities of 30

[sec], and all 30 seconds the ambiguities computation process id reset.

To conclude, using GLONASS and GPS measurements, the difficulty is to compute

the double difference for the GLONASS carrier phase. A parametrization of the

phase double difference equation is necessary to eliminate the GLONASS clock off-

sets unknowns. The analysis of ambiguities resolution techniques shows the complex-

ity of the process but it is already tested by a lot of scientists. Their multiple experi-

mentations show that to obtain optimal solutions with a least squares estimation, the

design of appropriate functional and stochastic modelling is required as with cor-

rects models, the solutions become unbiased. The distinction of a correct ambigui-

ties set from all candidates can be improved by more realistic stochastic modeling

of the receiver‟s system noise and an appropriate validation procedure of the results

[Kim & Langley 2000]. The functional model is particularly difficult to create because

some errors are correlated, e.g. ionospheric or tropospheric delays. The time correla-

tion due to high sampling rate can induce same problems [Teunissen 1997]. The sto-

chastic modeling shows also some difficulties in his optimization because of quasi-

random errors in dynamic motion like multipath, that aren‟t normally distributed [Kim

& Langley 2000]. In the numerous researches done on ambiguities resolution, func-

tional modelling received more attention than stochastic one [Kim & Langley 2000].



The entire process

of ambiguities reso-

lution applied in

PLANSoftTM is sum-

marized in Figure 5.

Figure 5: PLANSoftTM

ambiguities resolution flowchart

VI.2.5.5 RELIABILITY OF THE FIXED AMBIGUITIES FOUND

We must now evaluate the reliability of this fixed ambiguity before integrating them

or not in the final solution. Two types of tests are realized: the predict ambiguity suc-

cess rate and the F-test.

First to predict the ambiguity success rate, the performance of the integer ambiguity

chosen is evaluated using the probabilistic properties of the integer ambiguity esti-

mators [Kim & Langley 2000]. For this prediction, the probability to estimate the cor-

rect integer ambiguity is evaluated. This probability is the integral of the probability

density function over the pull-in-region of the correct integer solution [Teunissen

2002]. This pull-in-region is the area in which the float ambiguity solution is pulled to a

certain fixed solution [Teunissen 2002].

GPS double-difference ambiguities

PLANSoftTM Ambiguities resolution :

‘Float’ solution

Proces

LegendLink

between steps

Data

LAMBDA method

“Float“ estimated ambiguities

GLONASS double-difference ambiguities

Preparation process


Correleted ambiguities

?

‘Fixed’ solution

GLONASSGPS NN ,

Fixed ambiguities

Introduction in position double-difference equation to resolve it

Ambiguities decorrelation and estimation of integer

ambiguities by minimization

ZQZQandaZzwith

ZzzzQzz

a

T

z

T

n

z

T

z

ˆˆ

21ˆ

ˆˆ

,)ˆ()ˆ(min

GLONASSGPS NN ,

Conditional least squares

Ambiguities decorrelation and estimation of integer

ambiguities by minimization

n

n

T

nZnnnQnn ),ˆ()ˆ(min 1

ˆ

No Zes



(30)

This computation of integer ambiguity success rate can be approximated by lower

bounds [Teunissen 2002]. The lower bound approximation used to predict the suc-

cess rate of ambiguities resolution for integer decorreleted ambiguities as given in

equation (27), is derived as follows [Teunissen, 1998]:

(31)

where is the predicted success rate,

is the unknown decorrelated integer ambiguities,

n is the number of ambiguities,

is the integral of the standard normal distribution

from – to x,

1, n].

The ambiguity success rate threshold is fixed at 90.00(%) for this project experiments.

This probability computation requires only knowledge about the variance-

covariance matrix of real-valued estimates , which could be computed prior to

the ambiguities being fixed. Another test must attest the correctness of the integer

ambiguity.

A particular form of the ratio test is applied in the PLANSoftTM, the F-test. The statistical

Fisher test assesses the global congruence of fixed ambiguities and requires tree

steps [Denli 2008, Keong 1999]:

Establish the null hypothesis,

Describe the decision rule,

Accept or reject the hypothesis

Under null hypothesis Ho, the test statistic has an F-distribution.

1. The null hypothesis is Ho:

2. The decision rule is :

(32)

with the test quantify, the total number of epoch used typically in 10 seconds, the ith residuals of each integer ambiguity,

the covariance matrix of decorreleted ambiguities.

The computation is only possible for uncorrelated measurements between

two epochs. Then it is possible to compute the common variance:

(33)

With the common variance,

and the variance of each ambiguity type.

Finally the statistic is given by:



(34)

With the test quantify,

.

3. Ho is rejected if T > F1- => Fisher table

If Ho is rejected, the computed fixed ambiguity can‟t be used in double-

difference positioning equation.

The general ambiguity resolution process should not take more time than one epoch

to be implemented in real time. For this post treatment, the computation time

reached about 30 seconds. A misclosure threshold of 0.3 [cycles] is applied for the fix

validation phase. The general process of integer ambiguities acceptance is de-

picted in Figure 6 .

Figure 6: General process of PLANSoftTM

ambiguities resolution

Add to ‘ incorrect fixed ambiguities’ list and

don’t use it for fix solution

PLANSoftTM ambiguities processing Flowchart :

No

Proces

Légende

Link between stepsData

“Fixed“ solution

Detremine search volume of

ambiguities

Yes

Preparation process


The ambiguities passed the

tests?

Float ambiguities estimation

Test the potential ambiguity sets by:

- Predict success rate- F-test Add to ‘ fixed

ambiguities’ list and update the actual

used ambiguities in double difference

positioning equation

Read observation

Reset filter



VI.2.6 CYCLE SLIP DETECTION

The signal loss causes cycle slip. Ambiguities must be re-estimated after it. The time

required to compute new fixed ambiguities affects the quality of positioning.

Cycle slip detection can be done with two methods [Cannon & Lachapelle 2009]:

The Phase Velocity Trend Method, for single frequency case using carrier

phase and Doppler measurements,

The kinematic cycle slip detection for dual frequency measurements, using

dual carrier phase measurements. This technique is more precise for very

clean data.

This second mode was applied to the data process with the PLANSoftTM, with a

phase rate cycle slip threshold of 4 [cycle].

VI.3 ANALYSIS TOOLS

In order to analyze the PLANSoftTM position computation, different statistic tools will

be used. These statistical parameters are applied to the errors related to the posi-

tions computed with the PLANSoftTM. These errors are computed by differencing the

solution with the „true coordinates‟ given by the GNSS-INS solution and converting

them into North, East, and Up errors (E, N, U). The quality of the GNSS-INS reference

data must be previously assessed.

VI.3.1 REQUIREMENTS DEFINED BY THE APPLICATION

The quality of positioning based on satellites signals must respond to specific criteri-

ons that qualify the accuracy, the precision, the integrity, the availability and the

continuity. Depending on the application domain, these criterions are more or less

demanding.

When working with measurement in static mode for surveying, high quality is re-

quired. For surveying, the accuracy and precision of data are important criterions.

Longer acquiring time is required to reach high positioning quality, that id obtained

thanks to greater measurements redundancy. In difficult environments, like in moun-

tains, in the bottom of an open-cast mine, in forests, or urban canyons, shorter

measurement periods can be problematic to track signal and reach the expected

level of accuracy and availability. But for data collected in static mode, the meas-

urement place can easily be chosen to avoid this kind of constraints due to ob-

structed environments.

For dynamic satellite positioning, obstacles are more problematic and it is more diffi-

cult to avoid a decrease of quality. A high elevation mask due to the surrounding

topography, for example trees or buildings, can prevent to successfully fix the inte-

ger carrier phase ambiguity, inhibiting high precision positioning. In motion, it is not

possible to improve the positioning quality by increasing the measurement redun-

dancy, because the receiver doesn‟t stay in the same position for a long time. A

higher frequency could help to better describe the motion, but it doesn‟t offer more

redundancy for each surveyed point. For measurements collected in dynamic

mode, the required quality‟s criterion depends on the type of motion and the appli-

cation. The pedestrian in motion needs an approximate precision of half a footstep‟s

length to distinguish a pedestrian trajectory from surroundings manmade or natural



objects. For sportive applications, like skiing, the skiers‟ line trajectories have to be

estimated with a 10 cm accuracy level, and an accuracy of 5 cm for gate survey is

required [Lachapelle et al 2009]. For road or rail transport, the quality of positioning

doesn‟t need to be more precise than the road width, because Map matching

technique forces the trajectory to remain on the road. For maritime applications, the

quality depends on the location, more precise positioning with good reliability is

necessary in coastal and port zones. Although the accuracy‟s position is important,

the air transports need above all particularly good integrity, availability and continu-

ity.

This report studies pedestrian trajectory applications for precise positioning. The pre-

cision aimed the decimetre level to allow topometric use. To obtain precise posi-

tioning for kinematic data, differential carrier phase positioning is required. This dif-

ferential positioning must be done with a short baseline, to improve the quality of

final position computed, because errors in measurements are more similar in close

environments, and they can be removed by double differencing computation. Due

to motion and changing environments, variable multipath errors could occur. These

are more difficult to remove in dynamic mode than in static mode because there is

less redundancy to remove these errors. Finally resolving the ambiguities is essential

to reach a high precision with carrier phase data. An error of even one cycle on a

single satellite can result in a position bias of many centimetres or decimetres de-

pending on the geometry. Cycle slips, requiring new ambiguities resolution, could

occur in obstructed environments. Therefore precise dynamic positioning is espe-

cially hard to reach in obstructed environments.

For static but even more for dynamic satellite positioning, there is a huge gain to use

more satellites, because accuracy, availability and reliability depend on the amount

of available satellites. The combination of multiple satellites increases the measure-

ments redundancy, it improves the constellation geometry. Furthermore the differing

inclination angle that involves slightly different position of the “shadow area” allows

better coverage worldwide. GLONASS satellites rise in higher latitude filling better the

lack of satellites in the North direction. This ensures a better coverage for the North

hemisphere. As explained for GLONASS in chapter III.1.4 GLONASS SPECIAL FEATURES,

different orbital inclination angles exist for each satellite systems. These different an-

gles imply different dilution of precision (DOP) derived for each systems for one spe-

cific location on the Earth. These satellite systems are complementary, thus for differ-

ent location, when one solution is bad the other is better. Indeed, the gain to use

different satellites systems becomes obvious.

The addition of GLONASS is also interesting for the ambiguities resolution process. The

model, which is dependent on the satellite geometry, has a complete and direct

impact on the ambiguities variance matrices. The efficiently of the ambiguities

search depends on this because, the geometry of the search space of the fixed

ambiguities follows from these matrices [Teunissen 1997]. During the process of am-

biguities decorrelation, very small ambiguity variances of conditional least squares

allows to decrease the three large conditional variance, allowing a more efficient

search of the right integer ambiguity [Teunissen 1995]. In this way, a good satellite

redundancy allows obtaining smaller ambiguity Conditional variances. The variance

between each set of conditional least-squares of estimated ambiguities is decreas-

ing, and so the right integer ambiguity search is easier. The dual frequencies data

have the same effect. The satellite elevation has as well an impact on the ambiguity

estimates and on the location, the size and the shape of the ambiguity search



space [Teunissen 1997]. When the satellite is in very high altitude orbit and when the

rate of data recording is high, the relative position of the satellite regarding the re-

ceiver changes slowly. As a result, the ambiguities become very poorly separable

from the baseline coordinates, and the estimated precision of the position will be

rather poor [Teunissen 1997].

With the multiple satellite systems under construction, the future promises an in-

creased satellite‟s availability, but appropriate hardware to receive the new signals

will be necessary.

If currently 24 GPS and 21 GLONASS satellites can already be used, within the next

few years, 30 Galileo satellites are expected from the EU, and 3 QZSS satellites from

Japan [Van Diggelen 2007]. Thus in a few years, we can expect at least 70 satellites

available in worldwide GNSS systems for satellite positioning. As we already have

seen it for the GPS and GLONASS combination, computing a position computation is

not always easy due to the differences between the two systems. But with appropri-

ate receiver and software, combined position will be computed using all satellites

available in the future.

VI.3.2 STATISTICS TOOLS

In order to verify the quality of the measurements different statistics tools are used.

VI.3.2.1 A PRIORI QUALITY OF COMPUTED SOLUTION

The number of available satellites and their geometry give a first quality criterion

about the computed solution. This criterion can be computed in scalar quantities,

named Dilution of Precision (DOP). These DOP are related to the volume formed by

the intersections between the receiver-satellite vectors and the unit sphere centred

on the receiver‟s location [Cannon & Lachapelle 2009]. A larger volume gives better

measures and so smaller DOP. A good DOP doesn‟t exceed 2 [Cannon & La-

chapelle 2009]. The size of these DOP‟s values depends on how many satellites are

used, and where they are in the sky. These DOP are entirely derived from the vari-

ance-covariance matrix. They depend on the User Equivalent Range Error (UERE)

associated with the standard deviation σ0 and on the observation model and its

corresponding design matrix. The covariance matrix for GNSS positioning is [Cannon

& Lachapelle 2009]:

(35)

where is the covariance matrix,

is the standard deviation of the UERE,

is the cofactor matrix,

is the design matrix of observation.

Comparing with the design matrix used for PDOP computation in the GPS only proc-

essing, the design matrix for GPS-GLONASS combination has one additional column

[Cai & Gao 2007]. This GPS-GLONASS design matrix corresponds to the unknowns of

the three position coordinates, the receiver clock offset, and the time difference

between the two systems [Cai & Gao 2007].



Several DOPs are in use depending on the geometrical plan analyzed:

The most popular parameter is the geometric dilution of precision (GDOP). It

combines the effect of satellite‟s position and error clock over the precision of

the final position solution and is computed with [Kaplan & Hegarty, 2006]:

, (36)

where is the Geometric Dilution of Precision,

is the diagonal component of the covariance matrix,

is the variance of error clock (time bias error),

is the a priori standard deviation or pseudorange error (UERE) factor .

The Position Dilution of Precision (PDOP) reflects the horizontal positioning

quality [Kaplan & Hegarty, 2006]:

(37)

where is the Position Dilution of Precision,

is the position diagonal component of the covariance matrix.

The Horizontal Dilution of Precision (HDOP) translates the horizontal positioning

quality. If the HDOP doubles, the position accuracy will get twice as bad, and

so on. [Kaplan & Hegarty, 2006]:

(38)

where is the Horizontal Dilution of Precision,

is the East and North diagonal component of the covariance matrix.

The Vertical Dilution of Precision (VDOP) reflects the horizontal positioning

quality. [Kaplan & Hegarty, 2006]:

(39)

where is the Vertical Dilution of Precision,

is the standard deviation of height.

And finally the Time Dilution of Precision (TDOP) gives the horizontal positioning

quality. [Kaplan & Hegarty, 2006]:



(40)

where is the Time Dilution of Precision,

is the standard deviation of error clock.

VI.3.2.2 CRITERIONS TO ASSESS ACCURACY AND PRECISION

The first quality parameters to evaluate are the precision and the accuracy of the

data set. Accuracy refers to the degree of closeness to the truth value, while preci-

sion refers to the aptitude of the system to repeat its solution.

First global statistical indicators, computed for all directions East, North and Height,

are presented separately.

The mean in each direction of the data set give information about the accu-

racy of the data.

The mean of absolute values. When we compare data computing the differ-

ences using absolute values, negatives values don‟t get compensated by the

positive ones. The mean of absolute differences provides realistic analysis of

the differences in position.

The median is more robust than the mean because it is less influenced by the

different outliers. The outlier‟s computation is presented below.

The standard deviation σ informs of the dispersion of the values around the

mean. The standard deviation gives the extent, the symmetry of the data‟s

accuracy. A small standard deviation is a stability indicator.

(41)

where zi is the ith recorded measurement,

, is the mean of recorded measurement,

n is the number of recorded measurement.

The mean standard deviation of all values of standard deviation gives a good

precision criterion of the entire data set. The computation of this standard de-

viation in specific geographic areas indicates the local environmental influ-

ence.

The root mean squared error (RMS) can be described as the fluctuation of the

standard deviation around the mean. It measures the dispersion of the resid-

ual distribution frequency (the difference) between an estimator and the true

value of the estimated quantity. This statistic indicator takes the data systema-

tization into account and gives information on the accuracy and precision of

the data set [Van Diggelen 2007]:

http://en.wikipedia.org/wiki/Estimator



(42)

where zdata,i is the ith recorded measurement,

zref, i is the corresponding reference data,

n is the number of compared data.

The use of the range, the minimum and the maximum of a data set allows the

study of the dispersion and the precision. The range is sensitive to outliers. The

1st and 3rd quartiles q(25%) and q(75%)are more robust statistics, non sensitive

to outliers. The 1st quartile separates the 25 % of the lower data in which 25%

of the values are lower than q(25%). The 3rd quartile separates the 75 % of

lower data.

The outliers are computed as the values smaller than a limit value according

to the following expression:

(43)

and

(44)

where is 1st quartile and is 3rd quartile,

is the interquartile range computed as .

Thanks to the histogram of the data, the dispersion of the data and the size of

outliers can easily be visualized.

The second category of global statistics indicators is computed in the local horizon-

tal plane. For these statistics and in order to get the same level of precision for com-

parison puposes, the mean is removed from the data set to obtain a normal distribu-

tion centred in zero [Bancroft 2007]. The plots will show the errors in position in two

dimensions and the corresponding global statistic with zero mean. This allows evalu-

ating the dispersion of values around the mean. These two dimension global statis-

tics indicators are the following.

The Distance Root Mean Square (DRMS) expresses the two dimensional accu-

racy. It‟s the circular radial error computed as [Kaplan & Hegarty, 2006]:

(45)

where is the East root mean square,

is the North root mean square.

The probability that a position is within the circle of DRMS radius varies be-

tween 63.2 % and 68.3 % [Seeber 2003].



The probability that a position stays within a certain region in the plane can

be represented by a relative error ellipse. The axes of the confidence ellipse

are function of the coordinates standard deviations and the chosen level of

probability, generally the 1σ probability level corresponding to 68.3% [Seeber,

2003]. The ellipse size is described by the eigenvalues of the covariance ma-

trix, which give the axes lengths [Bancroft 2007]. Then, the orientation of the

axes in the local frame is given by the eigenvector [Ghilani & Wolf 2006]. A

translation by the mean error of the data set is applied to compensate for for

the bias in the data. Finally to obtain a 95% confidence level, the confidence

ellipse must be multiplied by a scale factor of 2.447 [Cannon & Lachapelle

2009]. The semi-major axis a2D and semi-minor axis b2D that define the relative

standard error ellipse, are given by [Chan 2010, Chrzanowski 1981, Ghilani

and Wolf 2006]:

, (46)

, (47)

where is the semi-major axis,

is the semi-minor axis,

is the East and North errors standard deviation,

is the covariance between North and East errors.

The azimuth of the semi-major axis can be computed as follows [Chan

2010], [Chrzanowski 1981], [Ghilani & Wolf 2006]:

[rad] (48)

The third category of global statistics indicators is computed in 3D: East, North and

Height components together. For this three dimensions statistics and in order to have

the same level of precision of comparison purposes, the mean was removed from

the set of data to obtain a normal distribution centred in zero [Bancroft 2007]. The

plots will show the errors in 3D in position and the corresponding global statistic with

zero mean.

The Mean Radial Spherical Error (MRSE) is the radius of the sphere centred at

the true position, containing the position estimate in three dimensions with a

probability of 61 percent [Seeber,2003]:



(49)

The probability of a location to be within a certain region in 3D is represented

by a relative error ellipsoid, an extension into three dimensions of the error el-

lipse. The three eigenvalues of the covariance matrix give the scale factors of

the ellipsoid. The eigenvector gives the rotations applied to the three axes to

rotate the error ellipsoid into the mean errors orientation. The relative error el-

lipsoid represents the 39.4 % confidence region and is centred on the least

squares estimate of the position. When the axes lengths are multiplied by the

correct squared chi square value of 2.8, the error ellipse represents the 95%

confidence region [Cannon & Lachapelle 2009].

These statistic tools will be apply to analyze the reference‟s quality and the differ-

ences between the rover‟s solution and the last reference. These differences are

computed between the GNSS-INS data, used as reference, and the GPS/GLONASS

data processed with the PLANSoft. We assume that the GNSS errors would be re-

corded over an enough long time period to have a normal distribution. In reality

GNSS errors distribution doesn‟t behave as a normal distribution, but the Gaussian

model is a good approximation [Van Diggelen 2007]. The majority of GNSS errors like

multipath, atmospheric, and thermal noise errors aren‟t random variables and so are

non-Gaussian. But they all contribute to form a random variable in each position

axis, as far as the data set is recorded over a sufficiently long time period. According

to the central limit theorem, the sum of these random variables approximates a

Gaussian distribution [Van Diggelen 2007].

VI.3.2.3 INTEGRITY, CONTINUITY AND AVAILABILITY OF MEASURMENTS

The integrity is the measure of trust that can be placed in the correctness of the in-

formation supplied by a system. To have confidence that it is working correctly, the

ability of the system to provide position inside the truth level expected is tested.

Generally for a GNSS system, the probability that this integrity is not provided is called

the integrity risk and it is computed over a certain interval. This integrity risk translates

the fact that the positioning error remains under a certain threshold defined by an

Alarm Limit. If the errors surpass this limit, a notification must be provided within the

Time to Alarm announced [European Commission GALILEO, 2002].

The continuity is “the probability that the specified system performance will be main-

tained for the duration of a phase of operation, presuming that the system was

available at the beginning of that phase operation” [Ma 2000]. Loss of continuity

could occur because of poor geometry, planned maintenance on satellites, or such

unpredictable factors like loss of lock on one satellite. The continuity is usually de-

fined in GNSS systems by the continuity risk, the probability that the system will not

provide guidance information with the accuracy and the integrity required for the

intended operation [European Commission GALILEO, 2002].

Finally, the availability is the percentage of time during which at any location in the

coverage area, and at any time, the system is able to provide usable navigation

service [Kaplan, 2006]. During periods of non availability the integrity requirements

must still be met [European Commission GALILEO, 2002].



In this project information about the data integrity, continuity and availability is pro-

vided by means of three tools:

The accuracy envelope is based on the software based predicted

standard deviation. The graphic, with this accuracy envelope superposed on

the coordinates, gives a first information about the data‟s integrity. Firstly, the

predicted error vector is computed as follow:

(50)

where is the predicted error with a probability of 99.7 %,

is the two dimension standard deviation predicted by the Software,

is the two dimension velocity vector for each time,

is the orthogonal projection angle.

Then, the positions of the envelope points are computed starting from the ref-

erence position:

(51)

where is the accuracy envelope,

is the GNSS-INS reference vector position,

is the predicted error with a probability of 99.7 %.

This envelope is computed in both perpendicular directions of the GNSS-INS

reference as it can be observed in the following schema in Figure 7.

Figure 7: Envelope construction schema



This envelope is computed twice, first to estimate the reference quality and

second to estimate the correctness of the PLANSoftTM solution according to

the standard deviation estimated by the PLANSoftTM.

The Percentage of errors bigger than 10 [cm] in the horizontal plane and 20

[cm] in the vertical plane gives an overall indication about the ability of the

system to work at a precise point positioning level. This percentage reflects

the system‟s integrity and availability. The values of 10 [cm] in the horizontal

plane and 20 [cm] in the vertical plane are motivated by common require-

ments in topographical applications, e.g. to locate complementary sensors.

The percentage of fixed integer ambiguities gives overall information about

availability and continuity. This percentage is computed over the entire data

set. If ambiguities aren‟t fixed, the accuracy can not reach precise position-

ing. If the percentage of fixed ambiguities appears to be too small in a spe-

cific area, the positioning accuracy in this area is not considered as satisfac-

tory.

VII DATA ANALYSIS

Two types of data sets are analysed in this chapter. The first one allows testing the

GNSS position computed with the PLANSoftTM in trees environment. The second one

compares the impact of the same elevation mask but produced by two different

types of obstacles: some trees and a building. The data are compared with an INS-

GNSS reference.

The data analyzed, indeed the GNSS-INS data and then the PLANSoftTM GNSS posi-

tioning, are first presented. This section starts with the explanation of the different

parametrizations applied to the PLANSoftTM computations. Then the two experimen-

tal tests are presented separately comprising each time a short test description, the

quality of the reference, the presentation of the best post-processing parametriza-

tion and the main results of the statistical analysis.

The analysis of the data sets consists essentially in a statistical study. Due to the huge

disparity in the results obtained from one parametrization of PLANSoftTM computation

to another, no relevant conclusion on the choice of post-processing parametrization

can be done. In order to be able to identify which post-processing parametrization

should be chosen to achieve the best possible performances in a specific envi-

ronment more data is required achieving a statistically representative analysis.

VII.1 DATA ANALYSED

The measurements used for the analysis are the GNSS-INS reference data, and the

GNSS solution computed with the PLANSoftTM.

VII.1.1 GNSS-INS REFERENCE



The reference positioning data are computed with INS and GPS-GLONASS meas-

urements. This INS data were collected with the SPAN HG1700 (Synchronous Position,

Attitude and Navigation) Inertial Meas-

urement unit (IMU It is a complete

GPS/INS system built into one enclosure

that contains the NovAtel OEMV-3 re-

ceiver and the Honeywell HG1700 IMU

comprised of ring laser gyros and servo

accelerometers. The gyro rate bias is 1.0

deg/hr and the accelerometer bias is

1.0 mg [9]. The dual frequency GNSS

data are collected in two different loca-

tions to allow differential positioning. The

static basis and the moving rover are

both equipped with a dual frequency

antenna NovAtel GPS-702-GG, and with

a dual frequency receiver NovAtel

OEMV2-G. The INS and GNSS data are

combined with the Inertial Explorer

NovAtel Software. A post-processing

based on a Kalman filtering is applied to

the INS and GPS-GLONASS data to pro-

vide an accurate position, velocity and

attitude solution.

Figure 8 : Data collection initialization

The data processing step includes a static coarse alignment performed at the be-

ginning and the end of the data collection. This step allows computing the INS abso-

lute orientation using precise carrier phase positioning with fixed ambiguities. This

data collection period must last a sufficiently long time to estimate the initial INS er-

rors. This initial procedure is done in a static mode and in an open sky environment

as illustrated in Figure 8.

The IMU error model chosen for the ppost-processing is the profile SPAN Ground

(AG58). GNSS positions are computed with dual frequencies carrier phase data. A

tightly coupled solution is computed in both forward and reverse directions [8]. The

two distinguished solutions are combined. Finally, a Rauch-Tung-Striebel back

smoother reduces inertial errors growth during GNSS signal losses [8].

VII.1.2 GNSS PLANSOFT DATA

The dual frequency GNSS data are recorded with a rate of 2 Hertz in two different

locations to compute a differential solution. The static basis and the moving rover

are both equipped with a dual frequency antenna NovAtel GPS-702-GG, and with a

dual frequency receiver NovAtel OEMV2-G. A static initialization step is respected

before the start of kinematic operation. During this phase, the ambiguities corre-

sponding to all visible satellites can be resolved to start the data collection with a

good quality of positioning. This phase of ambiguities initialization is usually done

though a static baseline [Teunissen 2002]. During the kinematic recording, if cycle

slip appears, ambiguities are resolved on the flight. After recording, the GNSS posi-



tion is computed with the PLANSoft following the steps explained in the heading VI.2

PLANSOFTTM PROCESSING.

Different types of computations have been tested to find the most appropriate one

for each environment. The computations are always based on a relative positioning

with double differences. A Kalman filtering is applied to estimate the parameters.

The precision estimated a priori for the measurements are a standard deviation of

0.5 [m] for the code pseudorange, of 0.1 [m] for the Doppler and a standard devia-

tion of 0.02 [m] for the carrier phase. A 10° elevation mask is always applied to re-

move measurements from low satellites in the sky, because their data quality is de-

creased. The PDOP threshold used to estimate the variance-covariance matrix and

the position is fixed at 150 [n.u.]. And finally the detection of blunders are. The differ-

ent chosen parameters are presented in the Annex A1 and briefly in the following

lines.

1. The first computation uses carrier phase measurements of L1 wavelength only

of GPS and GLONASS to compute the position. The ambiguities are resolved

using GPS and GLONASS separately.

2. The second solution uses carrier phase measurements of L1 and L2 wave-

length of GPS only to compute the position. The ambiguities are resolved us-

ing GPS only.

3. This third solution is computed with carrier phase measurements of L1 and L2

wavelength of GPS and GLONASS. A L1 and L2 ionospheric free (IF) combina-

tion is computed for the data processing and for ambiguities resolution. The

ambiguities are resolved using GPS and GLONASS separately using the IF

combination.

4. Carrier phase measurements of L1 and L2 wavelength of GPS and GLONASS

are used to compute positions. A L1 and L2 widelane (WL) combination is

computed for the data processing and for ambiguities resolution. The ambi-

guities are resolved using GPS and GLONASS together according the WL

combination.

5. Carrier phase measurements of L1 and L2 wavelength of GPS and GLONASS

are used to compute positions. A L1 and L2 widelane (WL) combination is

computed for the data processing and for the ambiguities resolution, and a

forward and reverse solution process is applied. The ambiguities are resolved

using GPS and GLONASS together according the WL combination.

6. This computation requires GPS and GLONASS carrier phase measurements on

L1 and L2 wavelengths. A L1+widelane (WL) combination is computed for the

data processing and for the ambiguities resolution. The ambiguities are re-

solved using GPS and GLONASS together according the WL combination.



7. For this calculation only GPS and GLONASS pseudoranges are used. No car-

rier phase processing is applied.

8. This last computation needs L1 and L2 GPS and GLONASS carrier phase meas-

urements. A L1+widelane (WL) combination is computed to process the data

and solve the ambiguities.

A first analysis is systematically done on the results to compare the different pa-

rametrization‟s solutions. To underline the best result among all computations, the

color blue is used. The worst statistical result is highlighted in red as explained in the

legend below. Even if all computations are not shown in the following sections, this

color indexing is retained in the entire report. It enables to keep in mind the quality of

the solution compared to other computations that may not be exposed in the de-

tailed analysis, to keep it concise, but are available in the Appendix.

Legend: Best value

Best value more or less 1[cm]


Worst value more or less 5[cm]


Worst value

Table 1: Legend of the color indexing of the statistical results.



VII.2 DATA SET UNDER TREES CLOSE TO THE BOW RIVER

This first data set was collected in the Edworthy Parc near the Bow River. It enables

different analyses like assessing the global quality of PLANSoftTM solutions in such as

environment, assessing the ambiguities resolution‟s ratio in obstructed area, the gain

of adding GLONASS and to compare the errors related to the different types of fo-

liage. After a description of the test and the reference quality, these points of ana-

lyse are addressed.

VII.2.1 TEST DESCRIPTION

The data collection‟s environment contains open sky parts and parts with more or

less dense foliage, as visible in Figure 9. At the time of the data collection, May 12th,

2010, some leaves began to be visible on trees.

Figure 9: Visualization of the data collection trajectory on Google Earth.

For the analysis, the trajectory was divided in ten areas with different type of vegeta-

tion density.

- The Area 1 is used as a reference for the analysis because it is located in an

open sky environment.

- The Area 2 strides a sparse leafed-trees sector.

- The Area 3 crosses dense leafed-trees vegetation. Because of the foliage

density many cycle slips are expected in this area.

- The Area 4 goes along a fir-trees line. At the beginning of this part, the trajec-

tory passes under a roof corresponding to an area of about 25 [m2]. This pas-

sage tests the ambiguities resolution on the flight, and the resolution time.



- In the Area 5, the trajectory penetrates in dense fir-trees vegetation. The

vegetation covers the entire area. This part contains the more extreme condi-

tion of all the data set.

- The Area 6 is similar to the area 6 with a fir-trees line in the East side of the tra-

jectory, but without going under any construction witch congests the sky visi-

bility.

Before each passage under trees, a passage in an open sky zone during 45 sec-

onds was respected ensuring enough time for the ambiguity resolution.

- The Area 7 was crossed two times. For the outward trajectory, the previous

environment was on the bridge in open sky. And for the return trajectory the

previous environment was the area 6, with a fir-trees line in the East.

Figure 10 presents the different areas used for the analysis. The areas analysed

are drawn in bright orange.

Figure 10: Distribution of the different areas of analysis on Google Earth map.

Following a satellites geometry planning, the data collection took place between

10:15 am and 11:00 am. The DOP values and the satellites availability are actually

better during that part of the day (see Figure 11 and Figure 12). The Trimble's Plan-

ning software planned this satellites geometry using the GPS and GLONASS almanac

available through Trimble website [(12) Trimble, 2010], and dates from 11th May

2010. During this period, the poorest expected PDOP value was 1.33 (Figure 11) and

the lowest satellites number was 16 (around 11:00 9 GPS and 7 GLONASS satellites).



Figure 11: GPS and GLONASS DOP number forecast for 12

th May 2010 by Planning Soft-

ware of Trimble

Figure 12: GPS and GLONASS satellite number forecast for 12

th May 2010 by Planning

Software of Trimble.

VII.2.2 GNSS-INS REFERENCE FOR THE BOW RIVER DATA SET

The reference solution, computed with GPS-INS data, has a global mean standard

deviation (MSD) of approximately 3 centimetres in the East, the North and in the

Height coordinates (see Table 2). The best precision is reached in the open sky area

1 with a MSD in 2D (MSD2D) of 0.5 centimetres and a MSD of 0.5 centimetres in the

Height. The GNSS-INS precision is worse under the fir-trees in area 5 with a MSD2D



frothy times bigger than in open sky area and a MSD in the Height thirty times bigger

(see Table 2).

Reference quality

Area n°

INS-GNSS solution mean Standard deviation [m]

E N H 2D

all data 0.027 0.029 0.030 0.040

1 0.003 0.004 0.005 0.005

5 0.152 0.145 0.138 0.209

Table 2: GNSS-INS reference quality estimated with Inertial Explorer Software

The MSD for all datasets and estimated with Inertial Explorer NovAtel software can

be found in the Annex 3. As visible in Figure 13, the standard deviation varies strongly

depending on the type of environment. This variation motives an analysis distinguish-

ing the areas.

Figure 13: Variation of the standard deviation of the GNSS-INS reference

These differences in the quality of the reference solution must be taken into account

to analyse the PLANSoftTM solutions. Particularly in obstructed areas, the difference

between the PLANSoft TM and the reference solutions is affected by the imprecision

of the GNSS-INS solution. But in these obstructed environment, this reference impreci-

sion is small relative to the precision of the PLANSoftTM solution, which is worse. To as-

sess the GNSS-INS internal quality the biggest difference between forward and re-

verse solutions can be used. This gives a criterion to evaluate the computation ro-

bustness. In our case this maximum separation reaches 3.6 metres under fir-trees in

the area 5. This means an important difference between the two solutions com-

puted, and explains the bad final precision of the reference in this area. Observing

the accuracy envelope, one can see that the GNSS-INS quality changes according



to the environment. This accuracy envelope is computed with the equation (51) us-

ing the two dimensions standard deviation estimated by Inertial Explorer and the INS

velocity vector. We can observe that the precision of the data is good for the open

sky area 1 (Figure 14), and is worse for the fir-trees area 6 (Figure 15).

Figure 14: Accuracy envelope in the area 1 in Open sky, plot produced with the Software

Matlab.

Figure 15: Accuracy envelope in the area 6 with a fir-trees line on the East of the trajectory,

plot produced with the Software Matlab.

Usually we observe that after a sufficiently long transition in an open sky area the

GNSS-INS reference precision becomes better. If during a too long period of time the

ambiguities can‟t be resolved, the precision of the reference is seriously affected.

This effect is clearly visible in Figure 16. The red elements of the plot describe the posi-

tion and quality after a static period. It can be observed that the accuracy enve-



lope is quite thin. In the second case, the return trajectory was done under the trees

without any period of open sky allowing the ambiguities resolution. The correspond-

ing envelope is larger because the accuracy is worse.

Figure 16: Changes in GNSS_INS reference quality according to the previous environment

crossed, area 5 under fir-trees, plot produced with the Software Matlab.

VII.2.3 GNSS PLANSOFT SOLUTION FOR THE BOW RIVER DATA SET

In order to define the best solutions to analyse, eight post-processing computed ac-

cording to the parametrization explained in chapter VII.1.2 GNSS PLANSOFTTM DATA

were analysed. The results of these eight computations are compared for the entire

data sets and for the seven areas, resulting in fifty five scenarios analysed. Compar-

ing these fifty five scenarios, the computations 5 and 6 give generally the best

planimetric results for the data collected under trees near the Bow River. These two

solutions use GPS and GLONASS carrier phase measurements. The computation 5 is a

forward and reverse solution applied to dual frequencies data and with L1 and L2

widelane WL combination used for the ambiguities resolution. The computation 6

uses L1 and L2 wavelengths with a L1 and WL combination. The computation pa-

rametrization choice is done comparing some statistics: the RMS, the percentage

with errors bigger than 10 [cm] in the plane and 20 [cm] in the height and the per-

centage of resolved ambiguities. This comparison process is visible in the tables in

Annexe 2 and Annexe 5.

The best positioning solution in the vertical plane is generally obtained with the

computations 2 and 6 (Annexe 2). If the data are analyzed by environment, it

emerges that in fir-trees the best solutions are estimated with the computations 5

and 6. However the data in leafed trees environment, computations 4 and 5 stand

out to deliver the best solutions. In open sky or slightly covered areas, the computa-

tions 1 and 6 provide the best results in the horizontal plane. The heights are gener-



ally better with different computation combinations than the ones used for 2D. To

choose the processing parametrization used for the analysis, quality in the horizontal

plane prevails over the one in the altimetry.

Consequently computations 5 and 6 are used more often in the following analysis of

the PLANSoftTM solutions. In order to compare GPS only and GPS plus GLONASS solu-

tions, the computation 2 (GPS alone) and the computation 4 (GPS and GLONASS)

are compared in the following chapter VII.2.4.4 GAIN OF GNSS VERSUS GPS ALONE.

VII.2.3.1 GLOBAL QUALITY OF THE COMPUTATIONS 5 AND 6 FOR THE GLOBAL DATA SET

A global quality analysis of the computations 5 and 6 can be visualized in Table 3.

The combined forward and reverse solution does not provide very good global RMS,

especially for height coordinates. That results from the fact that a bad precision is

observed for the forward and reverse process computation 5 under the fir-trees

coverage of the area 5 (see Annexe 6). This local bad precision affects the global

quality of the entire computation 5.

The global planimetric accuracy of the data set reaches a 2DRMS of 0.554 [m] for

the computation 5 and 0.63 [m] for the computation 6. The accuracy in the height is

two times worse, with a HRMS of 1.284 [m] for the computation 5, and 0.952[m] for

the computation 6. In both cases, between 75 and 65 percent of the PLANSoftTM po-

sitions‟ errors are smaller than 10 [cm] in the horizontal plane and 20 [cm] in the ver-

tical one.

In the two solutions used for this analysis, the percentage of resolved ambiguities is

relatively high; around 85 percent of the ambiguities in these data sets are fixed.

Table 3: Global analysis of the entire data set for the computations 5 and 6.

A high percentage of resolved ambiguities should insure a good positioning accu-

racy and precision. But some time a high percentage of fixed integer ambiguity is

Co

mp

uta

tio

ns

n°

Computation parameters Analysis of difference with INS-GPS

Process Satellites

used

Phase solution

type

Percentage of fixed integer

ambiguities [%]

Estimated position RMSE accuracy [m]

Percentage with errors bigger than 10[cm] plani and

20[cm] alti[%]

E N H E N H

5

Process forward

and reverse

solu-tions

GPS and GLONASS

L1 and L2 +

wide-lane

84.3 0.447 0.328 1.284 37.6 39.5 35.9

6 GPS and

GLONASS

L1 + wide-lane

86.0 0.440 0.451 0.952 28.2 38.7 26.6



not related to precise RMS (see Annexe 5). Indeed certain types of computation

could help to reduce errors despite the fact the ambiguities aren‟t resolved.

Despite a quite high PDOP threshold of 150, the position‟s estimation failed nine

times in the data sets. These points are located in highly obstructed locations, i.e.

under the roof and under the fir-trees.

After comparison, the entire data set of the computation 6 shows slightly better re-

sults than the computation 5. But splitting the analysis into areas, the computation 6

performs only better in more open sky areas (the numbers 1 and 2) and for areas

with fir-trees (the areas 5 and 6, see Annexe 2). Finally, because their post-processing

quality is quite similar, computations 5 and 6 will both be used for the following

analysis. As detailed earlier, for the combined forward and reverse computation 5,

different qualities are obtained depending on the surroundings obstructions. So it is

more relevant to perform the analysis area by area as strong variations in the results‟

quality can be observed depending on the environment. Therefore following analy-

sis will be done for each area.

VII.2.4 DATA ANALYSIS

The data analysis uses the statistical tools described in chapter VI.3 ANALYSIS TOOLS.

Statistic indicators are computed for each processing type (computations 1 to 8 de-

fined in chapter VII.1.2 GNSS PLANSOFTTM DATA) and for the entire data set as well as

for each area (see chapter VII.2.1 TEST DESCRIPTION). As explained in the previous

chapter, based on their identified good performances after a first analysis of all sce-

narios, the computation 5 and 6 were chosen for the analysis. The computations 2

(GPS alone) and the computation 4 (GPS and GLONASS) are used to analyse the

gain of GLONASS versus GPS alone. Based on the analysis of the entire experimental

data, major conclusions have been extracted. For the concision of the report, only

those are presented in what follows.

VII.2.4.1 INTERNAL QUALITY OF GNSS PLANSOFT DATA

The PLANSoftTM reliability envelope enables to evaluate the ability of the PLANSoftTM

to provide position within the predicted confidence interval. To be reliable, the

PLANSoftTM solution must be inside the envelope‟s contour. The envelope is com-

puted with the equation (51) , using the two dimensions standard deviation and the

velocity vector estimated by the PLANSoftTM. As explained in chapter VI.3.2.3 INTEG-

RITY, CONTINUITY AND AVAILABILITY OF MEASURMENTS, the envelope is computed

from the GNSS-INS position.

The accuracy of a solution is more difficult to estimate in obstructed environments

because in these areas the observations are less redundant degraded by multiple

losses of satellites‟ signals. In fact an estimated standard deviation computed with

fewer observations will be less significant and therefore less representative. So to see

if the accuracy of the PLANSoftTM solutions is well estimated by the PLANSoftTM, the

worst case scenarios must be analysed. Consequently obstructed areas were cho-

sen for the analysis of the reliability.



The data sets analysed are the areas 3, 4 and 6 processed with the computations 5

and 6. As it can be observed in Table 4, these solutions reflect bad conditions for

precise positioning due to the obstruction encountered, e.g. PDOP values are some-

time bigger than 2.2. In the area 4, a roof causes multiple losses of satellites‟ signals

implicating bad PDOP and a low number of satellites in certain parts of the area.

Quality of the solutions analyzed

Solutions analyzed: Comp. 5 area 3

Comp. 5 area 4

Comp. 5 area 6

Comp. 6 area 3

Comp. 6 area 4

GNSS-INS Refer-ence quality

Standard deviation σ2D [m]

0.04 0.04 0.105 0.04 0.04

Standard deviation σH [m]

0.03 0.03 0.09 0.03 0.03

A priori solution quality

PDOP (min-max) [-] 1.3 - 2.2 1.4 - 3.3 1.5 1.5 - 2.1 1.5- 23.8

Satellite number (min-max)

9 to 18 7 to 16 16 to 17 12 to 17 4 to 17

Availability and continuity of the solution

Percentage of Fixed ambiguities %

78% 83% 5% 98% 88%

Table 4: Quality of the solution analyzed for the PLANSoftTM

reliability.

In the leafed-trees dense coverage area 3, variations in the size of the reliability en-

velope can be observed. These different widths result from the fact that the trees

induce different elevation angles. They are higher in the North part of the area and

smaller in the South (down left the plots) (see also Figure 18 and Figure 19). In this

strongly congested environment, the reliability of the PLANSoftTM solutions is quite

good because the trajectory is always located inside the light-blue envelope (see

Figure 17). The larger parts of the reliability envelope translate the important differ-

ences between the PLANSoftTM solution (in blue) and the GNSS-INS reference (in red).

These differences seem to appear in the case of signal losses and faulty ambiguities

resolution in the GNSS PLANSoftTM data set.



Figure 17: PLANSoft

TM reliability envelope for the computation n°5 (combined forward and

reverse solutions) in the area 3.

Figure 18: Sky view of the trajectory in the area 3 on Google

Earth.

Figure 19 (in the right): Photo of the

obstructed environment in the area 3

in the dense part of the foliage.

For the same area 3, but for the computation 6 using L1 and L2 wavelength with a L1

and WL combination, the positions computed by the PLANSoftTM are worse esti-

mated by the software, because they are more often outside of the reliability enve-

lope. Standard deviations computed for these positions were better estimated than

with the forward and reverse computation 5. As visible in Figure 20, the GNSS PLAN-

Soft solution (in blue) exits the envelope (in light-blue). The analysis shows that the

better the solution is, the better the estimation is. And in our case, the computation 5

forward and reverse solution produces the best results in this area 3.



Figure 20: PLANSoft

TM reliability envelope with the computation 6 L1 and L2 wavelength

with a L1 and WL combination solution, in the area 3.

The availability of the PLANSoftTM solution is good also for the other obstructed pas-

sages in the area 4 near the East fir-trees line. For the computation 5, the accuracy

of the PLANSoftTM solution is correctly estimated (see Figure 21). This passage induces

cycle slips in practically all satellites signals. In the worst case, approximately in the

middle of the roof, only 5 to 4 satellites, essentially GPS, are tracked against 15 to 17

before entering the wooden construction. For this difficult area, the probability of the

bad solution location is well estimated by the PLANSoftTM.


reliability envelope with the computa-

tion 5 forward and reverse solution, in the area 4.

Figure 22: Sky view of the trajectory

in the area 4 from Google Earth,

with the approximate position of the

roof.



As expected, in this difficult environment

covered with a roof, the computation 6

isn‟t always located in the reliability enve-

lope (see Figure 23). In the worst case the

solution (in blue) is 50 centimetres outside

of the reliability envelope (see Figure 23).

However the accuracy estimation of the

PLANSoftTM solution remains consistent for

this extreme case.

Figure 23: PLANSoft

TM reliability envelope with the computation 6 in the area 4.

In the area 6, near the fir-trees line in the East, the reliability of the PLANSoftTM solution

wasn‟t well estimated. The maximal distance between the solution (in blue) and the

reliability envelope reaches 25 centimetres (see Figure 24).


reliability envelope with the

computation 5 forward and reverse solution, in the

area 6.


in the area 6 on Google Earth



On the contrary the reliability envelope fits well the PLANSoftTM solution for the com-

putation 6 using L1 and L2 wavelength with a L1 and WL combination (see Figure

26.) For this area 6, the computation 6 gives the best processing quality (see Annexe

2). This observation consolidates the conclusion stating that the quality of the accu-

racy‟s estimation depends on the quality of the computed solution, worse is the solu-

tion and worse is the accuracy estimation.

Figure 26: PLANSoft

TM reli-

ability envelope with the com-

putation 6 forward and reverse

solution, in the area 6.

Globally, there are a good agreement between the PLANSoftTM estimated position-

ing quality and the assessed accuracy even with few satellites in view. Despite the

difficulties due to the surroundings, the errors on the estimated solution don‟t exceed

0.5 meters for the computations 5 and 6. This quality estimation of PLANSoftTM solu-

tions depends on the accuracy of the solution. To estimate the global quality of the

PLANSoftTM precision estimation, assessing the mean difference between each posi-

tion and the reliability envelope could be interesting. This should be further investi-

gated.



VII.2.4.2 IMPACT OF THE AMBIGUITIES RESOLUTION

The data sets analysed are collected in the areas 4 and 7 processed with the com-

putation 5. As we can observe in Table 5 these solutions reflect bad conditions for

precise positioning, because of the encountered obstructions. In the area 4, a roof

causes multiple losses of signal implicating PDOP bigger than 2.2 and low available

satellites in certain part of the area. The receiver used is a geodetic receiver and not

a high sensitivity one. Thus, the number of satellites tracked could be increased with

aiding tracking loop techniques.



Comp. 5 area 7

GNSS-INS Reference quality

Standard deviation σ2D [m] 0.04 0.06

Standard deviation σH [m] 0.03 0.05

A priori solution qual-ity

PDOP (min-max) [-] 1.4 - 3.3 1.3-2

Satellite number (min-max) 7 to 16 12 to 18

Availability and conti-nuity of the solution

Percentage of Fixed ambiguities % 83% 96%

Table 5: Quality of the solutions analyzed for ambiguities resolution.

The quality of the GNSS solution depends on the local environment and on the pre-

vious presence of obstructions. The precedent environment influences directly the

quality of the GNSS PLANSoftTM position. If all ambiguities are resolved after a phase

located in open sky, the position is more stable. But if previous obstructions brought

cycle slips over certain satellite‟s signals, some ambiguities may be not resolved yet.

So the effects of news cycle slips, caused by the new environment, are added to

the previous one and the quality of the new position is affected.

This situation is visible in the area 7, which is situated in the side of a fir-trees line illus-

trated in green in the Figure 27. The errors due to cycle slips are observed in the re-

turn journey depicted in brown and cyan. This return trajectory was located in trees

environments before entering this area. In the outward journey, drawn in red and

blue, the precision of the GNSS PLANSoftTM solution is better because the previous

environment corresponded to open sky.



Figure 27: Comparison of PLANSoft

TM solutions based on the environment crossed before en-

tering the anlysed area. It uses the PLANSoftTM

computation n°5 in area 7.

Different positioning qualities for practically the same satellite geometry occur sev-

eral times in the data set. In fact, with less obstruction in the preceding environment,

ambiguities are better resolved and the final position is more precise.

The passage under the 25 m2 roof in the area 4 is now analysed to assess the ambi-

guities resolution and the position‟s estimation in difficult environment. As exposed

earlier, this passage causes cycle slips in practically all satellites‟ signals. In the worst

case, approximately in the middle of the roof, only 5 to 4 satellites, essentially GPS,

are tracked against 15 to 17 before the roof site. Only two cycles slips are detected

during this passage (Annexe 4). This kinematic cycle slip detection applied appears

to underestimate the reality, because cycle slips are detected only for the satellite

number 9 and 22 for the GPS times corresponding to the time spend under the roof.

The phase rate cycle slip threshold of 4 [cycle] applied to the data set can perhaps

be increased. The errors over the GNSS PLANSoftTM position is around 1.5 [m] in the

middle of the roof. But approximately 5 meters after the roof area, the positions are

accurate again to 30 centimetres. However, until the pedestrian reaches the end of

the fir-trees line and a more open sky area, the differences between PLANSoftTM posi-

tions and the GNSS-INS reference remain close to 30 centimetres. This constant error

looks may be associated to false ambiguities resolution due to the presence of the

fir-trees line.



Figure 28: Accuracy envelope in the area 4, with a fir-trees line on the East of the trajectory,

plot using the PLANSoftTM

computation 5 forward and reverse process.

Figure 29: Sky view of the trajectory in the area

4 in Google Earth, with the approximate posi-

tion of the roof.

Figure 30: Picture of the Roof crossed.



VII.2.4.3 COMPARISON OF DIFFERENTS ENVIRONMENTS

Four different environments are compared using always the computation 6, which

uses L1 and L2 wavelength with a L1 and WL combination solution. To insure similar

satellite geometry for each data set, the data have been collected during a period

of some 15 minutes.

The first area is the open sky area 1 (see Figure 31 and Figure 32). This area is situated

in the West side of the data set.

Figure 31 : Sky view of the trajectory com-

putation 6 in the area 1 on Google Earth.

Figure 32: Picture of the open sky area 1.

The second area, used for comparison

purposes, is the sparse leafed-trees area

2 (see Figure 33, Figure 34 and Figure 35

This area allows a good visibility of satel-

lites, but some obstructions are pro-

duced by the trees boles. At the time of

the data collection no leave is present

on these trees.


computation 6 in the area 2 on Google

Earth.



Figure 34: Picture of the sparse leafed-trees area

2, taken from the West side.

Figure 35: Picture of the sparse leafed-trees area

2, taken from the East side

The third area analyzed goes along the fir-trees line in the East side (see Figure 36

and Figure 37).

Figure 36: Sky view of the trajectory computation 6 in the area

6 on Google Earth.

Figure 37: Picture of the fir-trees

line in East side area 6.

The fourth area analyzed is situated under a dense coverage of fir-trees (see Figure

38 and Figure 39).

1 2



Figure 38: Sky view of the trajectory computation 6 in the

area 5 on Google Earth.

Figure 39: Picture of the dense fir-trees

cover area 5.

The quality of the analyzed scenarios is presented in Table 6.



Comp. 6 area 2

Comp. 6 area 5

Comp. 6 area 6

GNSS-INS Reference quality

Standard deviation σ2D [m] 0.005 0.009 0.21 0.06

Standard deviation σH [m] 0.005 0.008 0.14 0.05


PDOP (min-max) [-] 1.5 - 1.7 1.5 - 1.7 1.4 - 19.6 1.4 - 2.6

Satellite number (min-max) 15 to 17 13 to 17 5 to 17 10 to 17

Availability and con-tinuity of the solu-tion


100% 100% 30% 96%

Table 6: Quality of the scenarios analyzed for environments comparisons.

As expected, the satellites geometries are better for the open sky area 1 and for the

area 2 with spare trees.

The areas in open sky 1 and under sparse trees number 2 have both the maximum

percentage of ambiguities resolved (see Table 7 and Table 8). The horizontal accu-

racy is better in the open sky area with a 2DRMS of 0.05 [m] compared to a 2DRMS

of 0.06 [m] in the area 2 with sparse trees. In the altimetry, the HRMS are also better

for the open sky area 1. The accuracy reached in this area allows precise position-

ing. As visible in Table 7 and Table 8, more than 99 percent the PLANSoftTM errors are



smaller than 10 centimetres in the horizontal plane and 20 centimetres in the height.

The PLANSoftTM solution is really very precise in open and slightly obstructed areas.

Area 4 in open sky

Co

mp

uta

tio

ns

n° PLANSoftTM parameters Analysis of difference with INS-GPS

Process Satellites

used

Phase solution

type

Percentage of fixed inte-ger ambigui-

ties [%]

Estimeted position RMSE accuracy [m]


20[cm] alti[%]

E N H E N H

6 No

special process

GPS and GLONASS

L1 + wide-lane

100 0.025 0.038 0.067 0.00 0.00 0.00

Table 7: Statistic analysis of the area 1 in open sky for the computation 6.

Area 5 with sparse leafed-trees

Co

mp

uta

tio

ns

n° Analysis of difference with INS-GPS

Process Satellites

used

Phase solution

type


ambiguities [%]



20[cm] alti[%]

E N H E N H

6 No

special process

GPS and GLONASS

L1 + wide-lane

100 0.037 0.047 0.114 1.02 0.68 0.34

Table 8: Statistic analysis of the area 2 with sparse leafed-trees for the computation 6.

Some of the errors, depicted in Figure 40, in the sparse trees area 2 come from multi-

path effects, probably due to reflected signals on the surrounding boles trees. Some

differences between the PLANSoftTM solution and the INS reference come from the

lack of satellites signals too. In fact, in the open sky area 17, satellites are tracked

and arriving in the sparse trees area some positions are computed with 15, 14 and

even 13 satellites measurements. This loss of observations result in a slightly worse po-

sitioning quality in the area 2. When several signal‟s losses occur, the PLANSoftTM er-

rors still remains over several metres until the obstruction stops and the satellite signal

can be tracked again. This happens when ambiguities can‟t be fixed again and this

process can take up to 30 seconds. But usually they are resolved within a few sec-

onds. This effect will be explained in the analysis of the two following areas. In the

area 1 and 2, the cycle slips don‟t occur on enough satellite‟s signals to produce the

same effect.



Figure 40 : Zoom on the plot of the area 2 with a

possible multipath effect.

Figure 41 : Sky view of the trajectory computa-

tion 6 in the area 2 on Google Earth.

For the more open sky areas 1 and 2 the

mean standard deviations are always

smaller than 1 [cm] for each coordinate

(see Table 9). The reference precision is

good enough in this area to make analy-

sis because no inaccuracy in the refer-

ence solution may bias the analysis. Table 9: Mean standard deviation of the reference for the areas 1 and 2.

Others analysis can be done, still using the computation 6, between the two last

data sets in fir-trees environment.

By comparing these results with the previous one in open sky areas, the solutions ap-

peared to be less good. These expected results occur because of the important ob-

structions of the areas 5 and 6 situated in more dense foliage.

Open sky areas

Area n°

INS-GNSS solution mean standard deviation [m]

E N H 2D

1 0.003 0.004 0.005 0.005

2 0.005 0.008 0.008 0.009



Area 9 with sparse a fir-trees line in the East C

om

pu

tati

on

s n

°

Analysis of difference with INS-GPS

Process Satellites

used

Phase solu-tion type

Per-centage of fixed integer ambi-guities

[%]



20[cm] alti[%]

E N H E N H

6 No

special process

GPS and GLONASS

L1 + wide-lane

10.8 0.350 0.611 1.647 82.2 98.1 100

Table 10: Statistic analysis of the area 6 with the fir-trees line in East for the computation 6.

The computation 6 gives especially good results for the area 5 compared with other

computations.

Area 7 with dense fire-trees coverage

Co

mp

uta

tio

ns

n°


Process Satellites

used

Phase solu-tion type

Per-centage of fixed integer ambi-guities

[%]



20[cm] alti[%]

E N H E N H

6 No

special process

GPS and GLONASS

L1 + wide-lane

29.7 1.146 1.052 2.678 80.3 80.5 88.1

Table 11: Statistic analysis of the area 5 with dense fir-trees coverage for the computation 6

The two data sets in areas 5 and 6 have a small percentage of resolved ambiguities,

certainly because of the numerous obstacles.

The errors are very dispersed in both data sets, especially in the area 5 (see Figure 42

and Figure 43). The PLANSoftTM positions are better in the area 6 (see Figure 44 and

Figure 45). This area is approximately exposed to forty percent of open sky, whereas

the area 5 is totally covered. In this both areas, errors result from small multipath ef-

fect or signal absorption by the foliage of the fir-trees. But the biggest errors are cre-

ated by the multiple cycle slips because of loss of signal.



Figure 42: Histogram of

the data computation 6

in the area 6.

Figure 43: Histogram of the

data computation 6 in the area

5.

Figure 44: 3D error ellipsoid represent-

ing 95% confidence region with of the

computation 6 in the area 6 with trees

line in the East side.

Figure 45: 3D error ellipsoid representing 95% confi-

dence region of the same data but in the area 5 under fir-

trees.



The number of satellites used to compute the positions varies strongly in the area 5 of

dense foliage. As a consequence the DOP varies strongly too (see Figure 47).

Figure 46: Satellites geometry and errors on the position for the computation 6 in the area 6..

Figure 47: Satellites geometry and errors on the position for the computation 6 in the area 5.



The quality of the reference is not excellent in these two areas, particularly in the

area 5. The 2DRMS of the area 5 reaches 0.21 [m]. As it can be seen in Figure 48, the

maximal standard deviation of the reference reaches 42 centimetres. This inaccu-

racy of the reference solution must be considered in the analysis. The GPS-GLONASS

solution computed with the NovAtel software Inertial Explorer without a combination

with INS data is not as good as the PLANSoftTM solution. So the poor performances of

the GPS-INS reference can be attributed to the inaccuracy of GNSS only positions.

Fir-trees areas

Area n°

INS-GNSS solution mean Stan-dard deviation [m]

E N H 2D

5 0.152 0.145 0.138 0.209

6 0.068 0.080 0.086 0.105

Table 12: Mean standard deviation of the reference for the areas 5 and 6.

Figure 48: Evolution of the standard deviation estimated by Inertial Explorer in the area 5.



VII.2.4.4 GAIN OF GNSS VERSUS GPS ALONE

The comparison of the performances with and without GLONASS was done with the

computation 2 (GPS alone) and the computation 4 (GPS and GLONASS). These two

processing use both dual frequencies measurements and do not combine forward

and reverse solutions. Except the addition of GLONASS observations for the compu-

tation 4, another difference distinguishes the two computations. A different combi-

nation of observations is applied at each computation. The computation 2 has a L1

and L2 ionospheric free (IF) combination. The computation 4 has a widelane (WL)

computation using L1 and L2 observations. But this difference of combinations hasn‟t

a capital influence in the results.

The scenarios analysed are the open sky area 1 and the dense leafed-trees foliage

area 3. The main initial conditions, which influence the quality of these scenarios, are

presented in the Table 13. As expected, the PDOP are bigger for the computation 2

using only GPS measurements. The percentage of ambiguities resolved is worse in

the area 3 because of the trees presence.



Comp. 4 area 1

Comp. 2 area 3

Comp. 4 area 3


Standard deviation σ2D [m] 0.005 0.005 0.04 0.04

Standard deviation σH [m] 0.005 0.005 0.03 0.03


PDOP (min-max) [-] 1.7 - 2.08 1.5 - 1.7 1.8 - 3.3 1.5 - 2.1

Satellite number (min-max) 9 to 11 15 to 17 8 to 11 12 to 17



100% 100% 79% 69%

Table 13: Scenarios analyzed to see the gain of GLONASS.

In the open sky area 1, the benefit of GLONASS augmentation in the horizontal

plane is not really visible (see Table 14). However in the altimetry plan, the GPS

computation 2 offers results more precise of 1 centimetre.

Co

mp

uta

tio

ns

n° Analysis of difference with INS-GPS

Satellites

used

Phase solu-

tion type

Percent-

age of

fixed

integer

ambigui-

ties [%]

Estimeted position

RMSE accuracy [m]

Percentage with

errors bigger than

10[cm] plani and

20[cm] alti[%]

E N H E N H

2 GPS L1 and L2 100 0.025 0.039 0.064 0 0 0

4 GPS and

GLONASS

L1 and L2

+widelane 100 0.026 0.038 0.075 0 0 24

Table 14: Statistic analysis of the area 1 in open sky for the computations 2 and 4.



By comparing the histo-

grams of the computa-

tions 2 (GPS alone) and 4

(GPS and GLONASS), the

gain thanks to GLONASS

augmentation isn‟t rele-

vant in this open sky area

1 (see Figure 49 and Figure

50).

Figure 49: Histogram of the data computation 2 (GPS alone)

in the open sky area 1.

Figure 50: Histogram of the data computation 4 in the open

sky area 1.

However in the leafed-trees area 3, the gain of GLONASS augmentation is clearly

visible. The numerous obstructions have less impact if more signals can be used to

estimate a solution. This is explained by the fact that the probability of tracking ob-

structed signals is reduced. However the percentage of resolved ambiguities is

smaller for the GPS-GLONASS computation 4 as visible in Table 15. But the better

accuracy in the horizontal plane in the GPS-GLONASS computation 4 confirms the

gain of GLONASS augmentation. The 2DRMS is 1.15 [m] for the computation 2 (GPS

only) and 0.81 [m] for the computation 4 (GPS-GLONASS). The altimetric solutions

have a similar accuracy.



Co

mp

uta

tio

ns

n°


Satellites

used

Phase so-

lution type

Per-

centage

of fixed

integer

ambigui-

ties [%]

Estimeted position

RMSE accuracy [m]

Percentage with

errors bigger than

10[cm] plani and

20[cm] alti[%]

E N H E N H

2 GPS L1 and L2 78.57 0.695 0.910 0.466 71.83 69.44 41.27

4

GPS and

GLON-

ASS

L1 and L2

+widelane 68.65 0.437 0.686 0.462 65.48 73.81 60.32

Table 15: Statistic analysis of the area 3 under leafed-trees for the computations 2 and 4.

Comparing Figure 51 and Figure 52, it is clear that DOP values are smaller for the

GPS-GLONASS computation 4. The number of satellites visible by the receiver in-

creases with the addition of the GLONASS satellites. As a result, the errors on the posi-

tion decrease for the GPS-GLONASS computation 4.

Figure 51: Satellites geometry and errors on the position for the computation 2 (GPS only) in

the area 3.



Figure 52: Satellites geometry and errors on the position for the computation 4(GPS and

GLONASS) in the area 3.

The 3D error ellipsoid of the GPS only computation 2 is slightly bigger than the one for

the GPS-GLONASS computation (see Figure 51 and Figure 52).

The histogram of the GPS only computation 2 shows a larger errors dispersion along

the East and North coordinates, with a bigger standard deviation (see Figure 53 and

Figure 54). This reflects the important errors impacting certain positions when less sat-

ellite are tracked.

Figure 53: Histogram of the computation 2 (GPS only) in the area 3.



Figure 54: Histogram of the computation 4 (GPS-GLONASS) in the area 3.

Previous studies on the PLANSoftTM computation have demonstrated that in all of the

visibility condition tested, GLONASS augmentation with the fix of GLONASS ambigui-

ties improve both the overall rate of correct fix and the rate of detection for incor-

rect fix [Ong et al 2010]. So, as a consequence the position‟s quality must be im-

proved too. The present study demonstrates above all that the GLONASS added

value is more important in obstructed zones compared to open areas. In open ar-

eas, the gain of GLONASS is less visible. The same conclusion can be done for all kind

of GNSS augmentation.



VII.3 ANALYSIS OF THE INFLUENCE OF THE NATURE OF OBSTACLES OVER THE SO-

LUTION

The two following data sets were collected in order to compare the effect of the

nature of surrounding obstructions on the position‟s estimation.

VII.3.1 TEST DESCRIPTION

This data set is composed of one part located along a line of trees and a second

part located along the CCIT building in the University of Calgary (see Figure 55 and

Figure 56). The obstruction mask of 60° is identical for the two datasets and was

measured with a clinometer. The period of time between the two data sets is 1 hour.

Therefore the satellite constellation can be considered as identical for both experi-

ments. Each data collection has lasted approximately 7 minutes.

Figure 55: Picture of the straight trajectory fol-

lowing the road side nearby the trees line.

Figure 56: Picture of the straight trajectory fol-

lowing the road side nearby the building.



VII.3.1.1 GNSS_INS REFERENCE FOR THE TREES AND BUILDING DATA SET

As exposed in the Table 16, the reference position precision reaches 7 millimetres in

the three axis directions for the area with a trees line obstruction. The reference posi-

tion precision of the building line area is worst. It reaches approximately 4 centime-

tres.

Quality of the solutions analysed

Solutions analysed: Comp. 4 trees line

obstruction Comp. 4 building

obstruction


Standard deviation σ2D [m] 0,009 0,062

Standard deviation σH [m] 0,007 0,041

Table 16: Statistic analysis of the area with trees line obstruction and of the area with the

building obstruction for the computation 4.

The trajectory near the trees line couldn‟t be computed with a combined forward

and reverse solution because a problem occurred in the data collection. However,

the environment is clear enough to compute a good reference solution based on

the forward only solution. This is visible in table 16.

VII.3.2 GNSS PLANSOFTTM SOLUTION FOR THE TREES AND BUILDING DATA SET

After a comparison of all computation parametrization, the computation 4 provides

good results for both areas. It is not the only good one, but this computation has a

solution of constant quality for both areas. Therefore, this computation is chosen for

the analysis.

The initial conditions of the PLANSoftTM computations 4 are presented for the two

areas compared in the following table 17. The PDOP of the trees line area are less

dispersed and smaller than for the second area. The number of available satellites

used for the PLANSoftTM computations is smaller for the building obstruction area.

And the percentage of ambiguities resolved is quite pore in this building area.

Quality of the solutions analysed

Solutions analysed: Comp. 4 trees line

obstruction Comp. 4 building

obstruction

Apriori solution quality

PDOP (min-max) [-] 1.3 - 2.35 1.22 - 5.13

Satellite number (min-max) 10 to 12 6 to 12


Percentage of fixed ambigui-ties %

100% 15%

Table 17: Statistic analysis of the area with trees line obstruction and of the area with

the building obstruction for the computation 4.



VII.3.3 DATA ANALYSIS

A first comparison is done with one of the best PLANSoftTM post-processing, the com-

putation 4 using dual frequencies GPS and GLONASS measurements with a free

ionospheric computation. Only for the building obstacle, the quality of the INS-GNSS

reference seems to be worse than the one from PLANSoftTM. The INS-GNSS positions,

computed with the NovAtel software Inertial Explorer, are more dispersed (see Figure

57 and Figure 59). The true trajectory was straight but it isn‟t the case for the INS-

GNSS data depicted in red in the following plots. Contrary the PLANSoftTM solution

follows a straight trajectory

Figure 57: Magnification of a part of the trajec-

tory calculated with the 60° building elevation

mask using the data computation 4.

Figure 58: Sky view of the corresponding refer-

ence trajectory on Google Earth.



Figure 59: Magnification of the trajec-

tory with the 60° building, elevation

mask using the computation 4.

The quality of the combined INS-GNSS

solution is certainly affected by the poor quality of the GNSS only solution computed

by Inertial Explorer (see Figure 60). It is interesting to notice that he NovAtel Software

GNSS solution is not as good as the PLANSoftTM GNSS solution. With a dispersion

around 3.5 meters on each side of the true trajectory, this Inertial Explorer GNSS solu-

tionis not so precise than the PLANSoft one.

Figure 60: Plot of the GNSS solution produced with Inertial Explorer.

Scale 5 [m]



The poor quality of the reference occurs

only near the building with an elevation

mask of 60°. Along the trees line, the

reference solution is better (see Figure

61).

Figure 61: Plot of the trajectory with the

60° trees line elevation mask using the

data computation number 4.

As for the PLANSoftTM GNSS solution, the Inertial Explorer GNSS solution is computed

with a double differencing method, including a troposphere correction.

Because more multipath is expected from the building‟s obstacle than the trees line,

improved blunder detection in PLANSoftTM might explain why the last provide more

accurate results than the GNSS-INS. The NovAtel software might be not rejecting too

many observations as the PLANSoftTM does it and computes them again until obtain-

ing better residuals. The PLANSoftTM process could better remove these multipath

errors. To verify this hypothesis, the number of measurements should be increased in

order to augment the statistical signification of the experimental results. In the future,

it would be interesting to redo these tests using a more reliable reference, e.g. using

a theodolite. A multipath detection test could be added in the PLANSoftTM software.

This detection could be done by comparing each new computed position with the

previous position. If the distance between the satellite and the receiver is abnormally

bigger compared with the previous distance, a multipath effect may be identified.

The detection threshold would then be a sensitive parameter to adjust for multipath

detection. This threshold corresponds to the maximal accepted difference between

two positions and it would depend on the data sampling rate.



VIII CONCLUSION AND PERSPECTIVES

All analyses are based on the PLANSoftTM software solution. This software was devel-

oped in the PLAN research group essentially to perform dynamic precise positioning.

The flexibility of PLANSoftTM enables to use different measurements and different

measurements combination in order to achieve the best possible navigation solu-

tion. This software provides many outputs that help to understand the results. The

output files provide also all necessary information on the reliability of the computa-

tion. These reliability indicators are given for each GPS time and they consist in the

estimated standard deviations, the number of fixed ambiguities, the results of the

two tests that verify the reliability of the ambiguities, as explained in chapter VI.2.5.5

RELIABILITY OF THE FIXED AMBIGUITIES FOUND the predicted ambiguity success rate

and the ratio of the F-test.

As a first conclusion, the analysis based on the envelope of the reliability plots has

shown that globally the position estimated with PLANSoftTM is accurate even if only a

few satellites are in view. Secondly the quality estimation in PLANSoftTM depends on

the accuracy of the solution itself.

A key element to obtain precise satellite positioning is to use carrier phase meas-

urements and therefore to resolve ambiguities. However in congested environment,

cycle slips prevent from continuously tracking signals, introducing new unknown in-

teger number of whole cycles. Such new carrier phase ambiguity terms must be

computed to allow precise positioning again. From the previous statistical analysis it

can be concluded that the nature of the environment that precedes an obstructed

area has a strong impact on the quality of the final navigation solution. As described

in chapter VII.2.4.2 IMPACT OF THE AMBIGUITIES RESOLUTION the success rate of the

ambiguity resolution depends on the history of resolved ambiguities and thus on the

previous environment crossed. Indeed, if obstructed environments must be surveyed

during a data collection, good quality of position can be reached only if the ambi-

guities were resolved in the previous environment, which is generally an open sky

one. Facing this conclusion, it is important to plan ahead the trajectory taking the

surrounding obstructions and the open sky areas into account. Using an airborne

photography can help to visualize and understand the environment targeted for the

data collection.

Because the ambiguity resolution step and the signal losses effect the position com-

puted with the carrier phase measurements, very precise positioning is difficult to

achieve in obstructed environments. Errors can easily reach 1 metre or even more in

these difficult areas. But the analysis conducted in this research demonstrated that

the PLANSoftTM often performs as well as the GNSS-INS solution. For dynamic applica-

tions, in a lot of the different areas analysed, the use of GPS and GLONASS meas-

urements combined is accurate enough. For precise positioning at the decimetre

level in open sky and in lightly obstructed areas, the PLANSoftTM GLONASS-GPS posi-

tioning provide the same performance level as the GNSS-INS post-processed with

Inertial Explorer software. It is astonishing to see that even in obstructed environ-

ments, the PLANSoftTM GLONASS-GPS provides good results too. The good quality

level of the navigation solution and the reduced cost of this solution, i.e. the ab-

sence of additional INS sensors, stimulate the use of this method even in motion.



The analysis concludes that the GLONASS gain is more relevant in obstructed envi-

ronments, like with trees and buildings, than in open sky environment as the satellite

geometry is improved. The probability to track more signals is obviously improved by

adding GLONASS satellites. In open sky area too the addition of GLONASS satellites

increases the measurements redundancy. However as detailed in section VII.2.4.4

GAIN OF GNSS VERSUS GPS ALONE, measurements with GPS only provide already

enough redundant observations to ensure a precise position. Overall the different

orbital inclination angles (64.8 degrees for GLONASS compared to 55 degrees for

GPS) make the two different satellites systems complementary and improve the

worldwide coverage. As a consequence, often extremely bad DOP values are less

observed with combined GPS and GLONASS measurements. The worldwide cover-

age is improved also because with the different orbite inclination, the distribution of

the satellites in the sky is optimized. Because of the higher inclination angle, the lack

of satellites in the North direction is better filled in places like Canada. As seen in the

chapter VI.3.1 REQUIREMENTS DEFINED BY THE THE APPLICATION, the addition of

GLONASS is also interesting for the ambiguity resolution process. The model, which

depends on the satellite geometry, has a complete and direct impact on the co-

variance matrix of the ambiguities. The efficiently of the ambiguities search depends

on this because the geometry of the search space for the fixed ambiguities follows

from these matrices [Teunissen 1997]. In the future multiple satellite systems can be

used to augment GPS measurements, increasing the redundancy in the data and

the reliability of the positioning. With the use on multiple satellite systems, the satellite

geometry and availability will be improved, especially in obstructed environments

like in urban canyons or near dense vegetation coverage.

While looking for the best possible PLANSoftTM solution, different settings for the post-

processing have been highlighted. The combined reverse and forward solution with

dual frequency GPS and GLONASS data (computation 5) gives especially good re-

sults, with some exceptions in very congested environments. Computation 4, using

dual frequency GPS and GLONASS data with a computation combination of L1 and

L2 widelane, produces good solutions too. The third parametrization chosen for the

analysis is the computation 6 that uses L1 and L2 carrier phase from GPS and GLON-

ASS satellites, with a combination of L1 and widelane. However it is difficult to estab-

lish a direct relationship between the parametrization and the type of environments.

As seen in chapter VII.2.4.3 COMPARISON OF DIFFERENT ENVIRONMENTS, from one

site to another the best possible computation changes, even if the type of environ-

ment is composed of the same kind of trees. From one solution to another the suc-

cess rate of the ambiguity resolution changes rapidly. It would be interesting to in-

vestigate this element more deeply. Whether some computation types are more

appropriate for certain kinds of environment, the nature of the obstructions could

become a new parameter to add in the software. Therefore doing tests to compare

the impact of the nature of obstacles with similar elevation masks could be relevant.

This was started in the last tests. However the duration of the data sets should be

longer to increase the statistical significance.

This resolution of the ambiguity parameters is based on least squares estimation. The

way to obtain optimal solutions is an appropriate functional and stochastic model-

ling. Using GLONASS and GPS measurements, the difficulty is to compute the double

difference for the GLONASS carrier phase. A parametrization of the phase double

difference equation is necessary to eliminate the GLONASS clock offset unknowns.



Finally the objectives of the project are well carried out. The understanding of the

computation wasn‟t sufficient for relating the effect of the different environments

with the parametrization of the post-processing. This happened due to the poor re-

dundancy of available data for the analysis. The difficulties to augment GPS data

with GLONASS measurements were studied in depth and the gain was analysed in

different tests. Through these tests, the study of the positioning quality in difficult envi-

ronments was well assessed. Achieved statistical results are surprisingly good even

though the environments tested were extreme.



IX TABLES DES ILLUSTRATIONS

IX.1 TABLE OF FIGURES:

Figure 1: PDOP value on the 17th March 2010 around 6:30 pm given by the Russian

Space Agency [2]. ................................................................................................................ 18 Figure 2: PLANSoft flowchart ................................................................................................ 21 Figure 3: Double difference schema .................................................................................. 25 Figure 4: Diagram of ambiguities decorrelation by pusing tangents method. ............ 30 Figure 5: PLANSoftTM ambiguities resolution flowchart ...................................................... 33 Figure 6: General process of PLANSoftTM ambiguities resolution ..................................... 35 Figure 7: Envelope construction schema ........................................................................... 44 Figure 8 : Data collection initialization ................................................................................ 46 Figure 9: Visualization of the data collection trajectory on Google Earth. ................... 49 Figure 10: Distribution of the different areas of analysis on Google Earth map. .......... 50 Figure 11: GPS and GLONASS DOP number forecast for 12th May 2010 by Planning

Software of Trimble ................................................................................................................ 51 Figure 12: GPS and GLONASS satellite number forecast for 12th May 2010 by Planning

Software of Trimble. ............................................................................................................... 51 Figure 13: Variation of the standard deviation of the GNSS-INS reference .................. 52 Figure 14: Accuracy envelope in the area 1 in Open sky, plot produced with the

Software Matlab. ................................................................................................................... 53 Figure 15: Accuracy envelope in the area 6 with a fir-trees line on the East of the

trajectory, plot produced with the Software Matlab. ...................................................... 53 Figure 16: Changes in GNSS_INS reference quality according to the previous

environment crossed, area 5 under fir-trees, plot produced with the Software

Matlab. .................................................................................................................................... 54 Figure 17: PLANSoftTM reliability envelope for the computation n°5 (combined

forward and reverse solutions) in the area 3. .................................................................... 58 Figure 18: Sky view of the trajectory in the area 3 on Google Earth. ............................. 58 Figure 19 (in the right): Photo of the obstructed environment in the area 3 in the

dense part of the foliage. .................................................................................................... 58 Figure 20: PLANSoftTM reliability envelope with the computation 6 L1 and L2

wavelength with a L1 and WL combination solution, in the area 3............................... 59 Figure 21: PLANSoftTM reliability envelope with the computation 5 forward and

reverse solution, in the area 4. ............................................................................................. 59 Figure 22: Sky view of the trajectory in the area 4 from Google Earth, with the

approximate position of the roof. ....................................................................................... 59 Figure 23: PLANSoftTM reliability envelope with the computation 6 in the area 4. ....... 60 Figure 24: PLANSoft

TM reliability envelope with the computation 5 forward and reverse solution, in

the area 6. .................................................................................................................................. 60 Figure 25: Sky view of the trajectory in the area 6 on Google Earth .............................. 60 Figure 26: PLANSoft

TM reliability envelope with the computation 6 forward and reverse solution, in

the area 6. .................................................................................................................................. 61

Figure 27: Comparison of PLANSoftTM solutions based on the environment crossed

before entering the anlysed area. It uses the PLANSoftTM computation n°5 in area 7.

.................................................................................................................................................. 63 Figure 28: Accuracy envelope in the area 4, with a fir-trees line on the East of the

trajectory, plot using the PLANSoftTM computation 5 forward and reverse process. ... 64



Figure 29: Sky view of the trajectory in the area 4 in Google Earth, with the

approximate position of the roof. ....................................................................................... 64 Figure 30: Picture of the Roof crossed. ............................................................................... 64 Figure 31 : Sky view of the trajectory computation 6 in the area 1 on Google Earth. 65 Figure 32: Picture of the open sky area 1. .......................................................................... 65 Figure 33: Sky view of the trajectory computation 6 in the area 2 on Google Earth. . 65 Figure 34: Picture of the sparse leafed-trees area 2, taken from the West side. .......... 66 Figure 35: Picture of the sparse leafed-trees area 2, taken from the East side ............ 66 Figure 36: Sky view of the trajectory computation 6 in the area 6 on Google Earth. . 66 Figure 37: Picture of the fir-trees line in East side area 6. ................................................. 66 Figure 38: Sky view of the trajectory computation 6 in the area 5 on Google Earth. . 67 Figure 39: Picture of the dense fir-trees cover area 5. ..................................................... 67 Figure 40 : Zoom on the plot of the area 2 with a possible multipath effect. ............... 69 Figure 41 : Sky view of the trajectory computation 6 in the area 2 on Google Earth. 69 Figure 42: Histogram of the data computation 6 in the area 6. ..................................... 71 Figure 43: Histogram of the data computation 6 in the area 5. ..................................... 71 Figure 44: 3D error ellipsoid representing 95% confidence region with of the

computation 6 in the area 6 with trees line in the East side. ........................................... 71 Figure 45: 3D error ellipsoid representing 95% confidence region of the same data

but in the area 5 under fir-trees. .......................................................................................... 71 Figure 46: Satellites geometry and errors on the position for the computation 6 in the

area 6.. .................................................................................................................................... 72 Figure 47: Satellites geometry and errors on the position for the computation 6 in the

area 5. ..................................................................................................................................... 72 Figure 48: Evolution of the standard deviation estimated by Inertial Explorer in the

area 5. ..................................................................................................................................... 73 Figure 49: Histogram of the data computation 2 (GPS alone) in the open sky area 1. ..................... 75

Figure 50: Histogram of the data computation 4 in the open sky area 1. .................... 75 Figure 51: Satellites geometry and errors on the position for the computation 2 (GPS

only) in the area 3. ................................................................................................................ 76 Figure 52: Satellites geometry and errors on the position for the computation 4(GPS

and GLONASS) in the area 3. .............................................................................................. 77 Figure 53: Histogram of the computation 2 (GPS only) in the area 3. ........................... 77 Figure 54: Histogram of the computation 4 (GPS-GLONASS) in the area 3. ................. 78 Figure 55: Picture of the straight trajectory following the road side nearby the trees

line. .......................................................................................................................................... 79 Figure 56: Picture of the straight trajectory following the road side nearby the

building. .................................................................................................................................. 79 Figure 57: Magnification of a part of the trajectory calculated with the 60° building

elevation mask using the data computation 4................................................................. 81 Figure 58: Sky view of the corresponding reference trajectory on Google Earth. ....... 81 Figure 59: Magnification of the trajectory with the 60° building, elevation mask using

the computation 4. ............................................................................................................... 82 Figure 60: Plot of the GNSS solution produced with Inertial Explorer. ............................. 82 Figure 61: Plot of the trajectory with the 60° trees line elevation mask using the data

computation number 4. ....................................................................................................... 83



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X ANNEXES OF COMPUTATIONS:

Annexe 1:

Scen

ario

n°

Short definition of the scenarios

General processing options Phase processing op-

tions

Computation Satellites Phase

Filter used

Blunder detection

process or speci-

ality

Satelites used

Phase solution

type

Ambiguities type fixed

1 Kalman

filter

yes level 0.1

%

GPS and GLONASS

L1 GLONASS and GPS separatly

G-G L1 G and G separetly

2 Kalman

filter

yes level 0.1

% GPS L1 and L2

GPS sepa-ratly

GPS L1+L2

3 Kalman

filter

yes level 0.1

%

GPS and GLONASS

L1 and L2 GLONASS and GPS separatly

G-G L1 and L2 G and G separetly

4 Kalman

filter

yes level 0.1

%

GPS and GLONASS

L1 and L2 +widelane

GLONASS and GPS together

G-G L1 and L2 G and G together

5 Kalman

filter

yes level 0.1

%

Process forward and re-verse

solutions

GPS and GLONASS

L1 and L2 +widelane


G-G L1 and L2+widelane G and G together proc-ess foward and reverse

solutions

6 Kalman

filter

yes level 0.1

%

GPS and GLONASS

L1 + wide-lane


G-G L1+widelane G and G together

7 Kalman

filter

yes level 0.1

%

GPS and GLONASS

no carrier phase proc-essing

G-G code only

8 Kalman

filter

yes level 0.1

% GPS

L1 + wide-lane

GPS sepa-ratly

GPS L1



Annexe 2:

All areas

Area n°

Better PLANSoft solution

E N H

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

all data

2 1 3 4 3 4 2 3 4

3 2 4 3 4 3 2 2 3 4

1 4 3 2 1 4 1 1 1 3 4 2 1 3 4 1 2

2 1 4 1 1 2 3 3 1 1 4 2 1 2 4 1 1 1 3

4 1 3 2 4 4 2 4 3

5 3 2 4 1 3 4 2 1 4 3

9 3 4 4 3 2 3 2 4

6 2 3 4 4 2 1 3 4 2

8 2 4 3 2 3 4 1 4 3

7 4 3 4 3 2 4 3 2

To-tal

11 7 0 13 24 23 7 13 12 4 0 17 34 18 0 5 6 24 0 13 14 24 0 8

Fir-trees areas

Area n°


E N H

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

4 1 3 2 4 4 2 4 3

5 3 2 4 1 3 4 2 1 4 3

9 3 4 4 3 2 3 2 4

6 2 3 4 4 2 1 3 4 2

7 4 3 4 3 2 4 3 2

To-tal

4 0 0 5 11 10 4 9 8 0 0 3 15 9 0 3 1 11 0 9 9 14 0 0

Leafed-trees areas

Area n°


E N H

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

3 2 4 3 4 3 2 2 3 4

8 2 4 3 2 3 4 1 4 3

To-tal

0 0 0 4 8 3 3 0 0 2 0 7 7 3 0 0 0 2 0 3 4 4 0 3



Open sky areas

Area n°


E N H

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

1 4 3 2 1 4 1 1 1 3 4 2 1 3 4 1 2

2 1 4 1 1 2 3 3 1 1 4 2 1 2 4 1 1 1 3

To-tal

5 7 0 3 2 6 0 4 4 2 0 4 8 4 0 2 5 8 0 1 1 2 0 5

Final results


E N H

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Legend

4 1stbetter solution

Computation type with the bigger number of good quality solution

3 2nd better solution

2 3rd better solution

2nd Computation type with the big-ger number of good quality solu-

tion

1 4th better solution

The areas 8 and 9 are not analysed in the rapport, but it is relevant to take

them in account for a global analysis. The area 8 is situated near a leafed-

trees line in the North direction. The area 9 contains two lines of fir-trees in East

and West sides.



Annexe 3: Reference quality in the Bow River data set

All areas Legend

Area n° INS-GNSS solution Standard deviation [m]

Best value

E N H 2D

all data 0.0272 0.0293 0.0297 0.04

Best value more or less 5[mm]

Fir-trees areas



E N H 2D


6 0.0266 0.0305 0.0322 0.0404

7 0.1516 0.1445 0.1383 0.2094

Worst value more or less 5[mm] 8 0.0209 0.0245 0.025 0.0322

9 0.0676 0.0802 0.0863 0.1049

Worst value

11 0.0381 0.0491 0.0512 0.0622

Leafed-trees areas


E N H 2D

3 0.0254 0.0286 0.0295 0.0383

10 0.0376 0.048 0.0503 0.061

Open sky areas


E N H 2D

4 0.0028 0.0041 0.0049 0.0049

5 0.0054 0.0076 0.0082 0.0093



Annexe 4:

Number of cycle slips detected in the entire data set for the computation

number 6 using L1 and L2 wavelength with a L1 and WL combination solution.

Two cycles slips are detected in the time of going under the roof. This cycle

slips are detected on for the satellite number 9 and 22.



Annexe 5: Summary of the quality analysis for the entire Bow River data set

Scen

ario

n°

Computation parameters Analysis of difference with INS-GPS

Process Satel-lites used

Phase solution

type

Ambiguities type fixed


ambiguities [%]


Percentage with er-rors bigger than

10[cm] plani and 20[cm] alti[%]

X Y Z X Y Z

1 GPS and GLON-

ASS L1

GLONASS and GPS separatly

71.76 0.448 0.486 1.076 35.94 47.60 39.67

2 GPS L1 and

L2 GPS sepa-

ratly 77.23 0.506 0.696 0.966 31.46 41.98 28.86

3 GPS and GLON-

ASS

L1 and L2

GLONASS and GPS separatly

"unable to compute"

4 GPS and GLON-

ASS

L1 and L2

+widelane


83.84 0.457 0.390 1.190 35.90 39.37 31.47

5

Process forward

and reverse

solu-tions

GPS and GLON-

ASS

L1 and L2

+widelane


84.26 0.447 0.328 1.284 37.57 39.53 35.90

6 GPS and GLON-

ASS

L1 + wide-lane


86.02 0.440 0.451 0.952 28.18 38.66 26.64

7 GPS and GLON-

ASS

no car-rier

phase process-

ing

0.00 0.522 0.589 1.231 77.66 83.51 78.64

8 GPS L1 +

wide-lane

GPS sepa-ratly

83.23 0.537 0.556 1.243 33.58 44.59 32.98



Annexe 6:

Sc

enar

io n

°


Process Satellites

used Phase so-

lution type


ambiguities [%]



20[cm] alti[%]

E N H E N H

1 GPS and

GLONASS L1 7,12 1,135 1,039 2,765 87,96 90,69 98,18

2 GPS L1 and L2 9,52 1,294 1,847 2,363 92,49 91,03 95,05

3 GPS and

GLONASS L1 and L2 "unable to compute"

4 GPS and

GLONASS L1 and L2 +widelane

26,64 1,186 0,829 3,362 83,39 81,93 92,34

5

Process forward

and reverse

solutions

GPS and GLONASS

L1 and L2 +widelane

26,64 1,249 0,640 3,683 84,67 82,30 100,00

6 GPS and

GLONASS L1 + wide-

lane 29,74 1,146 1,052 2,678 80,29 80,47 88,14

7 GPS and

GLONASS

no carrier phase

processing 0,00 1,126 1,104 2,818 89,05 91,61 97,81

8 GPS L1 + wide-

lane 19,74 1,182 1,179 3,099 85,56 87,75 89,95

Documents

AMBIGUITIES RESOLUTION WITH GPS AND GLONASS ......Leslie, Cyril my desk neighbour, Nicola, Martine, Melania, Anshu for the many discus-sions and advices that have enriched my stay