Presentation_AFCEA_Conference_Ambrosini

April 10, 2008 “GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR

PRECISE RELATIVE POSITIONING OF FORMATION FLYING SATELLITES” of Michelangelo Ambrosini

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All rights reserved, 2008, Thales Alenia Space

Chapter of Rome

M.Sc. in Advanced Communication and

Navigation Satellite Systems

AFCEA’s International Student Conference 2008

“GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW

SIMULATOR FOR PRECISE RELATIVE POSITIONING OF FORMATION FLYING

SATELLITES”

Brussels, April 10 2008 of Michelangelo Ambrosini


Observation Systems & Radar Business Unit – Satellite System Engineering – Integrated Control Systems

Page 2 M.Sc. IN ADVANCED COMMUNICATIONS AND NAVIGATION SATELLITE SYSTEMS

“GPS DATA PROCESSING METHODS USING SW TOOLS AND THE GPS RECEIVER SW SIMULATOR FOR


April 10, 2008

Introduction to the study

1. Master of Science (M.Sc.) in Advanced Communications and

Navigation Satellite Systems of the University of Rome “Tor

Vergata” achieved in February 2008

2. Internship in the Observation Systems & Radar B.U. – Satellite

Systems Engineering – Integrated Control Systems of Thales

Alenia Space Italy S.p.A. (TAS-I) based in Rome, Italy

3. Study of a future TAS-I/ASI (Italian Space Agency) Low Earth Orbit

Satellite in Formation Flying with COSMO Sky-Med Constellation

Satellites for Remote Sensing and Earth Observation

4. High Accuracy Levels in the Relative Baseline Determination

between COSMO Sky-Med Satellites and the future Formation

Flying Satellite for reasons of High Level of SAR images

Resolution using Interferometric Techniques and GPS Carrier

Phase Data Processing Methods






April 10, 2008

Mission Requirements

High Accuracy Levels in the Relative Baseline Determination between COSMO Sky-Med Satellites and the future Formation Flying Satellite for reasons of High Level of SAR images Resolution using Interferometric Techniques

Main Arguments

Mission Accurate Baseline Determination On-Board Processing Models & Algorithms using GPS Carrier Phase Data

Theory and SW Tooling Implementation & Testing of the GPS Data Processing Methods

Overview & Synthesis of the GPS Orbital Receiver SW Simulator

GPS Receiver SW Simulator Architecture, Performances & Test Campaign Results

Simulations Numerical Results & Test Performances

Targets

Simulations Results near to Real On-Board GPS Receiver Physical behaviour

Simulations Results near to Real GPS Signal Degradation & Delay Sources

High level of Accuracy in the Formation Flying Satellites Receivers Baseline Determination

Next Steps

SW Tools integration in the Satellite System & Subsystems Platform SW Simulator

Algorithms Tests SW Performances: From Post-Processing to On-Board Real-Time SW implementation

Main topics






April 10, 2008

Spacecraft formation flying is commonly considered as: - a key technology for advanced space missions

The distribution of sensor systems to multiple platforms offers:

- improved flexibility and redundancy

- shorter times to mission

- the prospect of being more cost-effective

compared to large individual spacecraft

Satellite formations in Low Earth Orbit provide: - advanced science opportunities that cannot (or less easily) be realized

with single spacecraft (such as):

- measuring small scale variations in the Earth’s gravity field

- higher resolution imagery and interferometry

Spacecraft formation

flying missions






April 10, 2008

Fundamental issues of spacecraft formation flying:

- the determination of the relative state (position and velocity)

between the satellite vehicles within the formation

- knowledge of these relative states in (near) real-time is

important for operational aspects

- some of the scientific applications, such as high resolution

interferometry, require an accurate post-facto knowledge of

these states instead

- therefore a suitable sensor system needs to be selected for each

mission

Spacecraft formation

flying missions






April 10, 2008

Formation Flying for

Earth Remote Sensing






April 10, 2008

Classification of active microwave formations

Formation Flying for

Earth Remote Sensing






April 10, 2008

Mission Objectives & Scenario

The Program is an experimental Mission both for scientific contribution and for the innovative technological aspects

The Program shall operate in strict coordination with COSMO-SkyMed, without any impact at Space and Ground level

The Program will be developed in order to guarantee a maximum level of commonality with COSMO in terms of synergies, developments, operations and maintenance

The Mission objectives are:

to provide additional products wrt the COSMO-SkyMed ones

to realize a “demonstrator” for the testing of Interferometric, Bistatic, Radargrammetric techniques

to fly in formation with one satellite of the COSMO-SkyMed constellation, avoiding to interfere with COSMO-SkyMed mission and operations






April 10, 2008


Selected Configurations for Interferometric and Bistatic acquisitions

from the Reference COSMO-SkyMed orbit

Leader-Follower

Cartwheel

Pendulum






April 10, 2008


Reference: Hill’s coordinate frame






April 10, 2008

Simulated Physical Quantities

The SW Simulator reproduces two different main scenarios:

- The first one is represented by the Simulated Operative Behaviour

Physics in which the GPS Receiver operates that is the Orbital

Mechanics and the Physical Degradations and Delays which affect

the In-Space GPS Signal transmitted from GPS Satellites to the In-

Orbit GPS Receiver.

- The second one is about the GPS Receiver Behaviour and

Performances as far as:

Receiver estimations and measures of the GPS Signal Degradations

due to the Received GPS Signal (Code and Phase) Acquisition and

Tracking Processes;

Pseudo-range and Pseudo-range-Rate Equations Systems Resolution

for the In-Orbit Receiver Position and Velocity determination;

GPS Receiver SW

Simulator Overview






April 10, 2008

SIMULATION

STARTING DATA

RECEIVERS SPS

POSITION AND VELOCITY SOLUTION

RECEIVERS

ORBITAL PROPAGATION

GPS SATELLITES

ORBITAL PROPAGATION

RECEIVERS SIGNAL

DEGRADATIONS MEASUREMENTS

RECEIVERS SIGNAL

DEGRADATIONS ESTEEMS

RECEIVERS INNER

LOOPS DEGRADATIONS

MEASUREMENTS

POST PROCESSING

(RTK & MLAMBDA METHOD)

FORMATION SPS

POSITION AND

VELOCITY

BASELINE SOLUTION

RECEIVERS EXACT

POSITION AND VELOCITY

SOLUTIONS

FORMATION EXACT

POSITION AND

VELOCITY

BASELINE SOLUTION

FORMATION

BASELINE ACCURACY

SW Simulator Logical Scheme

GPS Receiver SW

Simulator Overview






April 10, 2008

3D ECI Propagated Receiver Position & Velocity Dynamics

Receiver 3D Orbital Position Receiver 3D Orbital Velocity

GPS Receiver SW

Simulator Overview






April 10, 2008

3D ECI NORAD Propagated GPS Satellites Position &

Velocity Dynamics

GPS Satellites 3D Orbital Position GPS Satellites 3D Orbital Velocity

GPS Receiver SW

Simulator Overview






April 10, 2008

GPS Signal Degradation & Delay Models (1)

Receiver Clock Bias Delay Effect

Measures Dynamic Ionospheric Delay Effect Measures Dynamic

Receiver 1st Order Relativistic Delay

Effect Measures Dynamic

GPS SAT PRN N°1 2nd Order Relativistic

Delay Effect Measures Dynamic

GPS Receiver SW

Simulator Overview






April 10, 2008

GPS Signal Degradation And Delay Models (2)

GPS SAT PRN N°1 L1 and L2 Carrier Frequencies

Signal to Noise Ratio (SNR) Measures Dynamic

GPS SAT L1 Carrier Frequency

Multipath Delay Effect Measures Dynamic

GPS SAT PRN N°1 C/A Code Gain

Pattern Delay Effect Measures Dynamic

GPS SAT L1 Carrier Frequency Relativistic Doppler

Delay Effect Measures Dynamic

GPS Receiver SW

Simulator Overview






April 10, 2008

Receiver Measures Determination

GPS SAT PRN N°1 Free Space GPS Signal

Propagation Time Delay Dynamic

GPS SAT PRN N°1 L1 Carrier Frequency

Pseudo-range Measures Dynamic


Pseudo-range Rate Measures Dynamic


Integrated Pseudo-range Measures Dynamic

GPS SAT PRN N°1 L1 Carrier Phase

Integrated Doppler Measures Dynamic

GPS SAT PRN N°1 L1 Carrier Phase Integrated

Doppler Rate Measures Dynamic

GPS Receiver SW

Simulator Overview






April 10, 2008

GPS Satellites Visibility Determination

GPS PRN Satellites Visibility Dynamic

Visibility: Mean Value and Standard Deviation

Number of GPS Satellites

Visibility Dynamic

GPS Receiver SW

Simulator Overview






April 10, 2008

Physical Quantities Mean Value 1σ

CLOCK BIAS 1.8005e-008 [sec] 1.03937e-008 [sec]

CLOCK BIAS RATE 1.0e-011 [sec/sec] 0.0[sec/sec]

IONOSPHERE 1.0081 [m] 0.9904 [m]

MULTIPATH 0.1083 [m] 0.1823 [m]

GPS 1° ORDER RELATIVITY 2.2203e+003 [m] 3.9047e+003 [m]

RECEIVER 1° ORDER

RELATIVITY

9.2628e+003 [m] 5.3478e+003 [m]

RECEIVER 2° ORDER

RELATIVITY

0.0226 [m] 0.0081 [m]

CARRIER DOPPLER

EFFECT

6.6936 [m]

387.5065 [Hz]

213.9529 [m]

1.2307e+004 [Hz]

GAIN PATTERN 0.0045 [m] 4.0079 [m]

Receiver Measures Statistics: Mean Value and Standard Deviation

GPS Receiver SW

Simulator Overview






April 10, 2008

Receiver SPS Position & Velocity Solutions Accuracy

Receiver SPS 3D ECI Position Components (X,Y,Z) Error Dynamics

Receiver SPS 3D ECI Velocity Components (U,V,W) Error Dynamics

GPS Receiver SW

Simulator Overview






April 10, 2008

∆x, 1σ

[m]

∆y, 1σ

[m]

∆z, 1σ

[m]

∆vx, 1σ

[m/s]

∆vy, 1σ

[m/s]

∆vz, 1σ

[m/s]

Pos, 1σ

3D [m]

Vel 1σ

3D

[m/s]

121.06 480.38 456.41 4.438 10.572 9.144 34.946 9.121

∆x, 1σ

[m]

∆y, 1σ

[m]

∆z, 1σ

[m]

∆vx, 1σ

[m/s]

∆vy, 1σ

[m/s]

∆vz, 1σ

[m/s]

Pos 1σ

3D

[m]

Vel 1σ

3D

[m/s]

121.09 480.45 456.46 6.156 14.417 12.394 35.117 12.628

L1 Carrier Frequency ECI Position and Velocity Solutions Precision

L2 Carrier Frequency ECI Position and Velocity Solutions Precision

GPS Receiver SW

Simulator Overview






April 10, 2008

Navigation Solution Performance Requirements (Laben Test Report)

GPS Receiver SW

Simulator Overview






April 10, 2008

DOP Determination

Receiver L1 Carrier Frequency GDOP Measures Dynamic Receiver L1 Carrier Frequency PDOP Measures Dynamic

Receiver L1 Carrier Frequency PDOP Measures Dynamic

GDOP, PDOP and TDOP Mean Value and Sigma

GPS Receiver SW

Simulator Overview






April 10, 2008

Relative positioning models:

- Single difference model

- Double difference model

Relative Spacecraft Positioning:

- Integer ambiguity resolution:

- Integer ambiguity estimation

- Integer ambiguity validation

- Proposed processing strategy:

- Sequential kinematic filter (Real Time Kinematic/RTK approach)

GPS Observations & Relative

Spacecraft Positioning






April 10, 2008

Relative positioning models: Single & Double difference models

Overall viewing geometry for relative (spacecraft) positioning using differenced

GPS observations. GPS satellites j and k are commonly observed by both

receivers and thus SD and DD observations can be formed. This is not the case

for GPS satellites h and m, which are only observed by one receiver








April 10, 2008

Overall Processing And Positioning

Strategy:

• Complete initialization of all DD ambiguities

• Partial (re)initialization of new DD ambiguities

• Relative positioning with DD carrier phase

observations and known integer ambiguities








April 10, 2008

STEP 1: Measures initialization & acquisition processes

STEP 2: Observables double difference DD and covariance matrices construction

STEP 3: Initial differential ambiguities determination: the MLAMBDA method

- Floating point solution

- Reduction and de-correlation processes

- Search process

STEP 4: Ambiguities fixing & ionosphere free combination processes

STEP 5: Relative positioning & ambiguity-fixed-ionosphere free DD carrier phases








April 10, 2008

The well-known LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) method has been widely used for the integer least-squares (ILS) estimation problems in positioning and navigation

- The LAMBDA method consists of two stages: reduction and search

- We presented a modified LAMBDA method (MLAMBDA) which improves both this two stages

- The key to the algorithm is to compute the factorization with symmetric pivoting, de-correlate the parameters by greedy selection and lazy transformations, and shrink the ellipsoidal region during the search process

- Numerical simulation showed that MLAMBDA can be much faster than LAMBDA implemented in Delft’s LAMBDA package for high dimensional problems

- This will be particularly useful to integer ambiguity determination when there are more GNSS satellites visible simultaneously, with carrier phase observations on three frequencies in the future

MLAMBDA: A Modified LAMBDA method

for Integer Least-squares Estimation






April 10, 2008

The LAMBDA method:

- Reduction process:

- Integer Gauss transformations

- Permutations

- The reduction algorithm

- Discrete search process

Modifying the LAMBDA method: (MLAMDA)

- Modified reduction - Symmetric pivoting strategy

- Greedy selection strategy

- Lazy transformation strategy

- Modified reduction algorithm

- Modified search process








April 10, 2008

Numerical simulations

Satellite B Orbital Position 3D

ECI components

Baseline between sat A and B

3D ECI components








April 10, 2008


Satellite B Orbital Position

X ECI component esteem

solution accuracy


Y ECI component esteem

solution accuracy


Z ECI component esteem

solution accuracy








April 10, 2008


Baseline error X ECI component

Baseline error Y ECI component

Baseline error Z ECI component

Baseline ECI error norm








April 10, 2008


Satellite B error norm PDOP for Satellite A

PDOP for Satellite B

ECI 3D error

Components

Mean values

(meters)

1σ

(meters)

Δx (1°) 0.0149 0.0138

Δy (2°) 0.0237 0.0114

Δz (3°) 0.0375 0.0460

ECI satellite B 3D vector components

accuracy Mean Value and Standard Deviation








April 10, 2008

Conclusions

- From a careful statistical study and from an accurate comparison between the SW Simulator Data Graphics and those reported in the Laben Lagrange Test Reports we can conclude that the GPS SW Simulator supplies statistically the same results of the real Lagrange Receiver (ENEIDE Mission)

- The SW Simulator also reconstructs the Lagrange Mission Operative Environment simulating the physics which governs both the Receiver Orbital Dynamic and the GPS Constellation Orbital Dynamic considering all types of orbital perturbations

- The simulations of the GPS data processing with the SW tools for the accurate baseline determination have reached the requested preliminary mission performances which are accuracies on each ECI component in space of the order of 1 cm as Standard Deviation in very short computational time for simulations time periods of 1 orbit

Conclusions & Future Developments






April 10, 2008

Future Developments

- Now the work is to develop new strategies and algorithms to make

more robust and accurate the data processing performances and

integrate these SW tools in the Mission Satellite Platform SW

Simulator in Matlab which will be used for the simulations of the

Satellite System and Subsystems in the preliminary mission

requirements design phase

- The future step will be to decode all these SW tools from Fortran

and Matlab to the ADA code in which the Satellite On-Board SW is

implemented and try to reach the target of obtaining the same

statistical real-time GPS data processing performances On-Board

and higher level of accuracy (of the order of 1 mm) in the ground-

based post-processing

Conclusions & Future Developments






April 10, 2008

Michelangelo Ambrosini

Thank you very much for your attention!

Do you have any question?

Brussels, April 10 2008

Michelangelo Ambrosini

Thales Alenia Space Italia

S.p.A. (TAS-I)

Observation Systems & Radar

Business Unit

Satellite System Engineering

Integrated Control Systems

Via Saccomuro, 24 - 00131 -

Rome, Italy

Mobile: (0049)3382376754

E-mail:

michelange.ambrosini@tiscali.

it

Public Profile URL:

http://www.linkedin.com/in/mic

helangeloambrosini

On-line Curriculum Vitae URL:

http://ctif.uniroma2.it/mastercv

/ambrosinim/CV_Ambrosini_E

NG.pdf

mailto:[email protected]

mailto:[email protected]

http://www.linkedin.com/in/michelangeloambrosini

http://www.linkedin.com/in/michelangeloambrosini

http://ctif.uniroma2.it/mastercv/ambrosinim/CV_Ambrosini_ENG.pdf



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