INDEGREE PROJECT VEHICLE ENGINEERING,

SECOND CYCLE, 30 CREDITS

,STOCKHOLM SWEDEN 2017

The Usage of Gyros in North Finding Systems

QUENTIN LE GALL

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES

2

PREFACE

The work presented in this paper has been carried out at Thales Optronique, Elancourt, France between July 2016 and

December 2016 under the supervision of Jean-Marie Petit, the Geolocalisation and Inertial Technique Expert at Thales

Optronique, and Dr. Gunnar Tibert, Associate Professor at the Department of Aeronautical and Vehicle Engineering at KTH

Royal Institute of Technology.

Thales is a French multinational company working in several fields: Space, Avionics, Land and Air-Systems, Secure

communications, Ground Transportations and Defence Mission System. The main activity of Thales Group is to design and build

electrical systems and provides services for aerospace, defence, transportation and security markets. It is the 10th

largest defence

contractor in the world.

Thales Optronique (TOSA) is a division of the Thales Group. TOSA designs optronic systems mainly for the aeronautic industry

with search and track systems but also for military industry with ground cameras. Camera SOPHIE is one of the best-sellers of

TOSA and has been exported worldwide for target location.

I would like to thank my Thales supervisor Jean-Marie for having offered me the opportunity to work on this interesting topic and

for his guidance and help throughout the project. I have learned a lot thanks to him and I am very grateful.

I would also like to thank Gunnar for being the supervisor of this thesis, for answering all of my questions and for helping me

with the redaction of this paper.

Many thanks to all the great people working in the department of control and servomechanism for having welcomed me and

created such a good working atmosphere.

Quentin Le Gall

Elancourt

January, 2017

3

ABSTRACT

As surprising as it may seem, accurate north finding, with an error of only several milli-radian, is still a very difficult

task and has been achieved only with very expensive systems. On the contrary, there are very simple systems that give the

azimuth with an angular error five times superior but for a price a hundred times inferior. Moreover, these systems generally are

non-autonomous (i.e. they are environment dependent and can lose their precision in many situations). This assessment leads to

the following relevant question: Is it possible to design a north finding system with good precision, for a moderated cost and that

works in any situation?

This report presents and evaluates a solution which attempts to answer this problem. This solution is based on a gyro-

compassing principle: a gyro measures the earth’s angular velocity in order to find the azimuth. This solution can be implemented

following several methods, this report presents and compares two of these implementations: Maytagging and Carouseling. The

comparison is made thanks to a theoretical study, a computer simulation and tests on a real model designed for this report.

Carouseling allows us, in theory, to reach an accurate azimuth, but puts mechanical constraints on the system. Maytagging

implementation seems adapted considering trade-off between precision and cost. Further improvements on gyros will certainly

make systems based on gyro-compassing the most efficient autonomous systems for north finding.

In this report, precisions reached by the different implementations are not made explicit for confidentiality reasons.

4

CONTENTS

Keywords .......................................................................................................................................................................... 5

Acronyms & Abreviations ................................................................................................................................................ 5

I. Introduction ............................................................................................................................................................... 5

A. Purpose of the project ........................................................................................................................................... 5

B. General Overview ................................................................................................................................................. 5

II. Background ............................................................................................................................................................... 5

A. Existing north finding system on camera.............................................................................................................. 5

B. Gyro-compassing .................................................................................................................................................. 6

C. Problem statement ................................................................................................................................................ 6

D. Integration on the existing system ........................................................................................................................ 7

E. Previous Work ...................................................................................................................................................... 8

III. Algorithms principle ............................................................................................................................................. 8

A. Carouseling ........................................................................................................................................................... 8

B. 4 points Maytagging ............................................................................................................................................. 9

IV. Experiment and results.......................................................................................................................................... 9

A. Hardware used ...................................................................................................................................................... 9

B. Software used ...................................................................................................................................................... 11

C. Carouseling results .............................................................................................................................................. 13

D. 4 points Maytagging results ............................................................................................................................... 16

V. Caroseling and Maytagging comparison ................................................................................................................ 19

VI. Model improvement ............................................................................................................................................ 20

A. Real situation measurement ................................................................................................................................ 20

B. Algorithm improvements .................................................................................................................................... 21

C. Temperature Drift compensation ........................................................................................................................ 22

D. New architecture ................................................................................................................................................. 23

VII. Conclusion and discussion .................................................................................................................................. 25

References....................................................................................................................................................................... 25

5

KEYWORDS

North finding, Maytagging, Carouseling, gyro-compassing

ACRONYMS & ABREVIATIONS

TOSA Thales Optronic

Ref Referential

NF NorthFinder

MEMS Micro Electro-Magnetic System

IMU Inertial Measurement Unit

ARW Angular Random Walk

ARRW Angular Rate Random Walk

CVG Coriolis Vibratory Gyroscope

RMS Root Mean Square

CPU Central Processing Unit

I. INTRODUCTION

Gyros are crucial sensors for the space industry. They

enable engineers to control and monitor satellites, rockets or

spaceships in space. Due to the fact that gyros are widely used

in many space applications and in many other fields, studies

are still carried out on them with the aim of improving their

performances and reducing their cost and size. These

improvements give engineers the opportunity to create new

applications and systems that could not have been feasible just

a few years ago. North finding system based on gyro is one of

these new applications that cannot be done without a high-

performance miniature gyro.

This thesis develops a north finding system based on a gyro

that could be used for a military camera developed by TOSA.

This kind of camera can locate a target very precisely within a

distance of several kilometres. To do so the camera needs to

locate itself with respect to its surrounding and to know in

which direction it is pointing. As a consequence knowing the

exact position of the North is primary and plays a significant

part in the precision of the whole system. A small error on the

North position will affect the pointing direction and therefore

the measured location of the target. Generally, the North

finding function is conducted by a magnetometer but it can

also be made with a method based on celestial stars. The

former system has good performance and is based on

electromagnetic fields. Nevertheless its precision is extremely

environment dependent because any metallic structure near the

system will interfere with the magnetic field and hence will

badly affect the magnetometer measurement. The second

system uses celestial stars as day markers, pointing the camera

towards known stars and knowing the camera position, the

North position can be deduced. Nonetheless this system is

limited because it cannot operate when the stars are not

visible. The first system is autonomous but all of them depend

on external phenomena which vary depending on the cameras

location. As a consequence, it appears that another

environment independent solution needs to be developed. This

new solution is the system presented in this report. It is based

on gyro-compassing and can reach, in theory, better

performance than magnetometers, in any given environment.

Nonetheless the costs of such a system need to be optimized in

order to represent a good alternative to the existing solutions.

A cost related trade-off will therefore be made throughout the

study.

A. Purpose of the study

The present thesis deals with the study and design of a North finding system that should be implemented in a camera to improve its targeting performance. Considering the military application, a lot of information is confidential and cannot be presented in this report. However, the theoretical background and design of the system will be treated. Previous internships have been conducted on the same study before I started this thesis.

The first objective of this study was to optimize the performance of an existing model, by analysing experimental results and improving both hardware and computing software. Once the required performance were reached, the second objective was to design a new architecture of the system taking into account its integration in the camera and keeping in mind the overall cost of the system.

For confidentiality reasons the angular precision aimed will be noted expressed in mrad. Every performance measurement will be made with respect to this parameter.

B. General Overview

The first part of this report focuses on the description of the gyro compassing principle for North finding. Two computing methods, Carouseling and Maytagging, will then be presented, and their application on the model will be compared. The comparison is made both through experiments and simulations. A conclusion sums up all the pros and the cons of each method.

The second part deals with the improvement of the system: the design and the specifications of an eventual new architecture are explained, the method adopted is Maytagging.

II. BACKGROUND

A. Existing north finding systems on camera

As previously mentioned, one of the systems currently

used for north finding is a magnetometer located in the

camera. It is a sensor that measures magnetic field. As the

lines of the Earth’s magnetic field are oriented from the South

to the North, the magnetometer finds the position of the north

by determining the orientation of these magnetic field lines.

This measurement method is extremely environmentally

dependent because any magnetic field source, e.g. an electric

motor, can disturb the measurement. Moreover, the Earth’s

magnetic field is not locally homogenous so the accuracy of

such a system can depend on where it is located. According to

the manufacturer, a magnetometer can typically find the north

with an accuracy of about 0.5°, in a perfect environment.

Another method used to find the North position is the celestial

north finding method. Knowing the current location of the

tripod and the date, the position of many stars in the sky can

be deduced. They are then used as day markers: the user

points the machine in the direction of several markers and the

6

system can compute the North position. To use this method,

the stars need to be visible which is not always the case.

In a real situation, the camera with its north finding system

is associated with a goniometer. A goniometer is a system that

can mechanically rotate with a very precise angle around two

axes. The rotation angle is read by the user on a scale. The

camera and the goniometer are put on a tripod as shown in

Figure 1. When the tripod is placed at a known location

(detected by the camera’s GPS), the North location is detected

with one of the previous methods and then, using the

goniometer, the user can rotate the camera relatively to the

North position and target anything. Knowing in which

direction the North is, the user can measure the difference in

angles between the North and the target. Combining this

information with the current location (GPS) and the distance

between the camera and the target (laser range finder), the

target can be fully located.

North

Target

Goniometer

Camera

Tripod

GPS location

Azimuth

Distance

Figure 1. Diagram of target location thanks to a camera.

The current precision given by the magnetometer (about

0.5°) is not enough for a precise target location. That is why

studies are conducted to find an alternative to this technology.

One of the major alternative solutions is based on Gyro-

compassing method.

B. Gyro-compassing

Gyro-compassing is a method for north finding based on the measurement of the Earth’s angular velocity by a gyro. When the gyro’s sensing axis is placed in a plane perpendicular to the Earth’s radius (grey plane in Figure 2), it can measure the projection of the Earth’s angular velocity vector in this plane. This projection is oriented in the North direction. Hence it is easy to see that the measurement of this projection is maximal when the gyro sensing axis is in the north direction as it is shown in Figure 2. Thus the detection of a maximum in the measurement can provide the north position. Nevertheless, the Earth’s angular velocity is very small (about , consequently the gyro needed for this application must be very accurate. Moreover, any error in the measurement, even a slight one, will have a direct impact on the position of the detected north and therefore on the targeting performance. Searching the maximum of a signal, which seems very simple at a first glance, can in fact be very complex when put into practice and requires very expensive and precise hardware. In this study, in order to provide a very competitive system, the costs shall be reduced to a minimum without lowering the

performance. In the following, a theoretical study of the measurement process is presented and the impact of different kinds of errors is quantified.

lat

lat

Figure 2. Diagram describing the horizontal plane and the direct frame (from

[3]).

C. Problem statement

The parameters used in equations are defined as follows:

· : Angle between the North and the direction pointed

the system is pointed towards equivalent to the

azimuth (Figure 3). This angle needs to be determined

by the system.

· : Angular speed of the gyro sensing axis around the

Up axis as described in Figure 3.

· : Angle between the gyro sensing axis and the axis

in the horizontal plane (Figure 3). If the

measurement is made during the rotation: and

it is considered that the origin of time is taken when

the rotation begins.

· : The latitude where the measurement is made.

· :

Earth’s angular velocity.

x body

y body

Xgyro

y gyro

= sensing axis

Figure 3. Rotation between and and between and

.

The three frames considered in the report are described in

Figure 3 and defined as follows:

· : It is made of the three vectors: North

, East and Down as shown in Figure 4. is

pointing towards the North and towards the Earth

7

center. The vector is defined such that is a

direct frame and is collinear to the Up axis but in the

opposite direction.

· : It is the Northfinder’s

frame. The transformation between the frames

and is a rotation around with angle

.

· : It is the gyro’s frame. The

transformation between the frames and

is a rotation around with angle .

North

lat

Equator

Northfinder

lat

Figure 4. Diagram of the frame associated with the Northfinder.

The gyro’s sensing axis is collinear with axis. Hence

doing the projection of the Earth’s angular velocity on the

horizontal plane and then on , the angular velocity

measured by the gyro ( ) can be expressed with the

following formula:

( 1 )

Knowing the latitude , the Earth’s angular velocity amplitude and the angle between the sensing axis and the axis , the position of the North with respect to the NF

system (azimuth ) can be deduced. This seems simple but in fact a large number of errors need to be rectified in order to find the North with precision.

The mechanical errors considered are described in Figure 5 and defined as follows:

· : Northfinder angular defect around axis .

· : Northfinder angular defect around axis .

· : gyro angular defect around axis

· : gyro angular defect around axis

astE

ownD

Gyro NorthFinder

orthNr

ownD

astEorthNr

ownD n

orthNr

astE

x bodyx gyro

Figure 5. Diagram of mechanical errors taken into account in azimuth computation.

The errors related to the gyro are :

· b: gyro bias. This is a constant error which is added by the gyro to the measurement. This error depends on the temperature and can change after each on/off cycle.

· db: gyro bias drift. The bias can drift through time with a coefficient db.

· FE: scaling factor error. Scaling factor is the coefficient used to convert voltage into rad/s for a gyro. It can drift through time and temperature. To take into account the drift in temperature it is easier to consider a scaling factor error.

· dF: scaling factor error drift. It is the drift through time of the scaling factor error.

· Noise: generally gyros have specific kind of noises which are described by the Allan Variance Curve. Further explanations in section IV.A.3).

Assuming that the angles are small, the gyro measurement with all errors can be described with the following formula where “t” is the measurement duration:

( 2 )

Errors presented in ( 2 ) can be removed or reduced using several algorithms. The part III of this report presents two algorithms: Carouseling and Maytagging. These algorithms aim to reduce the impact of errors on the final result which is the azimuth.

D. Integration on the existing system

As it has been said, the north finder system will be used for

a camera to improve the targeting precision, provided that the

performance is good enough. Consequently, the model must

be adapted to be mounted on a tripod (camera support) as

shown in Figure 6.

8

Northfinder

Thermal imager

Spirit lev el

Tripod

Figure 6. Diagram of the NF integration.

The mechanical interface must be designed in order to

keep the performance of the NF system.

Moreover the usage process of the system needs to be defined.

To do so, two scenarios can be envisaged: 1. The user deploys the tripod and puts only the NF

system and the goniometer on it. The NF locates the north position and the user puts the goniometer to zero in the direction of the North. Then, without moving the tripod, the user replaces the NF system with the camera. The user can now find the location of any target relatively to the zero goniometer and as a consequence to the North. The location of any target is hence known.

2. The NF system is integrated in the goniometer. The user deploys the tripod with the camera and the gonio + NF system, waits several minutes and then any target can be located.

The second scenario seems to be more user-friendly but it

will be more difficult to compact the NF system with the

goniometer. Although the choice between these two scenarios

does not need to be made in order to find the best detection

method, it must be kept in mind in the design of the final

architecture and that can impact the performance of the NF

system.

E. Previous Work

Many papers have been published concerning the usage of

gyro-compassing in north finding systems. Several papers

describe the theoretical background of North finding using a

MEMS gyroscope and highlight the impact of the gyro used in

the system on the north finding performance [1] [2] [3]. They

analyze the compromises made on the gyro’s performance in

order to obtain a reasonable performance for reasonable cost

and size. They also describe and compare different

measurement methods like Carouseling and Maytagging.

Moreover some papers present a complete north finding

system with a certain final precision around more than 10

mrad after several minutes [3] [4] [5]. The present paper is

largely based on the papers mentioned above. In addition, our

aim is to reach better north finding performances for a

minimal cost.

Previous internships have been conducted at Thales

Optronique focusing on the theoretical feasibility of gyro-

compassing and the design of a model. The study presented in

this report is largely based on these previous works.

III. ALGORITHM PRINCIPLES

A. Carouseling

Carouseling is a complex algorithm to put into practice. It

can remove gyro bias, scaling factor errors and can also

strongly reduce the impact of other errors such as bias and

scaling factor drifts. Carouseling is based on the measurement

of the Earth’s angular velocity in the horizontal local plane, in

many directions. The gyro sensing axis is put into rotation on

the local horizontal plane around the Down axis (Figure 3). A

measurement is taken in 2000 directions per round with an

angle step , this angle step is monitored very closely with

an encoder. Measurements are made on one and a quarter

turns, in order to make a quadrature phase shift of the signal.

This artificially creates, over a turn, two angular velocity

measurements in two perpendicular directions: one around the

gyro’s sensing axis X and another around its perpendicular Y

(equation ( 3 )).

( 3 )

This method is equivalent to having two perpendicular

gyros, one gyro is therefore not in use, which saves cost (gyros

being the most expensive equipments of the system). The two

measurements will be used to find the final azimuth using the

arc-tangent function. Moreover, the errors related to the gyro

are the same in both directions therefore they will be easier to

remove.

The angle step is monitored very closely because it is

used to match the gyro measurements with precise

orientations. Knowing the orientation of every

measurement, permits to demodulate the signals X and Y. The

measurements X and Y are multiplied by the rotation matrix

of the rotation around the Down axis and of angle , equation

( 4 ).

=

( 4 )

is a constant, consequently measurements X and Y

over a turn are sinusoidal. Unlike the bias error which is

constant and only impacts the mean value of the sinusoid. The

demodulation of X and Y transforms the sinusoidal part into a

constant and the constant part into a sinusoid. Integrating this

over a turn, removes the sinusoidal part of the demodulated

signal, which is the bias error, equation ( 5 ). In equation ( 5 ),

j is the number of turn made. It must noticed that equations

( 4 ) and ( 5 ) give the same result because in these equations,

errors are not considered.

9

( 5 )

The demodulation can be made by using a matrix made of

cosines only. This will have a positive impact during the

integration because all of the cosines components will be

removed over one turn. A part of the bias and scaling factor

drift is therefore eliminated after integration. The average

value over two turns is taken in order to reduce the gyro

Angular Random Walk (see IV.A.3). Finally, the scaling

factor error is removed by simplification in the division

when using the arc-tangent function as shown in

equation ( 6 ). Carouseling can be upgraded by doing alternated rotation,

by rotating the gyro sensing axis in one direction over one and a quarter turns, and in the other direction with the same range angle. This method allows us to avoid the use of a slip ring and completely removes the bias drift which is independent of .

Equations ( 3 ), ( 4 ) and ( 5 ) are true in the ideal case, they

are without any errors. The theory is the same with or without

errors.

Finally, the azimuth can be deduced with the following

formulas:

· Without errors:

( 6 )

· With errors and after limited developments:

( 7 )

Equation ( 7 ) highlights the remaining total error which

can be seen as a function of the scaling factor drift, the angular

velocity of the gyro sensing axis and the azimuth angle. Errors

due to bias, bias drift, scaling factor and inclination are

removed by Carouseling.

B. 4 points Maytagging

Gyro

sensitive

axis initial position

90°

1

23

4

90°

Figure 7. Diagram of 4 points Maytagging method.

4 points Maytagging is another measurement method also

based on the Gyro compassing principle, hence equation ( 2 )

is still true. With this method, the Earth’s angular velocity is

measured in four directions. Each direction is perpendicular to

the previous one as described in Figure 7.

The gyro measurement made in each direction can be

described with the following formulas, without any error:

( 8 )

( 9 )

( 10 )

( 11 )

The azimuth is easy to deduce thanks to the previous

equations using equation ( 12 ):

· Without errors:

( 12 )

· With errors:

( 13 )

Here and is the duration of

the measurement made in each direction. It is chosen based on

the Allan Variance curve associated with the gyro used.

Further explanations are in section IV.A.3).

The subtractions and remove

the bias. Equation ( 13 ) shows that many errors have still an

impact on the result with Maytagging.

IV. EXPERIMENTS AND RESULTS

A. Hardware used

Now that the measurement methods have been defined,

performance comparison needs to be done through

experiments.

Experiments are made in two steps: principle checking on

a rate table and then verification on a model made for this

application. Numerical simulation is also computed in order to

draw parallels between reality and theory.

1) The rate table

The rate table is a mono axis ACTIDYN table with its

rotation axis placed at vertical (Figure 8). The main

characteristics of the table are:

10

· Verticality precision of the rotation axis : ~ 10µrad

· Angular velocity stability (at low speed) : ~ 0.001%

· Angular resolution : ~1µrad

· Real time data reading precision : < 50µrad

· Wobble : < 5µrad (Wobble HF > 20 oscillations / round)

· Angular positioning precision : < 20µrad

The purpose of this table is to rotate the gyro sensing axis in the local horizontal frame with a constant speed. With this table the rotation is considered perfect without any positioning error or velocity error.

2) The model

The model is made of a rotating part which contains the

gyro, the gyro electronics and the power supply for the gyro as

it can be seen in Figure 9.

The rotation angle of the rotating part is measured by a 21

bits encoder with a resolution of more than 30µrad. The gyro

measurements are synchronised with the encoder

measurements. A TMS320 microcontroller is used to control

the model. The control accuracy of the motor’s angular

velocity is of around 1% and the positioning accuracy is better

than 2 mrad. Model horizontality is checked by two spirit

levels with a resolution of 100µrad, and the rotation axis is

vertical with a precision better than 150µrad.

The gyro output data is transferred to a microcontroller thanks to a cable which is then relayed to a computer. This cable winds up and unrolls itself around the rotation axis during the alternated movement. With such a configuration, the initial position needs to be known in order to turn the rotating part in the right way without pulling on the cable. As the complete rotation is made on more than one round in the Carouseling case, the number of rotations must be detected. This problem is solved manually before every measurement for Carouseling. Hence this method is no fully autonomous. This problem does not exist with the Maytagging method.

3) The gyro

The gyro used measures an angular velocity by measuring

the effect of the Coriolis force on a mechanical resonator. The

Coriolis force is induced by the rotational movement and is

proportional to the angular velocity.

A useful tool to characterize the performances of a gyro is the

Allan Variance. It is a plot, as seen in Figure 11, which

represents the RMS value of the gaps between successive gyro

output samples averaged over a time versus the averaging

time . Considering the gyro output signal sampled

with a frequency of and multiple of . The y axis is

given by equation ( 14 ):

( 14 )

With and ( : integer part of

X).

The Allan Variance curve quantifies the variation level of

a signal and often has the same pattern. Three different parts

can be identified on the curve as presented in Figure 11: the

first linear part with a negative slope is called Angular

Random Walk (ARW), the constant part is the Bias Instability

and the final increasing part is the Angular Rate Random

Walk (ARRW). ARW is like a white noise with a null mean

value, hence it decreases when averaging time increases. Bias

instability is a flicker noise and represents the minimum of the

Allan Variance curve, it is the ultimate precision of the gyro.

Finally, ARRW is the sum of white noises with the same

Figure 8. ACTIDYN rate table.

Model

DC Motor

Rotation axis

Rotary part

Encoder Gyro + its electronics

Gyro’s sensitive axis

MicrocontrollerMicr

Gyro + its

o’s senGyro’s

Computer

Figure 9. Diagram of the model.

Figure 10. NorthFinder model.

11

standard deviation: where represents the

noise ARRW at time t and a white noise.

In order to optimize the gyro performance, the gyro output

needs to be averaged over a duration that corresponds to the

bias instability on the Allan Variance curve. In Figure 11, the

duration shall be 1000 s. Every measurement must therefore

last 1000 s in order to reduce the noise induced by the gyro. It

must be noted that the curve presented in Figure 11 does not

correspond to the gyro used in the model.

The gyro used is a gyro with an angular range and a

bandwidth adapted to the application needs. Its precision is of

around 10°/h and its bias stability is about 0.02°/h (Allan

Variance minimum). A tradeoff between performance and cost

has been done for the gyro selection.

For confidentiality reasons the gyro’s specifications are not

precisely defined.

4) Support plate and inertiel unit (IMU)

In order to check the true performances of the NF model,

the latter is fixed on a support plate as shown in Figure 12.

The fixation interface is harmonized with a positioning pin

line with which an inertial unit is positioned. This IMU gives

the true North. The inertial unit model used is AIRINS III

(iXblue) which can give precisely the North position. The

harmonized precision between the IMU and the model is

better than 400µrad.

B. Software used

1) Computer simulation

A computer simulation of the model has also been

developed on MATLAB in order to draw parallels between

reality and theory and to check if the mathematical model is

relevant. The simulation is made of three main parts:

1. The first MATLAB script computes the gyro output

over a rotation around the vertical axis. It takes into

account mechanical errors ( , , ),

encoder output noise and motor angular velocity

instability (w) but not errors related to the gyro (bias

etc…). For Carouseling, it is based on equation ( 2 ).

Noise added to encoder affects α, it can be a

sinusoidal error or a random error. The error on w is

taken from a real measurement on the model.

2. The second script adds errors related to gyro: bias,

scaling factor error, bias and scaling factor drift and

noise. All these errors are put to their maximum

measured on the model. The noise is added through

functions identified on the Allan Variance curve

associated to the gyro as seen previously (ARW, bias

instability and ARRW). Finally a high frequency

noise is added to the gyro output computed.

3. The last script computes the north position only using

gyro output, simulated or not. It is the same script

used for both the simulation and the model.

The accuracy of the simulation is shown in part C.3)

and IV.D.3).

2) Model control software

Software used to control the model are programmed on

SIMULINK and they are automatically coded into C language

by MATLAB. Then they are implemented in the model’s

microcontroller and control the encoder, the motor and all the

data flow. Considering the different measurement methods,

two different softwares have been made for Carouseling and

Maytagging. In the Carouseling case, numerical computing is

not made in the model, instead all the data is sent to a

computer for post computing.

a) Carouseling

Figure 13 shows a state representation of the Carouseling

program implemented in the model.

This state representation can be summarized as follows:

1. Initialization: Configures all of the components, starts

timers and sends the initial bit set which tells the

computer that the measurement is starting. The start

position of the gyro is set manually in order to avoid

any problems with the cable from the gyro to the

microcontroller as explained in part A.2).

2. Encoder output checking: The encoder output is

constantly read at a frequency of 20 kHz in order to

detect when the angle step ( III.A) is passed or

Figure 11. Example of simulated Allan Variance curve (from [8]).

Figure 12. NF model and inertial unit AIRINS III fixed on the support plate.

12

when one and a quarter turn is done. This operation is

critical for the final precision that is why the reading

frequency is very high. By missing one angle step the

distribution of measurement points over one turn will

become unsymmetrical, consequently error terms that

should be removed by integration will not be.

3. Gyro and encoder data synchronous reading: as soon

as we pass the angle step, the data from the gyro and

the encoder are read simultaneously.

4. Data sending for post-computing: The

microcontroller is currently only used to manage the

state of the model. All of the data is sent to a

computer for post computing thanks to a serial port.

Implementing the complete Carouseling algorithm in

the model can be challenging because of the lack of

memory space (2000 32bits for each turn) and also

the limited computing power of the microcontroller.

The CPU can go into overload whilst by reading

simultaneously the encoder at high frequency,

controlling the motor and reading the gyro.

5. Rotation direction change: The direction of the

rotation is changed in order to avoid any winding

problems with the cable and to improve the

Carouseling algorithm.

The main difficulty for Carouseling is that the angular position

of the gyro (α) and the gyro output need to be read exactly at

the same time in order to compute the demodulation. In

reality, simultaneous events are impossible. In order to

measure as simultaneous as possible the data from the gyro

and from the encoder as simultaneously as possible, the

microcontroller asks the gyro its output, as soon as an angle

step is passed. After reception of the data, the microcontroller

reads the encoder angle. The acquisition time is perfectly

know (2.7ms) and assuming that the angular velocity of the

motor is perfectly constant, a time phase shift can be made.

This method can become irrelevant if the motor control is not

very efficient or if the acquisition time increases. This can be

the case when the CPU is overloaded because of multi-

tasking.

b) Maytagging

As with Carouseling, the control program is made on

Simulink and then self-coded into the target. Nevertheless,

unlike the Carouseling software, here the microcontroller

controls the model and computes all the calculations. No post

treatment is needed. The diagram presented in Figure 14

describes the program implemented in the microcontroller to

control the model and to compute the azimuth. The aim of this

program is to provide a first reading of the North location after

the first Maytagging. This value is then updated after each

Maytagging. The updated value is an average of the previous

and the new measurements. Hence the North location is

converging towards a value every time closer to the real

position of the North.

The role of each state mentioned in Figure 14 can be

described as follows:

1. Initialization: This state is the same as for

Carouseling.

2. Measure: The encoder angle, timers and gyro output

are read nearly simultaneously at a frequency of 20

kHz. The system is static and verified by checking

the encoder angle. Timers are read to check and

monitor the program. They ensure that every

computation is done within the computation time but

they have no final utility and could be removed to

optimize CPU load. All computation and storage is

done by a single microcontroller embedded in the NF

model. As a consequence there are limits in memory

size and computation power. To reduce significantly

the use of memory, a running mean is made during

the measurement in order to save only one value

instead of several thousand.

3. Value conversion and storage: This state does the

conversion of the data measured (gyro and encoder)

and saves it after each measurement.

4. Motion: The gyro rotates to an angle of 90°. The

motor is positioned with a precision better than 2

mrad, thanks to a simple gain corrector in the closed

loop.

5. Azimuth calculation: After the first 4 measurements,

the azimuth is calculated thanks to equation ( 12 ). It

is sent by a serial port to a computer that can display

the result.

6. Azimuth calculation + averaging: After the first

Maytagging, an updated value of the azimuth is

calculated every three measurements. The average

value between the old azimuth and the new one is

taken and it is sent to the computer.

Initialization1.

Encoder

output

checking

2. Rotation

direction

change

5.

Gyro and encoder

data synchonous

reading

3.

Data sending for

post-computing

4.

checking

5

Other

One and a

quarter turns

has been made

Angle step

passed

Figure 13. State representation of the Carouseling software.

13

Concerning Figure 14, the azimuth is computed first after 4

measurements and then every 3 measurements. This is due to

the fact that the system does not measure two times in a row in

the same direction. This trick enables the system to provide a

new azimuth faster after the first Maytagging. It can also be

noted that the system turns clockwise and counter-clockwise

in order to optimize the total duration of the several

continuous Maytagging.

Another aspect of embedded software is that the

microcontroller does every computation with single precision,

unlike a normal computer which uses double precision. Figure

15 shows the impact on the azimuth measured with a single

and a double precision algorithm. The difference between

single and double precision is acceptable for our desired final

precision. As the single precision computation is faster than

with double precision, all the calculations will be done with

single precision.

Azimuth measured with single and double

computation precision

Time (secondes)

Azi

mu

thm

ea

sure

d(

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 100 200 300 400 500 600 700 800 900

Single precision

Double precision

Figure 15. Comparison between azimuth given by a single (blue) and a double

(red) precision computation.

C. Carouseling results

1) Results on the rate table

To check the performances reachable with the Carouseling

algorithm, a first experiment is conducted with the rate table

used to do Carouseling alternated rotation. 2000 measurement

points are taken over one turn and the table angular velocity is

of 5 rpm. The results are shown below:

-200 -150 -100 -50 0 50 100 150 200 250 300-200

-150

-100

-50

0

50

100

150

X: -76.64

Y: -152.4

Angles de mesures du gyromètre (°)

Vite

sse d

e r

ota

tio

n m

esu

rée

pa

r le

gyro

mè

tre

(°/

h)

Enregistrement en carouseling sur table tournateGyro output with Carouseling on rotary table

Gyro position (deg)

An

gu

lar

ve

loci

ty(°

/h)

Figure 16. Example of gyro measurements over one going and coming,

angular velocity measured (°/h) versus gyro position (°).

The sinusoidal shape that can be seen in Figure 16 correlates

equation ( 1 ) with the variable and all the other constant

parameters. Evolution of the azimuth measured

Measure number

Azi

mu

thm

ea

sure

d(

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 3501.334

1.335

1.336

1.337

1.338

1.339

Measure number

Evolution of the North Cape measured

Figure 17. Azimuth measurements obtained with more than 300 Carouseling

of 6min.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

x 10-3

0

5

10

15

20

25

30

35

Ecart entre la mesure et la moyenne (rad)

No

mb

re d

e m

esu

re

Dispersion mesure du cap au nordAzimuth measurements dispersion

Gap between measurements and mean value ( )

Nu

mb

er

of

me

asu

rem

en

t

Figure 18. Histogram of azimuth measurements dispersion obtained with more

than 300 Carouseling of 6min.

Initialization

Motion

(+90°)

Measure

(4000 pts)

Value

conversion

and storage

Azimuth

calculation

Azimuth

calculation +

averaging

Me

(+000 pts)and agstorageorage

Motion

(+90°)

Measure

(4000 pts)

Value

conversion

and storage(+pts)

and storagest

Counter

clockwise

Clockwise

x 4 then x 3

x 3

Azimut

and storstor

x 4 x 4 then

MotionValue

Azim

stst

x x

uth

ulation +

eragingeragingeraging

(+oragestoragestorage

imut

storstor

33

After 4 measurements and then every 3 measurements.

Every 3 measurements.

1.

2. 3. 4.

2. 3. 4.

5.

6.

Figure 14. State representation of the program implemented in the

microcontroller.

14

Evolution of RMS value versus measurement duration

Time (minutes)

0 2 4 6 8 10 120.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4R

MS

va

lue

re

ach

ed

()

Figure 19. Evolution of Azimuth measurement dispersions (RMS) as a

function of Carouseling duration.

Assuming that the encoder offset is correctly determined,

the measurement precision can be quantified thanks to its

dispersion (i.e. computing the RMS value of the azimuth of

the set of measurements). The RMS value, hence the

precision, of the set of measurements presented in Figure 17,

Figure 18 and Figure 19, is mrad after minutes,

and mrad after minutes (Figure 19). The

precision aimed for seems to be reachable provided that the

model’s electro-mechanic characteristics are close to those of

the rate table.

2) Results with the model

The measurements are now made with the model. The

angular velocity is the same as before, i.e. 5 rpm.

The results are presented below:

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-100

-80

-60

-40

-20

0

20

40

Indice des mesures

Vite

sse

me

su

rée

gyro

(°/

h)

Données gyro après supression des données éronnées dues au CANGyro output with carouseling on the model

Number of measurement point

An

gu

lar

ve

loci

ty(°

/h)

Figure 20. Example of gyro measurements over one going and coming on the

model.

Figure 20 describes the same sinusoidal shape as in Figure 16.

The gap reduction between going and coming is only due to a

change in as described by equation ( 2 ).

Evolution of RMS value versus measurement duration

Time (minutes)

RM

S v

alu

e r

ea

che

d(

)

0.5 1 1.5 2 2.5 30.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Figure 21. Evolution of Azimuth measurements dispersion (RMS) as a

function of Carouseling duration.

Figure 20 also shows that the gyro measurement on the

model is noisier than the measurement on the rate table.

Nevertheless, Figure 21 highlights the fact that the RMS

dispersion is surprisingly very low. It can therefore be

deduced that a default cannot be seen through the RMS value,

which shows only measurement dispersion and not the true

azimuth error. Thanks to a running mean on the azimuth

measured at every turn, the RMS precision is computed over a

great number of backs and forths. This is made with a growing

duration of the averaging parameter which simulates the

measurement duration augmentation. Hence this precision is

based on a measurement made in a single orientation with

respect to the north position. Consequently, a constant

disturbance on this measurement does not impact the RMS

relative precision, but has an impact on the true azimuth

measured (value around which the measurements converge).

This explains why even with a low RMS value and hence low

measurement dispersion, the system precision can be very bad.

Moreover, the impact of the disturbances will change

according to the models orientation. This is due to the

displacement of all the disturbances in the gyro’s

measurement sinusoid when the model rotates around the

down axis. In this case, the model orientation is the angle

between the model zero encoder and the true azimuth.

Rotating the model around the down axis is therefore

equivalent to “moving” the true azimuth. In order to establish

the true dispersion and the true precision reachable with the

model, measurements need to be done for different model

orientations with respect to the north.

To do such measurements, the model is placed on the

support plate along with the inertial unit. The plate is rotated

in several directions, the azimuth variations obtained are then

compared to the azimuth variations given by the inertial unit.

Again, assuming that the encoder offset is done properly,

the azimuths measured by the model can be plotted as a

function of the orientation of the latter with respect to the

north position (= given by the inertial unit). The results are

presented in Figure 22. The RMS value of this measurement

set is mrad after minutes, which is far from the

performances obtained on the rate table and those desired.

15

Azimuth error versus model orientation

Azi

mu

the

rro

r(

-100 0 100 200 300 400 500 600-5

-4

-3

-2

-1

0

1

2

3

4

5

Model orientation (deg)

Figure 22. Azimuth error as a function of the model orientation with respect to

the North (for 3 minutes Carouseling).

It can be seen in Figure 22 that the azimuth error seems to

have a sinusoidal form. This correlates with equation ( 7 )

which links the model orientation (impacting the real azimuth

) with the azimuth measured through a

sinusoidal function.

The relevance of using the RMS value to check the

precision of Carouseling on the rate table is also questioned. It

is affected by the same problem as in the model. As the

performance of the model will doubtless be worse than on the

rate table, a comparison with the MATLAB simulation is

preferred to additional tests on the rate table.

3) Comparison with MATLAB model

In order to explain and compare the results described

previously, the NF system is simulated in MATLAB with all

the characteristics and errors known and identified in the

model. To better stick to reality, the simulated gyro output

(Figure 24) is compared to the real gyro output (Figure 23). In Figure 23 several disturbance peaks can be seen on the

gyro output. In order to get closer to reality six peaks with similar amplitude have been added to the simulated gyro output as showed in Figure 24. Note that these disturbance peaks are fixed with respect to the model, their positions in the sinusoid measurement are therefore a function of the model orientation. This phenomenon is induced by the fact that the measurement sinusoid is translated proportionally to the model orientation changes. This translation is visibly noticeable with the equation ( 1 ) which is a function of through a cosine (here errors are not taken into account). Changing the model orientation will change the which needs to be found with the measurement. Rotating the gyro’s sensing axis represented by the angle will then give a sinusoid measurement with as the initial phase. As a consequence, a change in the model orientation will proportionally change the starting point of the measurement on the sinusoid. Finally, a disturbance peak fixed with respect to the model will not move relatively to the starting point when the model orientation moves. Hence this peak moves on the sinusoid measurement.

Gyro output for carouseling on the model

Measurement number ( )

An

gu

lar

ve

loci

ty(°

/h)

3.8 3.9 4 4.1 4.2 4.3 4.4

x 104

-60

-50

-40

-30

-20

-10

Indice des mesures

Vite

sse

me

su

rée

gyro

(°/

h)

Données brutes gyro

Figure 23. Real gyro output.

Gyro output for carouseling obtained in simulation

Measurement number

An

gu

lar

ve

loci

ty(°

/h)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-30

-20

-10

0

10

20

30

40

Indice de la mesure

Données b

rute

s d

u g

yro

(°/

h)

Données brutes du gyro (°/h)

Figure 24. Simulated gyro output.

Azimuth error versus model orientation

Model orientation (deg)

Azi

mu

the

rro

r(

)

0 100 200 300 400 500 600 700 800-1.5

-1

-0.5

0

0.5

1

1.5

Figure 25. Azimuth error ( ) versus model orientation (deg) obtained in

simulation using the gyro output presented in Figure 24.

Figure 25 shows the azimuth error as a function of the NF

model’s orientation, obtained in simulation. This azimuth error

has a perfect sinusoid form and this result is relevant, in

comparison to the result obtained on the model (Figure 22).

This sinusoid form, seen in Figure 25, can be explained

physically: as it has been said previously the disturbance peaks

are moving on the measurement sinusoid because they are

fixed with respect to the model. As these peaks move in the

sinusoid measurement they will not have the same impact on

the measured azimuth because of the demodulation. During the

demodulation, a peak located on the maximum of the sinusoid

measurement will be divided by a large number whereas the

same peak located around the average value of the sinusoid

will be divided by a lower number. Consequently, in some

model orientation disturbances, peaks will have a large impact

on the azimuth measured. They will have a smaller impact

when the model is rotated with an angle of 90°. This gives the

sinusoid form on the azimuth error as it can be seen in Figure

25.

A solution to reduce the impact of these disturbance peaks

is to filter the gyro output as it can be seen in Figure 26. With

this filtering, the azimuth error is strongly reduced in

simulation as shown in Figure 27.

16

Gyro output before and after filtering obtained in

simulation

Measurement points

An

gu

lar

ve

loci

ty(°

/h)

500 1000 1500 2000

-20

-10

0

10

20

30

40

Indice de la mesure

Données b

rute

s d

u g

yro

(°/

h)

Figure 26. Gyro output obtained in simulation, before (blue) and after (red)

filtering.

Azimuth error versus model orientation

Model orientation (deg)

Azi

mu

the

rro

r(

)

0 100 200 300 400 500 600 700 800-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Figure 27. Azimuth error obtained in simulation after filtering.

Nevertheless, the same filtering has been done on the

model measurements and the azimuth error has not been

reduced and stays similar to Figure 22. The error seems to

result from another kind of disturbance than the one simulated.

After having taken a closer look at the gyro’s real output

presented in Figure 20 and Figure 23, it can be seen that the

sinusoid is deformed on certain location (for example around

measurement number in Figure 23). This can be

caused by slow disturbances. For example, a wobble or a

slight traction due to the cable will induce a small tilt of the

rotary part. These slow disturbances produce, on small

intervals, a slight variation of the angular speed around the

gyro’s sensing axis. It has a magnitude of several deg/hour

which perturbs the Earth’s angular velocity measurement to

the same extent.

To check if this kind of disturbance is the source of the

azimuth error seen previously, the simulated gyro output is

locally disturbed with a disturbance with an amplitude of 1°/h

during 0.5 s (i.e. on an angular range of 15°). This slow

disturbance is shown in Figure 28 but with a larger amplitude.

Gyro output obtained in simulation with a slow

disturbance

Measurement points

An

gu

lar

ve

loci

ty(°

/h)

500 1000 1500 2000 2500

-20

-15

-10

-5

0

5

10

15

20

Indice de la mesure

Données b

rute

s d

u g

yro

(°/

h)

Slow disturbance

Figure 28. Gyro output simulated with a slow disturbance.

Azimuth error versus model orientation obtained in

simulation with a slow disturbance

Model orientation (deg)

Azi

mu

the

rro

r(

)

0 50 100 150 200 250 300 350 400-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Figure 29. Azimuth error obtained in simulation with the gyro output similar

to the one presented in Figure 28.

The azimuth error obtained in simulations with the slow

disturbance on the gyro output is shown in Figure 29. It can be

seen that the result has also a sinusoidal form with similar

amplitude as found in Figure 22. Note that the average value

of this sinusoid is not null because the slow disturbance has

been simulated only during the goings and not the comings.

All the previous disturbances have been modeled on both

backs and forths.

Azimuth errors are mainly caused by these local and slow

disturbances created by perturbing torques due to the model’s

cable and/or by a slight wobble which is slow over one round.

Thanks to the simulation, the maximal disturbance

amplitude, up to which the error on the azimuth measured is

still acceptable, is of around 1.5µrad on an angular range of

10°. This constraint puts strong specifications on the

mechanical design of the system (similar to the rate table).

As a first conclusion, although Carouseling seems to be

very efficient in theory and considering that the rate table is

removing several errors, it is shown here that it is limited,

mainly by the severe constraints it induces on the mechanical

design.

D. 4 points Maytagging results

Unlike before, as the model was directly available,

Maytagging measurements are first carried out on the model

17

and then on the rate table to determine the ultimate

performance.

1) Results with the model

Several performance measurements have been made in the

same way as before for the Carouseling method. First of all,

the measurement duration has been set to 22 s for the four

measurement directions. This corresponds to 10 000

measurement points for each time. The first azimuth is given

by the model after one cycle of 4 points Maytagging. This

represents a duration of approximately 2 min.

Azimuth error versus model orientation obtained on

the model with one Maytagging

Model orientation (deg)

Azi

mu

the

rro

r(

)

-200 -150 -100 -50 0 50 100-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Figure 30. Azimuth error as a function of the model orientation with respect to

the North (for one Maytagging in 2 min).

Figure 30 shows the azimuth error (the gap between the

real and the measured azimuth) as a function of the model

orientation. As seen in Figure 30, the azimuth error amplitude

is much smaller in this case than in the Carouseling case

(Figure 22). It can also be noticed that this azimuth error does

not depend on the model orientation, it appears to be a random

error. The RMS value of this measurement set is:

mrad. Every experiment lasts 4 min because the

azimuth measured is an average of two azimuths from two

Maytagging which take 2 min each. Consequently, the

performances obtained are close to the required performances.

The results dispersion, for a fixed model orientation and with

15 Maytagging of 4 minutes, is of mrad.

In order to reduce the Maytagging duration, the time

within which the gyro measures the Earth’s angular velocity in

each direction, is reduced to 8.8 s. Moreover the measurement

orientation positioning is optimized by removing any

measurement done in a row in the same direction, as described

in section IV.B.2)b). The total duration for three Maytaggings

is now of 2 min and 30 s. Theoretically, the reduced duration

of the measurements has a very small impact, as it can be seen

on the Allan Variance of the gyro. At 8.8 s of measurement,

the Allan Variance curve shows that the bias stability is still

very low. On the contrary, increasing the number of

Maytagging will significantly reduce the dispersion of the

measurements.

Azimuth error versus model orientation obtained on

the model with 3 Maytagging

Model orientation (deg)

Azi

mu

the

rro

r(

)

0 50 100 150 200 250 300 350-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Figure 31. Azimuth error as a function of the model orientation with respect to

the North (for 3 Maytagging in 2 min and 30 s).

Figure 31 shows performance improvement obtained with

the new optimization: The RMS value of the azimuth error is

now of mrad after 2min30sec (result obtained over

23 measurements of 3 Maytaggings). This result seems to

fulfill the desired performances.

Another improvement could be to increase the number of

measurement points (4000 to 5000) and hence do 3

Maytaggings in 3 min.

In order to obtain the final performance of the model with

the 4 point Maytagging algorithm, the offset imprecision due

to the zero of the encoder must be taken into account. This

imprecision has approximately the same order of magnitude as

the performance on the azimuth. As a result, the absolute

performance reachable with the model is around mrad

RMS in 3 min, at a latitude of 48°. In addition, unlike the Carouseling method, constraints on

the mechanical design are reduced, the gyro positioning precision is the only critical point.

2) Results on the rate table

As previously with the Carouseling method, the ultimate

performances of the Maytagging method should be found by

using the rate table. With such a table, the positioning error of

the four measurements, which have a large impact on the final

precision, will be strongly reduced. In addition, the rotation

axis is very close to vertical and the gyro can be considered in

the horizontal plane. Nonetheless, it must be noticed that the

table is more advantageous for Carouseling than for

Maytagging (e.g. the fact that the angular velocity is extremely

constant is crucial for Carouseling but is not used for

Maytagging.).

All experiments are made only around one azimuth

because, as it has been seen previously, the azimuth error does

not depend on the orientation of the system for Maytagging. A

sample of the results is shown below:

18

Azimuth measured versus number of maytagging

Number of maytagging

Azi

mu

thm

ea

sure

d(

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

Reference Azimuth

Figure 32. Azimuth measured versus the number of Maytagging.

As it can be seen in Figure 32, the performance on the

table is of around mrad after 10 Maytagging (~10 min

on the table). This performance only considers the

measurement dispersion and not the difference between the

reference and the measurements. The gap between the

measurements and the reference is only caused by a poor

knowledge of the zero of the encoder. It is similar to an offset

which needs to be determined each time the model is

dismounted because of the change in the mechanical interface.

Performances on the table are not as good as on the model,

which can lead to confusion. Nevertheless, several things can

explain this phenomenon. Firstly, the table is always operating

to follow the position input, hence even when the system

should be static, the table is trying to reject any slight

disturbance. As a result, the gyro measures an additional

noise, as it can be seen in Figure 33 and Figure 34. Moreover,

the table accelerates much more than the model, this can

change the position of the gyro very slightly, in relation to the

table. These causes are extremely hard to measure but what it

is important is that, with these measurements, the ultimate

performance of the Maytagging method and with this gyro,

seems to have been reached. It will be very difficult and even

impossible with the given architecture to significantly improve

the performances already obtained.

3) Comparison with MATLAB model

Now that the real performance has been established on the

model, a comparison can be made with the simulation. Thanks

to this comparison, the relevance of the theoretical model can

be checked and parameters limiting the performance can be

identified. The gyro output obtained with the simulation is

presented in Figure 35 and is very similar to the real gyro

output from the model as seen in Figure 36.

Gyro output obtained in simulation

Measurement points

An

gu

lar

ve

loci

ty(°

/h)

0 2000 4000 6000 8000 10000 12000 14000 16000-50

-45

-40

-35

-30

-25

-20

-15

Measurement point

Angula

r velo

city (

°/h)

Gyro output obtained in simulation

Figure 35. Gyro output obtained in

Maytagging simulation.

Gyro output obtained in laboratory

Measurement points (x )

An

gu

lar

ve

loci

ty(°

/h)

0 1 2 3 4 5 6

x 104

-50

-45

-40

-35

-30

-25

-20

-15

Measure number

An

gu

lar

ve

locity (

°/h

)

Gyro output

Figure 36. Gyro output on the model in

laboratory.

Azimuth error versus model orientation obtained

with Maytagging simlation

Model orientation simulated (deg)

Azi

mu

the

rro

r(1

)

0 20 40 60 80 100 120 140 160 180-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Figure 37. Azimuth error versus model orientation obtained with Maytagging

simulation.

This simulated gyro output was obtained using all the

defaults identified on the model. The results of the simulation

based on the gyro output shown in Figure 35 are presented in

Figure 37. The simulated results are obtained after three

Maytagging in each model orientation. It must be noted that

the simulated results (Figure 37) are very similar to the results

obtained on the model (Figure 31) but with a lower RMS

value: mrad. This is due to the fact that there are more

azimuths measured in simulation than on the model. Hence it

can be concluded that the theoretical model used for the

simulation is relevant. In addition, parameters limiting the

Maytagging performance on the model can be identified

thanks to the simulation.

It has been identified that the bias drift induces a sinusoidal

form on the azimuth error as seen in Figure 38. This bias drift

is not perfectly known on the gyro and is hard to quantify.

Even though it could be very small, this default can

significantly impact the systems precision by increasing the

measurement dispersion while considering the whole

measurement range (0° to 360°). It must therefore be noted

Figure 33. Gyro output on the model.

Figure 34. Gyro output on the table.

1.28 1.285 1.29 1.295 1.3 1.305 1.31 1.315 1.32

x 105

15

15.5

16

16.5

17

17.5

18

18.5

19

19.5

20

Measurement point number

An

gu

lar

ve

locity m

ea

su

red

(°/h

)

Gyro output

2.16 2.18 2.2 2.22 2.24 2.26 2.28

x 105

-23

-22.5

-22

-21.5

-21

-20.5

-20

-19.5

-19

-18.5

-18

Measurement point number

An

gu

lar

ve

locity m

ea

su

red

(°/h

)

Gyro output

19

that bias drift has an impact on the results presented in Figure

31 although it is not clearly visible.

Azimuth error versus model orientation obtained with

Maytagging simlation with only bias drift error

Model orientation simulated (deg)

Azi

mu

the

rro

r(

)

0 20 40 60 80 100 120 140 160 180-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Figure 38. Azimuth error versus model orientation obtained with Maytagging

simulation with only bias drift error.

The simulation has also quantified the impact of other errors.

The following figures show the impact on the azimuth

measured by the ARW, the bias stability, the bias drift and the

angular positioning error of the gyro’s sensing axis.

Azimuth error measured versus ARW

ARW ( )

Azi

mu

the

rro

rm

ea

sure

d(1

)

Figure 39. Azimuth error measured

versus ARW.

Azimuth error measured versus bias stability

Bias stability ( )

Azi

mu

the

rro

rm

ea

sure

d(

)

Figure 40. Azimuth error measured

versus bias stability.

Azimuth error measured versus bias drift

Bias drift ( )

Azi

mu

the

rro

rm

ea

sure

d(

)

Figure 41. Azimuth error measured

versus bias drift.

Azimuth error measured versus positioning error

Positioning error ( )

Azi

mu

the

rro

rm

ea

sure

d(

)

Figure 42. Azimuth error measured

versus angular positioning error.

As it can be seen, ARW, bias stability and angular

positioning error all increase the measurement dispersion in

the same order of magnitude. The bias drift does not influence

dispersion but has a significant impact on the azimuth

convergence value. With the gyro used, ARW has a

negligible influence in comparison to bias stability and

angular positioning error. As said previously bias drift has not

been determined precisely but can be considered small. In

addition, on the model, the positioning error is of less than 2

mrad, its impact is therefore rather small in comparison to the

combination of the bias stability and the bias drift. That

explains why the results obtained on the rate table are similar

to those obtained on the model.

All these errors need to be reduced in order to improve the

systems performance. They establish the systems limits in

terms of precision whilst considering that the gyro used has

fixed bias stability and bias drift.

V. CAROUSELING AND MAYTAGGING COMPARISON

The following table compares the two methods as studied

and exposed in this report, Alternated Carouseling and 4

points Maytagging. This comparison is made with criteria that

impact performances or the solution implementation.

TABLE 1. COMPARISON BETWEEN CAROUSELING AND MAYTAGGING.

Criteria Alternated

Carouseling 4 points Maytagging

Gyro bias Removed Removed

Gyro bias drift

(linear) Almost removed Not removed

gyro ARW Reduced (mean) Reduced (mean)

Gyro scale factor

error Removed Removed

Gyro scale factor

error drift (linear) Almost removed Not removed

Inverse function

used for Azimuth

calculation

Arc-tangent

(max slope 1 and calculated value are in

the range : )

Arc-tangent

(max slope 1 and calculated value are in

the range : )

Control error of the

rotary part

Default averaged if

comparable to a noise

(Speed control)

Direct error on the

result

(Positioning control)

Angular and gyro

measurements

synchronization

Needed Not needed

Initialization

positioning

Need to know the initial position in order

to avoid pulling on the cable. A sensor needs

to be added.

Not needed (rotation

made over less than a round)

Wobble

Direct impact (could be

problematic, function of amplitude and

period)

Small impact (2nd order)

Various disturbing

torques: cable,

transmission…

Impact on the gyro measurement during

the rotation

No impact

TABLE 1 shows that Carouseling is more efficient in

removing geometric errors. Nevertheless, with a gyro with

sufficient quality, the Maytagging algorithm shows advantages

in terms of design and implementation constraints, which are

reduced in comparison to Carouseling. This is the main reason

why the results are much better for the model with the

Maytagging than with the Carouseling. As a reminder, the

results obtained, at room temperature and at latitude of ~48.8°

(Elancourt), are:

· Carouseling: mrad RMS in 3 minutes (Rq:

< mrad on rate table).

20

· Maytagging: mrad RMS in 3 minutes.

All things considered, in our model, the Carouseling

method is not as efficient as the Maytagging method because

of the mechanical constraints not respected by the model.

Nevertheless, Carouseling has a larger potential in terms of

precision than Maytagging through which the ultimate

performances have been reached. Consequently, for a system

with a precise mechanical design and which aims to deliver a

very accurate azimuth, the Carouseling method should be

used. On the other hand, for systems with strong cost

constraints, the Maytagging method is more relevant but will

give azimuths with a limited precision.

VI. MODEL IMPROVEMENT

The measurement methods have been compared over

performances made in an ideal environment and without any

volume and weight constraints. In order to make the system

competitive, it needs to be operative in any environment, at

any temperature, needs to be “user friendly” and integrated in

a portative system. This part focuses on the improvement of

the 4 points Maytagging method to keep performances in any

circumstances and at the same time, optimizing the system by

reducing costs, weight and size.

A. Real situation measurement

Firstly, the impact of a real measurement (i.e. a

measurement outside on a tripod) of the system precision

needs to be quantified. Performance will be checked by

targeting targets with perfectly known location (distance,

azimuth and latitude) thanks to a scope, placed under the NF

system (Figure 43). The line of sight of the scope is perfectly

(<400µrad) aligned to the positioning pin which positions the

NF system on the tripod. The NF model is designed to give the

azimuth with respect to this positioning pin. The tripod is

placed on the very same position that was used to locate the

targets. The localization was made with a very accurate

system (IMU). Targeting the targets with the scope, induces

that the NF system gives the azimuth of the target.

Experiments have been made on three targets. For

confidentiality reasons the results will not be exposed in this

report, nevertheless an analyse of the disturbances will be

made.

Gyro output obtained in real situation

Measurement points (x )

An

gu

lar

ve

loci

ty(°

/h)

0 1 2 3 4 5 6

x 104

-70

-60

-50

-40

-30

-20

-10

0

10

Indice des mesures

Vite

sse

me

su

rée

gyro

(°/

h)

Données brutes gyro

Figure 44. Gyro output in real situation.

As it can be seen in Figure 44, the gyro output is very

noisy in comparison to laboratory measurements Figure 36.

This is mainly due to two phenomena. Firstly, the tripod is not

a perfect rigid structure. The rotation of the gyro around the

vertical axis in the NF model makes the tripod vibrate at the

beginning of the measurement in each direction as it can be

seen in Figure 45 (with tripod) in comparison to Figure 46

(without tripod) both made in laboratory.

0 1 2 3 4 5 6

x 104

-80

-70

-60

-50

-40

-30

-20

-10

Indice des mesures

Vite

sse

me

su

rée

gyro

(°/

h)

Données brutes gyroGyro output obtained with a tripod

Measurement points (x )

An

gu

lar

ve

loci

ty(°

/h)

Figure 45. Gyro output in laboratory

when the NorthFinder model is on the

tripod.

Gyro output obtained without a tripod

Measurement points (x )

An

gu

lar

ve

loci

ty(°

/h)

0 1 2 3 4 5 6

x 104

-80

-70

-60

-50

-40

-30

-20

-10

Indice des mesures

Vite

sse

me

su

rée

gyro

(°/

h)

Données brutes gyro

Figure 46. Gyro output in laboratory

when the NorthFinder model is not on

the tripod.

This phenomenon can be reduced by waiting for the

vibration to dissipate before taking any measurements.

Nevertheless, it will take longer to measure an azimuth, the

performance of mrad at 3 minutes will be harder to reach.

The solution chosen to reduce this kind of disturbance is to

take a more rigid tripod in carbon fibre and also to keep the

system as close as possible to the ground as the height of the

tripod is adjustable. It can be noted that in real situation the

tripod is never fully deployed like in Figure 43.

The second disturbance is the wind, as the model is fully

open. The gear has an angular backlash of 1.5° as a

consequence during measurement the gyro is not fully blocked

and can slightly move if there is any disturbance (here the

wind). Gears without angular backlash have not been chosen

for the model because of a too short lifetime and a torque not

sufficient. To reduce the impact of the wind, the model will be

obviously closed. Moreover another design with a locking

system for the angular positioning system has been chosen in

order to prevent the gyro from moving during the

measurement. This new architecture is presented in section D.

Goniometer (2

axes)

Tripod

Northfinder

Scope

Figure 43. Real situation measurement system.

21

B. Algorithm improvements

1) Maytagging 6 points

An upgrade of the 4 points Maytagging method is to take 2

additional measurements. Based on Figure 7, the two

measurements are taken in directions 1 and 2 with the

following positioning order: 1-3-1-2-4-2. Measurements done

in these directions give respectively gyro outputs described by

equations (8) and (11). The azimuth is then calculated with

the following equation:

( 15 )

With and the gyro outputs when the gyro

is the second time in position 1 and 2. This method has one

significant advantage is that the theoretical azimuth

computation with errors is strongly simplified as it can be seen

in the following equation:

( 16 )

Nevertheless, taking measures in 6 directions will be

longer consequently a compromise needs to be made between

north finding speed and precision. Azimuth error versus model orientation

model orientation (deg)

No

rth

Ca

pe

err

or

()

0 50 100 150 200 250 300 350-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Maytagging 4 points

Maytagging 6 points

Figure 47. Azimuth error ( ) versus model orientation (deg) for

Maytagging 4 and 6 points.

Figure 47 shows the azimuth error versus the model

orientation. The RMS value of all these measurements is

around mrad for Maytagging 6 points and mrad

for 4 points Maytagging (from Figure 22). Maytagging 6

points and 4 points give similar results even if theoretically the

former is better. This can be explained by the fact that, as it

has been said before, the ultimate precision of the method with

the given gyro seems to have been reached, hence even with 6

points, the performances stay similar. Nevertheless, measuring

in 6 directions takes more time than in 4 directions, 4 points

Maytagging remains therefore the most efficient method. 6

points Maytagging can still be used to add more measurement

points for every 6 directions without impacting the

architecture. Based on the measurements made for

Maytagging 4 points, it just adds additional computation.

2) Positionning error correction

Angular positioning error of the gyro’s sensing axis around

the vertical axis has, in theory, a direct impact on the azimuth

measured. Hence it could be relevant to take into account

these errors in the azimuth calculation. In fact, the encoder

measures the real angular position of the gyro, it is then easy

to measure any angular error. If is the position error in the

rotation number i of angle + rad then taking equations ( 8

) to ( 11 ) in equation ( 12 ), the azimuth is given by the

following formula:

( 17 )

Then if is far from , an expansion around 0 gives:

( 18 )

Consequently, can be calculated by removing the second

part of the right hand side of equation ( 18 ) to .

Around , tends to have the same magnitude as hence

limited developments do not lead to simple formulas. With

this improvement, the RMS value of the measurements

presented in Figure 31 is improved by 0.1 mrad. This

improvement is small because the control of the motor is

already efficient (<2 mrad), and the are very small.

Considering that adding calculations will increase the

computation load, this improvement is not made for the

moment. A change in architecture to reduce the position error

seems to be a more relevant solution.

3) Computation optimization

As the final azimuth is given by an arithmetic mean based

on all the measurements from the start of the system, one

perturbed measurement (vibrations) can distorted the whole

measurement set. Consequently, there are relevant statistic

methods that can remove the inaccurate measurements. The

method choice is based on the number of incorrect

measurements among a measurement set. It has been

identified for the NF model that there are around 10% of

incorrect azimuth measurements. Hence a typical relevant

method to apply is the Ransac method. The principle of this

method can be described as follows:

1. It randomly takes a little number of measurements

and finds the best model (here linear) based on

the sample.

2. Every measurement is compared to this model

and if the difference is less than a value defined

by the user, the measurement is kept.

3. Then, if the number of measurement kept is more

than the proportion given by the user (here 90%),

the initial model is kept.

22

4. The steps 1 to 3 are done a large number of times

and the model with the less average error

computed in step 2 is chosen.

Despite the fact that this method is theoretically adapted

for rates of 10% of incorrect measurements, in the NF case the

random aspect of this method is too strong. Figure 48 shows

the final azimuth measured after 3000 seconds for a unique

measurement and computed several times with the Ransac

algorithm. It is easy to see that the method oscillates randomly

between two azimuths (0.1 and ). This method is hence

not relevant for this case.

Azimuth measured after 3000 secs with Ransac

Ransac number

Azi

mu

thm

ea

sure

d(

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 5 10 15 20 25 30

Figure 48. Azimuth measured after 3000 seconds (deg) versus Ransac

number.

A more simple method is chosen based on the standard

deviation value. Measures which have a difference of more

than 2 times the standard deviation of the whole measurement

set are removed.

Azimuth measured

Number of Maytagging

Azi

mu

th m

ea

sure

d(

0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60 70

Recursive Mean

Ransac 1D

Least square

Reference

Figure 49. Azimuth measured ( ) versus number of Maytagging computed

with several method.

Figure 49 shows the azimuth measured versus the number

of Maytagging done with the different methods. It can be seen

that the Ransac method gives the azimuths oscillating between

two values. It must be noted that the Ransac method is

implemented only after 10 Maytagging. The standard

deviation method (least squares method) is at first a bit

perturbed because of a lack of points but then it gives a slowly

convergent azimuth which is not exactly the same as for the

recursive mean. The gap between the reference and the other

curves is not meaningful because it mainly depends on the

offset set by the zero encoder. It can be defined in post

computation. In conclusion, even though the least squares

method does not show a significant advantage in comparison

to the recursive mean, it will increase the robustness of the

system by removing incorrect measurements.

C. Temperature Drift compensation

An important parameter when using a gyro is the

temperature. The gyro’s sensing axis, the bias and the scaling

factor drift with temperature. Moreover, the whole model can

be deformed because of thermal expansion. Hence it is

important to take into account this variation, especially for the

precision considered and the military use. System

performances need to hold typically from 20°C to + 70°C.

According to the gyro manufacturer, no temperature

compensation is made in the gyro concerning the sensing axis

because the drift is small. Nevertheless, it must be checked

and if needed, a slight correction must be made. First, the gyro

is tested alone because it is the most critical component

concerning the temperature drift. The gyro’s sensing axis drift

can be checked thanks to the rate table using the experiment

setting presented in Figure 50. More precisely, it is the angle

that can be measured. It is assumed that angle

undergoes the same drift as because the gyro has a

symmetrical design.

Gyro support

Sensing axis

Rate table

Gyro

Drift measured

Infrared lamp

Figure 50. Diagram of drift measurement on the rate table.

On the rate table, the gyro measurement can be described

by equation ( 2 ) with the rate table’s angular

velocity. This angular velocity is put to 120°/s which is very

high in comparison to the Earth’s angular velocity (15°/h),

hence is negligible. Moreover, taking the

average value over a turn, can also

be removed. Thus equation ( 2 ) can be written as follows:

( 19 )

The scaling factor error and drift are negligible in comparison

to 1 and the bias drift is also negligible based on the Allan

Variance curve of the gyro. Finally, equation ( 22 ) becomes

( 20 )

In comparison to , the bias b is also negligible.

Thanks to the table, is perfectly known and constant

and can be computed. An infrared lamp of 250W is used to

increase the gyro’s temperature (Figure 50).

23

measured versus temperature

Temperature (°C)

me

asu

red

()

20 25 30 35 40 45 50 55 60 65 70-9

-8

-7

-6

-5

-4

-3

-2

-1

0Measure 2 - 03/11/2016

Measure 1 - 02/11/2016

Measure 3 - 02/11/2016

Figure 51. ( ) versus temperature (°C).

The results of this experiment are shown in Figure 51.

is increasing when temperature is increasing of about

over 45°C. This variation confirms that

temperature can have a non-negligible impact on the azimuth

measured. Nevertheless, this result is not enough precise to

correct the azimuth measured by the model. The impact of the

temperature needs to be quantified also on the complete model

in order to make the best correction.

The difficulty in quantifying the impact of temperature on

the whole model is that the model is very sensitive to

vibrations and the thermal chambers, which are usually used

for temperature experiments, vibrate a lot. Hence the thermal

chambers must be stopped during each measurement which

cannot last long because of the temperature increase. Figure

52 shows the final azimuth measured with the model after

1000 seconds versus the temperature. The temperature range is

only from 5 to 30 °C because it is not relevant to do all the

temperature measurement for the model which will be used

only at these temperatures. Here only the identification of a

trend is important. The complete characterization would be

made for a final system. Azimuth measured after 1000 secs versus

temperature

Temperature (°C)

Azi

mu

thm

ea

sure

d(

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

Recursive mean results

Recursive mean quadratic approximation

Least square mean results

Least square mean quadratic approximation

Figure 52. Azimuth measured after 1000 seconds versus temperature.

As it can be seen in Figure 52 the azimuth tends to

decrease when the temperature increases. Over 25°C, the

azimuth measured decreases by approximately mrad.

Hence the temperature drift has the same magnitude as the

precision desired, it is crucial to take it into account in order to

reach the performance needed. As a consequence, a

temperature probe will be implemented on the model and

compensation will be made based firstly on the model

presented in Figure 52 and eventually on more precise

measurements made with the final architecture.

D. New architecture

The objective is now to reduce the costs, size and weight

of the system. The model architecture was suitable to obtain

the first results in laboratory but is not optimized for real

situation measurements. Hence, compromises must be made

and a new architecture needs to be designed in order to make

the system smaller, lighter and cheaper and at the same time

keeping the performance obtained.

1) Horizontality correction

On the model, the horizontality is checked with two

perpendicular spirit levels with a precision of 100µrad each.

For now, the model is manually placed as horizontally as

possible but this is laborious and will take too much time for

the user. Hence the model needs to take into account the

horizontality error. This error can be described with two

angles and around respectively and as described

in II.C. Nevertheless, it can be noted that has the same

impact as a change in latitude. As shown in Figure 53, if

positions 1 and 2 will give the same

azimuth. Moreover, as the latitude does not impact the

azimuth computation as seen in equations ( 6 ) and ( 7 ),

will not impact the system performances.

North

Equator

Position 2

Position 1

Figure 53. Diagram of the impact of on the Azimuth.

Consequently, the only defect angle needed is around

. The difficulty is that the exact position of the North is not

known at the beginning. Hence the model must do a first

Maytagging before correcting the error caused by . Two

perpendicular numerical inclinometers fixed in the plane

perpendicular to can give the inclination of this plane.

Hence knowing the azimuth, the tilt angle around the North

axis, i.e. , can be deduced. Then according to, equation ( 2 ),

the measured Azimuth can be directly corrected:

.

2) Internal Geneva wheel

For now, the four positions of the gyro are made with a

motor. As it has been seen there is no locking system in each

24

direction, which enables disturbances to make the gyro rotate

in the gears’ angular backlash. Moreover, the positioning error

is of around 2 mrad and, according to equation ( 18 ), has a

direct impact on the azimuth measured. Consequently, the

positioning system needs to be improved considering that only

four positions are interesting. This angular positioning need is

common for industrial systems and it can be done with an

indexer. Indexers are mechanical systems which can angularly

position a payload from 2 to several thousand positions per

turn at any speed and very precisely. There are different kinds

of indexer: gears systems, cam systems, a Geneva wheel and

ratchet systems. Each system has its pros and cons. For the NF

system, the indexer needs to position the payload in four

directions with a locking system for minimal costs and size

and as fast as possible. Considering all these criteria and based

on [6], the most relevant system seems to be: the internal

Geneva wheel. Figure 54 shows a diagram of an internal

Geneva wheel. The motor drives the input shaft and the cam.

The yellow pin goes into the grooves of the driven member

once per turn of the cam and drives the driven member which

rotates around the output shaft. The payload is fixed on the

driven member. When the pin is not in a groove the round part

of the cam presses on the driven member to block the position.

In Figure 54, the system is in the “blocking position”.

This new solution reduces the requirements of the motor in

terms of control (here no control is needed) and torque (the

lever arm is longer due to the fact that the input and output

shafts are parallel but not collinear).

As it can be seen in Figure 55, there are normal and

tangential forces of the driven member on the pin at the

contact point.

The tangential force is given by the following formula:

( 21 )

Where is the motor angular velocity, the payload’s

moment of inertia: , a coefficient

which depends on the number of angular positions needed :

for four positions, is the friction coefficient

, the driven member radius and

. Considering motion duration of 2 seconds

between two positions (+ ) which gives a motor angular

velocity of the maximal torque on the motor

is .

The system needs to stay in each direction several seconds

which is too long if the motor rotates continuously. As a

consequence, the motor will stop during a few seconds when

the pin is close to the center of the driven member as

represented in Figure 54.

According to [6], the angular error can be expressed as below:

( 22 )

Equation ( 22 ) shows that the angular error depends on ,

the backlash between the groove side and the pin,

regrouping the error on and the backlash in the ball

bearings and the center distance error between the input

and the output shafts. As a consequence, all of these errors

need to be reduced to a minimum and a compromise should be

found for : reducing the angular position error and in the

same time keeping the system small.

3) Possible architecture

While finding a mechanical solution, it must be kept in

mind that the system needs to be implemented on an existing

system: a camera on a tripod. Moreover, the NF system must

operate with the goniometer, hence the NF integration needs

to be adapted to goniometer’s rotations.

Figure 56 shows a possible architecture of the system NF +

Goniometer. As it can be seen in this figure, the NF system is

fixed on the goniometer. Consequently, the rotation around the

Up axis is made between the goniometer and the tripod. The

elevation rotation is made between the NF and the camera.

Moreover, the inner architecture of the NF is also described. A

single motor makes the Geneva wheel rotate around a fixed

axis thanks to a cam and a pin. A circular potentiometer

measures the orientation of the Geneva wheel in order to solve

any problems related to sudden shut down while the system is

running. This potentiometer is not as accurate as the encoder

used in the model because only a rough angular estimation is

now needed. This solution also reduces the total cost of the

system. The payload (the gyro and its electronics) is fixed on

the Geneva wheel. For cost reasons, the connection between

the payload and the microcontroller is not made by a slip ring

but by a classic cable.

Figure 54. 3D model of an internal Geneva wheel from [7].

Figure 55. Diagram of the internal Geneva Wheel.

25

Motor

++

++

Gyro

Gyro electronics

Inclinometer

Microcontroller

LCD

scr

ee

n

Power

Supply

Internal Geneva

wheel

++

+ +

Goniometer Goniometer

Potentiometer

Tripod

Camera

NorthFinder

Up Axis

Elevation Axis

CamPin

Figure 56. Diagram of a possible architecture of a system NorthFinder + Goniometer.

The main mechanical constraint in this architecture is that axes

and need to be perfectly collinear. Moreover, the gyro

sensing axis need to be as perpendicular as possible to axis .

VII. CONCLUSION AND DISCUSSION

This report has presented, tested and improved a complete

north finding system based on gyro compassing theory.

Firstly, two algorithms have been studied and compared:

Alternated Carouseling and 4 points Maytagging. The

comparison was made through a theoretical study, computer

simulations and real experiments made both on a model

designed for this application and on a rate table. It has been

shown that Carouseling is the most accurate algorithm because

it removes more geometric errors than Maytagging. Moreover,

in ideal conditions, i.e. using an efficient rate table,

Carouseling reaches better ultimate performance than

Maytagging. Nonetheless, on systems with less demanding

mechanical constraints, such as the model used, Carouseling

shows a loss of performance whereas Maytagging

performance remain the same as in the ideal case which

satisfied the initial requirements. Consequently, the

Carouseling solution must be kept for system which aims for a

very accurate azimuth without high cost limitations. On the

contrary, Maytagging is more relevant for projects that need to

limit their cost. Considering all the parameters of this study,

the Maytagging method has been chosen and improvements

have been proposed for the model. These improvements are

both hardware and software. A new mechanical architecture

has been designed with a Geneva wheel, reducing the number

of components and size of the model. Some software

improvements have also been explored but without presenting

a real improvement in the model performance. The difficulty

was that any small improvement is hard to quantify because it

is of the same order of magnitude as the Maytagging

precision. It is also a multi-variable problem with a lot of

unknown parameters which are nearly impossible to determine

alone. The solution adopted for this study seems to have

reached its limitation and only a change in the gyro used can

have a significant impact on the overall system’s

performances.

Surprisingly enough, accurate north finding is still difficult

to achieve for a reasonable price and no real solutions to

reduce the impact of vibration on performance for North

finding system based on gyro compassing, have been found

yet. Nevertheless, with the progress on gyros in terms of noise,

size and cost reduction, the gyro compassing system will soon

be able to provide very accurate azimuth for a minimal price.

REFERENCES

[1] Guofu Sun, Qitai Gu, "Accelerometer Based North

Finding System," IEEE, Beijing, P. R. of China, 2000.

[2] Burgess R. Johnson, Eugen Cabuz, Howard B. French,

Ryan Supino, "Development of a MEMS Gyroscope for

NorthFinding Applications," IEEE, Plymouth, 2010.

[3] Igor P. Prikhodko, Sergei A. Zotov, Alexander A. Trusov,

Andrei M. Shkel, “What is MEMS Gyrocompassing?

Comparative Analysis of Maytagging and Carouseling,”

JOURNAL OF MICROELECTROMECHANICAL

SYSTEMS, vol. 22, no. 6, p. 1257, DECEMBER 2013.

[4] Lucian Ioan Iozan, Martti Kirkko-Jaakkola, Jussi Collin,

Jarmo Takala, and Corneliu Rusu, “North Finding System

Using a MEMS Gyroscope,” Technical University of Cluj-

Napoca,Tampere University of Technology, 2010.

[5] Jin Seung Lee, Suk-Won Jang, Jae Gun Choi, and Tae

Gyoo Lee, "North-Finding System Using Multi-Position

Method With a Two-Axis Rotary Table for a Mortar,"

IEEE SENSORS JOURNAL, vol. 16, no. 16, p. 6161, 15

AUGUST 2016.

[6] Martin Jean, Mécanismes de transformation de

mouvement à contact local, Techniques de l'Ingénieur,

2004.

[7] NPTEL, "Lecture 5 : Indexing Mechanisms," NPTEL,

[Online]. Available:

http://nptel.ac.in/courses/112103174/module4/lec5/2.html.

[Accessed 06 12 2016].

[8] Alexander A. Trusov, Igor P. Prikhodko, Sergei A. Zotov,

and Andrei M. Shkel, "High-Q and Wide Dynamic Range

Inertial MEMS for North-Finding and Tracking

Applications," IEEE, Irvine, 2012.

www.kth.se