Spread spectrum signal tracking loop models and raw measurements accuracy improvement method

170 Pages·2005·5.86 MB·French

Thèse de l’Institut National Polytechnique de Toulouse (INPT) – n° 1917

Présentée à l’ENAC de Toulouse, le 15 Novembre 2002 par

Fabrice LEGRAND

MODELES DE BOUCLE DE POURSUITE DE SIGNAUX A SPECTRE
ETALE ET METHODE D’AMELIORATION DE LA PRECISION DES
MESURES BRUTES

Membres du jury :

Prof. Dr. Tony PRATT, (rapporteur)
Directeur technique GPS chez Parthus Ltd, Northampton, England

M. Jean-Luc ISSLER, (directeur)
Chef du département Radionavigation du CNES, Toulouse, France

Prof. Dr. Francis CASTANIE, (président du jury)
Directeur du laboratoire TéSA, Toulouse, France

Prof. Dr. Bernd EISSFELLER, (rapporteur)
Institut de Géodésie et de Navigation, University of the Federal Armed Forces, Munich, Germany

Dr. Dennis AKOS, (rapporteur)
Chercheur associé, Stanford University GPS Lab, Stanford, USA

Dr. Christophe MACABIAU, (directeur)
Chef du laboratoire CNS de l’ENAC, Toulouse, France

Version finale du rapport – Janvier 2005

Thesis of the Institut National Polytechnique de Toulouse (INPT), France

Presented at ENAC, Toulouse, France, on November 15, 2002 by

Fabrice LEGRAND

SPREAD SPECTRUM SIGNAL TRACKING LOOP MODELS AND
RAW MEASUREMENTS ACCURACY IMPROVEMENT METHOD

Examining board:

Prof. Dr. Tony PRATT, (thesis reviewer)
GPS Technical Director at Parthus Ltd, Northampton, England

Mr. Jean-Luc ISSLER, (thesis supervisor)
Head of the Radionavigation department of the CNES, Toulouse, France

Prof. Dr. Francis CASTANIE,
Director of the TéSA Laboratory, Toulouse, France

Prof. Dr. Bernd EISSFELLER, (thesis reviewer)
Institute of Geodesy and Navigation at the University of the Federal Armed Forces, Munich, Germany

Dr. Dennis AKOS, (thesis reviewer)
Research associate with the Stanford University GPS Lab, Stanford, USA

Dr. Christophe MACABIAU, (thesis supervisor)
Head of the CNS Research Laboratory of the ENAC, Toulouse, France

Final version of the report – January 2005

Avant-propos

Etant donné que les rapporteurs de cette thèse sont non-francophones, le manuscrit est rédigé en
anglais. Néanmoins, l’introduction, la conclusion, la table des matières ainsi que le résumé des
chapitres sont rédigés en français.
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Acknowledgments

Author wish to thank the CENTRE NATIONAL D’ETUDES SPATIALES (CNES, the French Space
Agency) and ALCATEL SPACE INDUSTRIES (ASPI) for having supported this research, and the
ECOLE NATIONALE DE L’AVIATION CIVILE (ENAC, the French Civil Aviation School) for
having provided accommodations during these years of work.

I specially wish to thank my thesis supervisors M. Christophe MACABIAU and M. Abdelahad
BENHALLAM from the ENAC, M. Jean-Luc ISSLER and M. Laurent LESTARQUIT from CNES,
M. Christian MEHLEN from ASPI for having put trust in me and given lots of their time to support
and help me.

I also wish to thank M. Eric CHATRE, M. Jean-Marc LISEZ and M. Cyril DUPOUY from STNA for
having provided technical assistance.

Thanks to the students, the trainees and the staffs of the ENAC, and of course to my family and friends
for their support and help.

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Contents

Avant-propos...............................................................................................................................................................................5
Acknowledgments.......................................................................................................................................................................7
Contents......................................................................................................................................................................................9
Tables des matières...................................................................................................................................................................13
INTRODUCTION..................................................................................................................17
Introduction...............................................................................................................................................................................19
CHAPTER I : RANGE MEASUREMENTS ON SPREAD SPECTRUM SIGNALS.....21
Chapitre I : Mesures de distance sur les signaux à spectre étalé................................................................................................21
I.1 INTRODUCTION AND DEFINITIONS ABOUT PSEUDORANGE AND RAW PHASE
MEASUREMENTS.............................................................................................................................................22
I.1.1 DEFINITION OF THE PSEUDORANGE................................................................................................22
I.1.1.1 RANGE AND PSEUDORANGE..............................................................................................................22
I.1.1.2 ERRORS ON MEASURED PSEUDORANGE............................................................................................23
I.1.2 INTRODUCTION ON THE PSEUDORANGE MEASUREMENT TECHNIQUE...........................................25
I.1.2.1 PSEUDORANGE INFORMATION EXTRACTION.....................................................................................26
I.1.2.2 INTRODUCTION ON RECEIVER ARCHITECTURE..................................................................................26
I.2 MODEL AND PROPERTIES OF GNSS SPREAD SPECTRUM SIGNALS...............................28
I.2.1 MODEL OF A RECEIVED SIGNAL......................................................................................................28
I.2.1.1 GENERAL EXPRESSION.....................................................................................................................28
I.2.1.2 DYNAMICS MODEL...........................................................................................................................29
I.2.1.3 CARRIER TO NOISE RATIO.................................................................................................................31
I.2.2 SIGNAL PROPERTIES........................................................................................................................31
I.2.2.1 INSTANTANEOUS CARRIER FREQUENCY AND DOPPLER FREQUENCY SHIFT.......................................31
I.2.2.2 AUTOCORRELATION FUNCTION OF SPREADING SIGNALS...................................................................32
I.2.2.3 CROSS CORRELATION FUNCTION OF SPREADING SIGNALS.................................................................33
I.2.2.4 POWER SPECTRAL DENSITY..............................................................................................................34
Appendix of Chapter I...............................................................................................................................................................37
Appendix I-1: Maximal length sequences and Gold codes........................................................................................................39
Appendix I-2: Correlation functions of a PRN signal based on Gold codes..............................................................................41
CHAPTER II : SEQUENTIAL MODELS OF DIGITAL TRACKING LOOPS............45
Chapitre II : Modèles séquentiels des boucles de poursuite numériques...................................................................................45
II.1 CARRIER PHASE TRACKING WITH COSTAS LOOP..............................................................46
II.1.1 MIXING WITH THE LOCAL SIGNALS / IQ DECOMPOSITION............................................................47
II.1.2 PREDETECTION FILTERING.............................................................................................................47
II.1.3 PHASE DISCRIMINATORS.................................................................................................................52
II.1.4 LOOP FILTERING.............................................................................................................................53
II.1.5 LOCAL SIGNALS GENERATION........................................................................................................54
II.1.6 DATA DEMODULATION....................................................................................................................55
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II.2 CODE TRACKING WITH DELAY LOCK LOOPS......................................................................57
II.2.1 CODE CORRELATORS......................................................................................................................58
II.2.2 CODE PHASE DISCRIMINATORS.......................................................................................................59
II.2.3 LOOP FILTERING.............................................................................................................................61
II.2.4 LOCAL CODE GENERATION.............................................................................................................61
II.3 SIMULTANEOUS CODE AND CARRIER PHASE TRACKING LOCK LOOPS.....................63
II.4 GAUSSIAN NOISE IN THE LOOPS...............................................................................................64
II.4.1 RF FILTERING EFFECT....................................................................................................................64
II.4.2 IN-PHASE AND QUADRATE BASEBAND NOISES.................................................................................65
II.4.3 CORRELATOR OUTPUT NOISES........................................................................................................66
Appendix of Chapter II.............................................................................................................................................................67
Appendix II-1: Series expansions of sine and cosine functions.................................................................................................69
Appendix II-2: Gaussian noise in the loops...............................................................................................................................73
CHAPTER III : SAMPLED PHASE PROPAGATION MODELS..................................79
Chapitre III : Modèles discrets de propagation de la phase.......................................................................................................79
III.1 TRADITIONAL DIGITAL CONSTANT-RATE MODEL............................................................80
III.1.1 GENERIC CLOSED LOOP MODEL......................................................................................................80
III.1.1.1 MODEL OF THE DISCRIMINATOR.......................................................................................................80
III.1.1.1.1 Generic non-linear model.................................................................................................................................80
III.1.1.1.2 Linear model....................................................................................................................................................81
III.1.1.2 DIGITAL LOOP FILTER.......................................................................................................................81
III.1.1.3 NCO MODEL....................................................................................................................................81
III.1.2 LINEAR CLOSED LOOP MODEL........................................................................................................82
III.1.3 LINEAR TRANSFER FUNCTIONS.......................................................................................................83
III.2 PROPOSED MULTI-RATE MODEL INCLUDING INTEGRATE & DUMP
PREDETECTION FILTERS..............................................................................................................................85
III.2.1 DESCRIPTION OF THE MODEL.........................................................................................................85
III.2.1.1 GENERIC CLOSED LOOP MODEL........................................................................................................85
III.2.1.2 MODEL OF THE DISCRIMINATOR INCLUDING THE I&D PREDETECTION FILTERS................................85
III.2.1.3 MODEL OF THE NCO WITH A HELD COMMAND SIGNAL....................................................................86
III.2.1.4 CLOSED LOOP MODEL.......................................................................................................................86
III.2.1.5 LINEAR TRANSFER FUNCTIONS AS A FUNCTION OF THE LOOP FILTER ORDER....................................89
III.2.1.6 VALIDATION OF THE NEW LINEAR MODEL........................................................................................91
III.2.2 EVALUATION OF THE TRACKING ERROR........................................................................................95
III.2.2.1 SENSITIVITY ON NOISE......................................................................................................................95
III.2.2.1.1 Phase noise model............................................................................................................................................95
III.2.2.1.2 Equivalent noise bandwidth of the loop...........................................................................................................96
III.2.2.1.3 Expression of the equivalent noise bandwidth as a function of the loop filter coefficients..............................99
III.2.2.2 SENSITIVITY TO DYNAMICS............................................................................................................103
III.2.2.2.1 Expression of the steady state error................................................................................................................103
III.2.2.2.2 Definition of the Steady State Error Factor....................................................................................................105
III.2.2.3 TOTAL TRACKING ERROR...............................................................................................................106
Appendix of Chapter III..........................................................................................................................................................109
Appendix III-1: Multi-rate linear model simplifications.........................................................................................................111
Appendix III-2: Loop filter coefficients expressed as a function of the poles of the loop transfer function – Usual digital
constant rate model..................................................................................................................................................................115
Appendix III-3: Equivalent initial value of the mth derivative of the averaged input phase.....................................................119
Appendix III-4: Generic Expressions of the linear transfer functions derived from the multi-rate model of loops.................121
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