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Applied and Numerical Harmonic Analysis Series Editor John J. Benedetto University of Maryland Editorial Advisory Board Akram Aldroubi Vanderbilt University Ingrid Daubechies Princeton University Douglas Cochran Arizona State University Hans G. Feichtinger University of Vienna Christopher Heil Georgia Institute of Technology Murat Kunt Swiss Federal Institute of Technology, Lausanne James McClellan Georgia Institute of Technology Wim Sweldens Lucent Technologies, Bell Laboratories Michael Unser Swiss Federal Institute of Technology, Lausanne M. Victor Wickerhauser Washington University Martin Vetterli Swiss Federal Institute of Technology, Lausanne

Applied and Numerical Harmonic Analysis J.M. Cooper: Introduction to Partial Differential Equations with MATLAB (ISBN 0-8176-3967-5) C.E. D’Attellis and E.M. Fern´andez-Berdaguer: Wavelet Theory and Harmonic Analysis in Applied Sciences (ISBN 0-8176-3953-5) H.G. Feichtinger and T. Strohmer: Gabor Analysis and Algorithms (ISBN 0-8176-3959-4) T.M. Peters, J.H.T. Bates, G.B. Pike, P. Munger, and J.C. Williams: The Fourier Transform in Biomedical Engineering (ISBN 0-8176-3941-1) A.I. Saichev and W.A. Woyczy´nski: Distributions in the Physical and Engineering Sciences (ISBN 0-8176-3924-1) R. Tolimieri and M. An: Time-Frequency Representations (ISBN 0-8176-3918-7) G.T. Herman: Geometry of Digital Spaces (ISBN 0-8176-3897-0) A. Proch´azka, J. Uhli˜r, P.J.W. Rayner, and N.G. Kingsbury: Signal Analysis and Prediction (ISBN 0-8176-4042-8) J. Ramanathan: Methods of Applied Fourier Analysis (ISBN 0-8176-3963-2) A. Teolis: Computational Signal Processing with Wavelets (ISBN 0-8176-3909-8) W.O. Bray and ˇC.V. Stanojevi´c: Analysis of Divergence (ISBN 0-8176-4058-4) G.T Herman and A. Kuba: Discrete Tomography (ISBN 0-8176-4101-7) J.J. Benedetto and P.J.S.G. Ferreira: Modern Sampling Theory (ISBN 0-8176-4023-1) A. Abbate, C.M. DeCusatis, and P.K. Das: Wavelets and Subbands (ISBN 0-8176-4136-X) L. Debnath: Wavelet Transforms and Time-Frequency Signal Analysis (ISBN 0-8176-4104-1) K. Gr¨ochenig: Foundations of Time-Frequency Analysis (ISBN 0-8176-4022-3) D.F. Walnut: An Introduction to Wavelet Analysis (ISBN 0-8176-3962-4) O. Bratteli and P. Jorgensen: Wavelets through a Looking Glass (ISBN 0-8176-4280-3) H.G. Feichtinger and T. Strohmer: Advances in Gabor Analysis (ISBN 0-8176-4239-0) O. Christensen: An Introduction to Frames and Riesz Bases (ISBN 0-8176-4295-1) L. Debnath: Wavelets and Signal Processing (ISBN 0-8176-4235-8) J. Davis: Methods of Applied Mathematics with a MATLAB Overview (ISBN 0-8176-4331-1) G. Bi and Y. Zeng: Transforms and Fast Algorithms for Signal Analysis and Representations (ISBN 0-8176-4279-X) J.J. Benedetto and A. Zayed: Sampling, Wavelets, and Tomography (ISBN 0-8176-4304-4) E. Prestini: The Evolution of Applied Harmonic Analysis (ISBN 0-8176-4125-4) O. Christensen and K.L. Christensen: Approximation Theory (ISBN 0-8176-3600-5) L. Brandolini, L. Colzani, A. Iosevich, and G. Travaglini: Fourier Analysis and Convexity (ISBN 0-8176-3263-8) W. Freeden and V. Michel: Multiscale Potential Theory (ISBN 0-8176-4105-X) O. Calin and D.-C. Chang: Geometric Mechanics on Riemannian Manifolds (ISBN 0-8176-4354-0) (Continued after index)

Kai Borre Dennis M. Akos Nicolaj Bertelsen Peter Rinder Søren Holdt Jensen A Software-Deﬁned GPS and Galileo Receiver A Single-Frequency Approach Birkh¨auser Boston • Basel • Berlin

Dennis M. Akos Department of Aerospace Engineering University of Colorado Boulder, CO 80309 U.S.A. Peter Rinder Vivaldisvej 148 DK-9200 Aalborg SV Denmark Kai Borre Danish GPS Center Aalborg University Niels Jernes Vej 14 DK-9220 Aalborg Ø Denmark Nicolaj Bertelsen Hornbækvej 116 DK-9270 Klarup Denmark Søren Holdt Jensen Department of Electronic Systems Aalborg University Fredrik Bajers Vej 7 DK-9220 Aalborg Ø Denmark Cover design by Joseph Sherman. MATLAB R and Simulink R are registered trademarks of The MathWorks, Inc. Mathematics Subject Classiﬁcation (2000): 34B27, 49-XX, 49R50, 65Nxx Library of Congress Control Number: 2006932239 ISBN-10 0-8176-4390-7 ISBN-13 978-0-8176-4390-4 e-ISBN-10: 0-8176-4540-3 e-ISBN-13: 978-0-8176-4540-3 Printed on acid-free paper. c2007 Birkh¨auser Boston All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkh¨auser Boston, c/o Springer Science+Business Media LLC, 233 Spring Street, New York, NY 10013, USA) and the author, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identiﬁed as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 www.birkhauser.com (EB)

Applied and Numerical Harmonic Analysis (Cont’d) J.A. Hogan and J.D. Lakey: Time-Frequency and Time-Scale Methods (ISBN 0-8176-4276-5) C. Heil: Harmonic Analysis and Applications (ISBN 0-8176-3778-8) K. Borre, D.M. Akos, N. Bertelsen, P. Rinder, and S.H. Jensen: A Software-Deﬁned GPS and Galileo Receiver (ISBN 0-8176-4390-7)

Contents Preface List of Figures List of Tables Abbreviations 1 Signals and Systems . . . . . . . 1.1 Characterization of Signals . . . . . . . . 1.1.1 Continuous-Time Deterministic Signals . . . . 1.1.2 Discrete-Time Deterministic Signals . . . . . . . . . . . . . . . . . 1.1.3 Unit Impulse . . . . . . . . . . . . . . 1.1.4 Rectangular Pulse . . . . . . . . . 1.1.5 Random Signals . . . . 1.1.6 Random Sequence of Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Sampling . . . . . 1.3 Characterization of Systems . . . 1.4 Linear Time-Invariant Systems . . 1.5 Representation of Bandpass Signals . . . . . . . . . . . . . . . . ix xiii xvii xix 1 1 . . 2 . . 3 . . 3 . . 4 . . 6 . . 7 . . 8 . . . . 9 . . 12 . . 14 17 . . 17 . . 18 . . 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 GPS Signal 2.1 Signals and Data . . . . 2.2 GPS Signal Scheme . . . . 2.3 C/A Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi Contents . . . . . . . . . . . 2.3.1 Gold Sequence . . . . . 2.3.2 Gold Sequence Generation—Overview . . . 2.3.3 Gold Sequence Generation—Details . . . . . . . . . . . . . 2.3.4 Correlation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Telemetry and Handover Words . . . 2.6.2 Data in Navigation Message . . . . . . . . . 2.4 Doppler Frequency Shift . . . . 2.5 Code Tracking . . 2.6 Navigation Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Galileo Signal . . . . . . . . . . . . . . . . . . . . 3.3 Message Structure . . . . 3.1 Signal Theoretical Considerations 3.2 Galileo L1 OS Signal . . . . . . Signal Generation . . . . . . . . Frames and Pages . . . . . . . . . . . . 3.2.1 . . . . 3.2.2 Coherent Adaptive Subcarrier Modulation . . 3.2.3 Binary Offset Carrier Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forward Error Correction and Block Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Time and Clock Correction Parameters . . . 3.4.2 Conversion of GST to UTC and GPST . . . . 3.4.3 . . . . . . . . . . . 3.3.1 . . . 3.3.2 Cyclic Redundancy Check . . 3.3.3 Service Parameters . . . 3.5 The Received L1 OS Signal . . . 3.4 Message Contents . . . . . . . . . . . . . . . . . . . . . . . . . 4 GNSS Antennas and Front Ends Filter . . . . . . . . . . . 4.1 Background . . . . . 4.2 GNSS L1 Front-End Components . . . . . . . 4.2.1 GNSS Antenna . . . . . . . . 4.2.2 . . . . . . . . . . . 4.2.3 Ampliﬁer . . . . 4.2.4 Mixer/Local Oscillator . . . . 4.2.5 Analog-to-Digital Converter . . . . . . . 4.3 Resulting Sampled Data 4.4 GNSS Front-End ASIC . . . . . . . . . . . 5.1 Receiver Channels 5 GNSS Receiver Operation Overview . . . . . . . . . . . . . . . . . . . . . 5.1.1 Acquisition . . . . . . 5.1.2 Tracking . . . . 5.1.3 Navigation Data Extraction . . . . . 5.2 Computation of Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Acquisition 6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 . . . 21 . . . 22 . . . 25 . . . 26 . . . 27 . . . 28 . . . 29 . . . 30 31 . . . 31 . . . 33 . . . 34 . . . 35 . . . 37 . . . 42 . . . 42 . . . 42 . . . 43 . . . 45 . . . 46 . . . 48 . . . 49 . . . 50 53 . . . 53 . . . 55 . . . 55 . . . 57 . . . 59 . . . 59 . . . 61 . . . 64 . . . 66 69 . . . 69 . . . 70 . . . 71 . . . 72 . . . 73 75 . . . 75

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A Software-Defined GPS and Galileo Receiver：A Single-Frequency A....pdf

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