Precision FMCW Short-Range Radar for Industrial Applications

361 Pages·2014·22.932 MB·English

by  Boris A Atayants, Vlacheslav M Davydochkin, Victor V Ezerskiy, Valery S Parshin, Sergey M Smolskiy

Precision FMCW
Short-Range Radar for
Industrial Applications
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Precision FMCW
Short-Range Radar for
Industrial Applications
Boris A. Atayants
Viacheslav M. Davydochkin
Victor V. Ezerskiy
Valery S. Parshin
Sergey M. Smolskiy
artechhouse.com
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Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the U.S. Library of Congress.
British Library Cataloguing in Publication Data
A catalog record for this book is available from the British Library.
ISBN 13: 978-1-60807-738-0
Manuscript created under the supervision of Dr.Sci. Professor Victor V. Ezerskiy and Dr.Sci.
Professor Sergey M. Smolskiy
English translation by Sergey M. Smolskiy
© 2014 ArteCh house
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Norwood, MA 02062
All rights reserved. Printed and bound in the United States of America. No part of this book
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mark.
10 9 8 7 6 5 4 3 2 1
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To Ryazan State Radio Engineering University, which recently celebrated its
60th anniversary, and JSC Contact-1, which recently celebrated its 20th anniversary
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Contents
Preface xv
Introduction xvii
ChAPteR 1
Counting Method of Estimation of Difference Frequency 1
1.1 Introduction 1
1.2 Main Calculation Relations 1
1.3 The Traditional Counting Method of Range Measurement 5
1.4 Sources of Range Measurement Errors by the FMCW Range-Finder 7
1.5 Adaptive Control of Frequency Modulation Parameters 8
1.6 Truncation Error of Range Measurement at Adaptive
Frequency Modulation 13
1.6.1 The Fixed Measuring Time Interval 13
1.6.2 The Measuring Time Interval Multiple to the Modulation
Half-Period 16
1.6.3 Calculation of the Range Result Correction 20
1.7 The Range Determination Error Caused by the Inaccuracy of
Modulation Adaptation 23
1.8 Noise Influence on the Accuracy of the Range Determination Using the
Additive Counting Method 25
1.9 Conclusions 31
References 31
ChAPteR 2
Weighting Method for the Difference Frequency Averaging 33
2.1 Introduction 33
2.2 The Truncation Error of the Weighting Method of Difference
Frequency Averaging 36
2.3 Truncation Error Minimization at the Weighting Average
Method of Difference Frequency by Optimization of
Weighting Function Parameters 45
2.4 Truncation Error Minimization of the Weighting Averaging
Method of the Difference Frequency by
Optimization of the FM Parameters 50
2.4.1 Application of Additional Slow-Frequency Modulation 50
2.4.2 Optimization of the FM Sweep 53
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viii Contents
2.4.3 Combined Optimization 55
2.4.4 The Combined Procedure of Error Minimization 56
2.5 Noise Influence on the Error of the Weighting Method of Difference
Frequency Averaging 56
2.5.1 The Measurement Error for the Weighting Function in the
Form of the Trigonometric Series 58
2.5.2 The Measurement Error for the Kaiser-Bessel
Weighting Function 62
2.6 Conclusions 64
References 64
ChAPteR 3
Estimation of the Difference Frequency by the Position of the
Spectrum Maximum 67
3.1 Introduction 67
3.2 Algorithms of Difference Frequency Estimation 68
3.3 Estimation of the Difference Frequency on the Basis of the Maximum
Position of the Spectral Density of Difference Frequency Signal 71
3.3.1 Analytical Estimation of the Truncation Error of
Range Measurement 71
3.3.2 The Truncation Error of the Difference Frequency Estimation
at the Weighting Functions of Dolph-Chebyshev and Kaiser-Bessel 74
3.3.3 Minimization of the Measurement Error on the Basis of the FM
Parameter Optimization 77
3.3.4 Error Minimization on the Basis of Optimization of Weighting
Function Parameters 80
3.3.5 Minimization of the Truncation Error Using Adaptable
Weighting Functions 86
3.3.6 Algorithms of Frequency Estimation Using Adaptable
Weighting Functions 86
3.4 Average Weighted Estimation of the Difference Frequency 88
3.4.1 The Truncation Error of the Average Weighted Estimation 88
3.5 Systematic Inaccuracy of Frequency Estimation for the Algorithm with
Correction Coefficients 91
3.6 Influence of Noise Interference on the Error of
Range Measurement 92
3.6.1 Statistical Characteristics of Estimation of the Spectral Density
of DFS and Noise Sum 92
3.6.2 Influence of Noise on Accuracy of the Central
Frequency Estimation 94
3.7 Conclusions 103
References 104
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Contents ix
ChAPteR 4
The Maximal Likelihood Method for Range Estimation According to the
Difference Frequency Signal 107
4.1 Introduction 107
4.2 Range Estimation Based on the Difference Frequency Signal 108
4.3 Peculiarities of Delay Time Estimation Using the Maximal
Likelihood Method 113
4.4 Main Factors Affecting the Measurement Error of Time Delay 116
4.5 Estimation of the Phase Characteristic of FMCW RF 121
4.6 Simulation of the Range Estimation Algorithm 130
4.6.1 Simulation Results at a Known Phase Characteristic 131
4.6.2 Simulation Results at the Unknown Phase Characteristic:
The Approach to Practical Estimation of the
Phase Characteristic 131
4.6.3 Reduction of the Noise Influence on the Accuracy of the
Phase Characteristic Estimation 134
4.7 Conclusions 135
References 136
ChAPteR 5
Effects of FM Nonlinearity 137
5.1 Introduction 137
5.2 The Mathematical Model of the Modulation Characteristic 137
5.3 Effects of FM Nonlinearity for the Counting Method of
Frequency Measurement 141
5.3.1 The Quadratic Modulation Characteristic 142
5.3.2 The Oscillating Modulation Characteristic 144
5.3.3 The Quadratic Modulation Characteristics with the
Oscillating Component 147
5.4 Effects of FM Nonlinearity for the Weighting Method of Difference
Frequency Averaging 147
5.5 Connection of the Correction Coefficient with Nonlinearity
Parameters of the MC 151
5.5.1 Quadratic Nonlinearity of Modulation Characteristics 151
5.5.2 Oscillating Nonlinearity of the Modulation Characteristic 151
5.5.3 Quadratic and Oscillating Nonlinearity of the
Modulation Characteristic 152
5.6 Estimation of the Correction Coefficient According to the Operating
Difference-Frequency Signal 153
5.6.1 The Algorithm Sequence 153
5.6.2 Simulation Conditions 154
5.7 Compensation of Modulation Characteristic Nonlinearity 155
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