Distributed Sensor Arrays: Localization

235 Pages·2017·6.94 MB·English

by  Prabhakar S. Naidu

Distributed Sensor Arrays
Localization

Distributed Sensor Arrays
Localization
By
Prabhakar S. Naidu
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Dedication
This work is dedicated to the memory of my mentor, the
late Professor B.S. Ramakrishna, who shaped my career
in the Department of Communication Engineering,
Indian Institute of Science, Bangalore, India.

Contents
Preface.......................................................................................................................xi
Acknowledgments ..................................................................................................xiii
Author ......................................................................................................................xv
Chapter 1 Distributed Sensor Arrays ....................................................................1
1.1 Regular Sensor Array ................................................................1
1.2 Wired Sensor Array ...................................................................2
1.2.1 DSA Response ..............................................................3
1.2.2 Focused Beam ..............................................................4
1.2.3 Boundary Array ...........................................................7
1.3 Autonomous Wireless Sensor Network ....................................7
1.3.1 Wireless Sensor Network (WSN) ...............................10
1.4 Types of Sensors ......................................................................12
1.4.1 Thermal Sensor ..........................................................13
1.4.2 Microphone ................................................................14
1.4.3 Hydrophones ...............................................................15
1.4.4 Accelerometer.............................................................16
1.4.5 Electromagnetic (EM) Sensors ..................................19
1.4.6 Electric Sensors ..........................................................19
1.4.7 Magnetic Sensors .......................................................19
1.4.8 Hall Effect ..................................................................20
1.4.9 Nanosensors ...............................................................21
References ..........................................................................................22
Chapter 2 Basic Inputs ........................................................................................23
2.1 Received Signal Strength.........................................................23
2.2 Lighthouse Effect ....................................................................25
2.2.1 Beam Generation ........................................................26
2.2.2 Prototype ....................................................................28
2.2.3 Events with Large Propagation Speed Difference .....28
2.3 Time of Arrival ........................................................................28
2.4 Time Difference of Arrival .....................................................31
2.4.1 TDoA with a Reference Transmitter ..........................32
2.5 Frequency Difference of Arrival .............................................32
2.6 Direction of Arrival ................................................................36
2.7 Phase Change...........................................................................38
2.8 Instantaneous Frequency .........................................................39
2.9 Summary .................................................................................39
References ..........................................................................................40
vii
viii Contents
Chapter 3 Estimation of ToA/TDoA/FDoA .......................................................41
3.1 Generalized Cross-Correlation ................................................41
3.2 Time Delay as FIR Filter .........................................................45
3.3 Eigenvector Approach .............................................................49
3.4 Subspace Approach .................................................................54
3.5 Capon’s Minimum Variance ....................................................57
3.6 Adaptive Notch Filter ..............................................................60
3.6.1 Adaptation Scheme .....................................................64
3.6.2 Delay Estimation ........................................................64
3.7 Instantaneous Frequency Spectrum ........................................67
3.8 Phase-Based Methods ..............................................................69
3.8.1 Multitone Signaling ....................................................71
3.8.2 Sliding FDFT .............................................................73
3.9 Frequency Difference of Arrival .............................................76
3.9.1 Adaptive Frequency Detector .....................................77
3.9.2 Computational Complexity ........................................82
3.10 Summary .................................................................................82
References ..........................................................................................83
Chapter 4 Localization ........................................................................................85
4.1 Received Signal Strength.........................................................85
4.1.1 Transmitter Coordinates .............................................87
4.1.2 Estimation Errors .......................................................90
4.2 ToA Measurements ..................................................................93
4.2.1 Simple Method ...........................................................93
4.2.2 Iterative Method .........................................................94
4.3 TDoA Measurements...............................................................99
4.3.1 Re-Minimization ........................................................99
4.3.2 Treat Range as a Variable .........................................103
4.3.3 Annihilation of Range Variable ...............................105
4.3.4 Direction Cosines .....................................................106
4.4 FDoA Measurements .............................................................108
4.4.1 Differential Doppler .................................................112
4.5 DoA Measurements ...............................................................113
4.5.1 Errors in Node Position ............................................114
4.5.2 Errors in DoA ...........................................................115
4.5.3 Analysis of Bias .......................................................118
4.5.4 Total Least Squares (TLS) .......................................119
4.6 Compressive Sensing .............................................................120
4.6.1 Compressive Sampling Matching Pursuit
(CoSaMP) .....................................................................122
4.6.2 Localization .............................................................123
4.6.3 Far Field ....................................................................123
4.6.4 Near Field .................................................................128
Contents ix
4.6.5 One-Bit Quantized Measurements ..........................130
4.7 Summary ...............................................................................135
References ........................................................................................136
Chapter 5 Hybrid Methods for Localization .....................................................137
5.1 Combined Use of FDoA and TDoA ......................................137
5.1.1 Narrow Band ............................................................137
5.1.2 Annihilating Matrix .................................................139
5.2 Direct Position Determination ...............................................140
5.3 DoA from Distributed Sensors ..............................................145
5.4 Expectation-Maximization Algorithm ..................................156
5.4.1 Expectation Step (E-Step) ........................................158
5.4.2 Maximization Step (M-Step)....................................160
5.4.3 Estimation of Transmitted Signal .............................162
5.5 Localization in a Multipath Environment .............................163
5.5.1 Time Domain ...........................................................163
5.5.2 Frequency Domain ...................................................169
5.6 Summary ...............................................................................173
References ........................................................................................175
Chapter 6 Self-Localization ..............................................................................177
6.1 Anchor-Based Localization ...................................................177
6.1.1 Cooperative Localization .........................................182
6.1.2 Subspace Positioning Approach ...............................184
6.2 Anchor-Free Localization......................................................189
6.2.1 Multidimensional Scaling ........................................189
6.2.2 Basis Point MDS ......................................................194
6.2.3 1D Space ...................................................................195
6.2.4 2D Space...................................................................195
6.2.5 3D Space ...................................................................197
6.2.6 Missing Data ............................................................199
6.2.7 Computational Load .................................................199
6.3 Clock Synchronization ..........................................................200
6.3.1 Single Reply .............................................................201
6.3.2 Double Reply ............................................................202
6.3.3 Linear Model ............................................................203
6.3.4 Joint Estimation of Offset, Skew (Drift), and Delay ....206
6.3.5 Estimation of Travel Time ........................................208
6.4 Summary ...............................................................................211
References ........................................................................................212
Index ......................................................................................................................213