Academic Press Library in Signal Processing - GBV · 2014. 2. 6. · Contents ix 3.06.8...

Academic Press Library inSignal Processing

Volume 3

Array and Statistical Signal Processing

Editors

Abdelhak M. ZoubirSignal processing Group,

Technische Universitat Darmstadt, Germany

Mats VibergDepartment of Signals and Systems

Chalmers University of Technology, Sweden

Rama ChellappaDepartment of Electrical and Computer Engineering and

Center for Automation Research,

University of Maryland,College Park, MD, USA

Sergios TheodoridisDepartment of Informatics & Telecommunications,

University of Athens, Greece

ELSEVIER

AMSTERDAM • WALTHAM • HEIDELBERG • LOI1DON,NEW YORK • OXFORD • PARIS • SAN DIEGC

U

SAN FRANCISCO • SYDNEY • TOKYO

Academic Press is an imprint of Elsevier

Contents

Introduction xxi

About the Editors xxv

Section Editors xxvii

Authors Biography xxix

SECTION I STATISTICAL SIGNAL PROCESSING

CHAPTER 1 Introduction to Statistical Signal Processing 3Abdelhak M. Zoubir

3.01.1 A brief historical recount 3

3.01.2 Content 3

3.01.3 Contributions 4

3.01.3.1 Quickest change detection 4

3.01.3.2 Distributed signal detection 4

3.01.3.3 Diffusion adaptation over networks 5

3.01.3.4 Non-stationary signal analysis—a time-frequency approach 5

3.01.3.5 Bayesian computational methods in signal processing 5

3.01.3.6 Model order selection 6

3.01.3.7 Performance analysis and bounds 6

3.01.3.8 Geolocation 6

3.01.4 Suggested further reading 6

Acknowledgments 6

References 7

CHAPTER 2 Model Order Selection 9

Visa Koivunen and Esa Ollila

3.02.1 Introduction 9

3.02.2 Example: variable selection in regression 11

3.02.2.1 AIC and the stepwise regression 12

3.02.2.2 Cross-validation and bootstrap methods 12

3.02.3 Methods based on statistical inference paradigms 14

3.02.3.1 Bayesian Information Criterion (BIC) 14

3.02.3.2 GLRT-based sequential hypothesis testing 16

3.02.4 Information and coding theory based methods 17

3.02.4.1 Akaike Information Criterion (AIC) 17

V

vi Contents

3.02.4.2 Minimum Description Length 19

3.02.5 Example: estimating number of signals in subspace methods 21

3.02.6 Conclusions 23

References 23

CHAPTER 3 Non-Stationary Signal Analysis Time-Frequency Approach 27

Ljubisa Stankovic, Milos Dakovic, and Thayananthan Thayaparan


3.03.2 Linear signal transforms 28

3.03.2.1 Short-time Fourier transform 28

3.03.2.2 Discrete form and realizations of the STFT 36

3.03.2.3 Gabor transform 45

3.03.2.4 Stationary phase method 46

3.03.2.5 Local polynomial Fourier transform 50

3.03.2.6 Relation between the STFT and the continuous wavelet

transform 52

3.03.2.7 Generalization 56

3.03.3 Quadratic time-frequency distributions 583.03.3.1 Rihaczek distribution 58

3.03.3.2 Wigner distribution 603.03.3.3 Ambiguity function 77

3.03.3.4 Cohen class of distributions 80

3.03.3.5 Kernel decomposition method 883.03.3.6 S-method 89

3.03.3.7 Reassignment in time-frequency 993.03.3.8 Affine class of time-frequency representations 104

3.03.4 Higher order time-frequency representations 1073.03.4.1 Wigner bispectrum 1073.03.4.2 Wigner higher order spectra 1083.03.4.3 Wigner multi-time distribution 110

3.03.4.4 Signal phase derivative and distributions definitions 1123.03.4.5 STFT based realization of higher order representations 1173.03.4.6 Higher order ambiguity functions 120

3.03.5 Processing of sparse signals in time-frequency 1243.03.5.1 Concentration measures 124

3.03.5.2 Sparse signals 1263.03.5.3 Compressive sensing and the L-statistics in time-frequency 131

3.03.6 Examples of time-frequency analysis applications 135

Contents vii

3.03.6.1 Time-frequency radar signal processing 1363.03.6.2 Biomedical signal analysis 137

3.03.6.3 Seismic signal analysis 137

3.03.6.4 Car engine signal analysis 137

3.03.6.5 Velocities of moving objects in video sequence 138

3.03.6.6 Time-variant filtering 138

3.03.6.7 Interference rejection in spread spectrum systems 139

3.03.6.8 Watermarking in the space/spatial-frequency domain 140

References and Further Reading 140

CHAPTER 4 Bayesian Computational Methods in Signal Processing 143

Simon Godsill


3.04.2 Parameter estimation 143

3.04.2.1 The linear Gaussian model 144

3.04.2.2 Maximum Likelihood (ML) estimation 146

3.04.2.3 Bayesian inference 147

3.04.2.4 Model uncertainty and Bayesian decision theory 158

3.04.2.5 Structures for model uncertainty 161

3.04.2.6 Bayesian model averaging 161

3.04.3 Computational methods 161

3.04.3.1 Expectation-Maximization (EM) for MAP estimation 162

3.04.3.2 Markov Chain Monte Carlo (MCMC) 163

3.04.4 State-space models and sequential inference 164

3.04.4.1 Linear Gaussian state-space models 164

3.04.4.2 The prediction error decomposition 166

3.04.4.3 Sequential Monte Carlo (SMC) 167

3.04.4.4 Particle filtering and auxiliary sampling 169

3.04.5 Conclusion 178

A Probability densities and integrals 178

A.1 Univariate Gaussian 178

A.2 Multivariate Gaussian 178

A.3 Gamma density 180

A.4 Inverted-gamma distribution 180

A.5 Normal-inverted-gamma distribution 181

A.6 Wishart distribution 181

A.7 Inverse Wishart distribution 182

References 182

viii Contents

CHAPTER 5 Distributed Signal Detection 187

Pramod K. Varshney and Engin Masazade


3.05.2 Distributed detection with independent observations 188

3.05.2.1 Conditional independence assumption 190

3.05.2.2 Other network topologies 194

3.05.2.3 Nonparametric rules in distributed detection 196

3.05.2.4 Energy efficient distributed detection and multi-objective

optimization 197

3.05.2.5 Channel aware distributed detection 197

3.05.3 Distributed detection with dependent observations 198


References 202

CHAPTER 6 Quickest Change Detection 209

Venugopal V. Veeravalli and Taposh Banerjee


3.06.2 Mathematical preliminaries 212

3.06.2.1 Martingales 212

3.06.2.2 Stopping times 213

3.06.2.3 Renewal and nonlinear renewal theory 214

3.06.3 Bayesian quickest change detection 217

3.06.3.1 The Bayesian i.i.d. setting 217

3.06.3.2 General asymptotic Bayesian theory 221

3.06.3.3 Performance analysis for i.i.d. model with geometric prior 225

3.06.4 Minimax quickest change detection 228

3.06.4.1 Minimax algorithms based on the Shiryaev algorithm 232

3.06.4.2 Optimality properties of the minimax algorithms 234

3.06.4.3 General asymptotic minimax theory 237

3.06.5 Relationship between the models 240

3.06.6 Variants and generalizations of the quickest change detection problem 241

3.06.6.1 Quickest change detection with unknown pre- or post-changedistributions 241

3.06.6.2 Data-efficient quickest change detection 244

3.06.6.3 Distributed sensor systems 247

3.06.6.4 Variants of quickest change detection problem for distributed

sensor systems 249

3.06.7 Applications of quickest change detection 250

Contents ix

3.06.8 Conclusions and future directions 251

Acknowledgments 252

References 252

CHAPTER 7 Geolocation—Maps, Measurements, Models, and Methods 257

Fredrik Gustafsson


3.07.2 Theory—overview 259

3.07.3 Estimation methods 260

3.07.3.1 Mathematical framework 260

3.07.3.2 Nonlinear filtering 261

3.07.3.3 Nonlinear filter theory 261

3.07.3.4 The extended Kalman filter 264

3.07.3.5 The unscented Kalman filter 265

3.07.3.6 The particle filter 267

3.07.4 Motion models 270

3.07.4.1 Dead-reckoning model 272

3.07.4.2 Kinematic model 274

3.07.5 Maps and applications 276

3.07.5.1 Road-bound vehicles 276

3.07.5.2 Airborne fast vehicles 278

3.07.5.3 Airborne slow vehicles 280

3.07.5.4 Underwater vessels 282

3.07.5.5 Surface vessels 283

3.07.5.6 Cellular phones 285

3.07.5.7 Small migrating animals 290

3.07.6 Mapping in practice 292


Acknowledgment 294

References 295

CHAPTER 8 Performance Analysis and Bounds 297

Brian M. Sadler and Terrence J. Moore


3.08.2 Parametric statistical models 298

3.08.2.1 Cramer-Rao bound on parameter estimation 299

3.08.3 Maximum likelihood estimation and the CRB 303

3.08.3.1 Asymptotic normality and consistency of the MLE 304

x Contents

3.08.4 Mean-square error bound 305

3.08.5 Perturbation methods for algorithm analysis 306

3.08.5.1 Perturbations and statistical analysis 306

3.08.5.2 Matrix perturbations 307

3.08.5.3 Obtaining the CRB through perturbation analysis of the MLE 308

3.08.6 Constrained Cramer-Rao bound and constrained MLE 308

3.08.6.1 Constrained CRB 308

3.08.6.2 Comments and properties of the CCRB 309

3.08.6.3 Constrained MLE 310

3.08.7 Multiplicative and non-Gaussian noise 310

3.08.7.1 Multiplicative and additive noise model 310

3.08.7.2 Gaussian case 311

3.08.7.3 Non-Gaussian case 311

3.08.8 Asymptotic analysis and the central limit theorem 313

3.08.8.1 Comments on application of the CLT 314

3.08.9 Asymptotic analysis and parametric models 315

3.08.9.1 Fourier transform 315

3.08.9.2 Least squares estimation 316

3.08.10 Monte Carlo methods 317

3.08.10.1 Using Monte Carlo to approximate an expectation 318

3.08.10.2 Computing the CRB via Monte Carlo 318

3.08.11 Confidence intervals 318


References 319

CHAPTER 9 Diffusion Adaptation Over Networks 323

AH H. Sayed

3.09.1 Motivation 323

3.09.1.1 Networks and neighborhoods 324

3.09.1.2 Cooperation among agents 326

3.09.1.3 Notation 326

3.09.2 Mean-square-error estimation 327

3.09.2.1 Application: autoregressive modeling 328

3.09.2.2 Application: tapped-delay-line models 3343.09.2.3 Application: target localization 336

3.09.2.4 Application: collaborative spectral sensing 3413.09.3 Distributed optimization via diffusion strategies 345

3.09.3.1 Relating the global cost to neighborhood costs 3473.09.3.2 Steepest-descent iterations 351

3.09.3.3 Adapt-Then-Combine (ATC) diffusion strategy 353

Contents xi

3.09.3.4 Combine-Then-Adapt (CTA) diffusion strategy 355

3.09.3.5 Useful properties of diffusion strategies 357

3.09.4 Adaptive diffusion strategies 359

3.09.5 Performance of steepest-descent diffusion strategies 364

3.09.5.1 General diffusion model 364

3.09.5.2 Error recursions 366

3.09.5.3 Convergence behavior 368

3.09.6 Performance of adaptive diffusion strategies 374

3.09.6.1 Data model 374

3.09.6.2 Performance measures 375

3.09.6.3 Error recursions 377

3.09.6.4 Convergence in the mean 379

3.09.6.5 Mean-square stability 381

3.09.6.6 Network mean-square performance 386

3.09.6.7 Mean-square performance of individual nodes 387

3.09.6.8 Uniform data profile 389

3.09.6.9 Transient mean-square performance 390

3.09.7 Comparing the performance of cooperative strategies 391

3.09.7.1 Comparing ATC and CTA strategies 392

3.09.7.2 Comparing strategies with and without information exchange 393

3.09.7.3 Comparing diffusion strategies with the non-cooperative

strategy 394

3.09.8 Selecting the combination weights 396

3.09.8.1 Constant combination weights 397

3.09.8.2 Optimizing the combination weights 398

3.09.8.3 Adaptive combination weights 401

3.09.9 Diffusion with noisy information exchanges 403

3.09.9.1 Noise sources over exchange links 404

3.09.9.2 Error recursion 405

3.09.9.3 Convergence in the mean 409

3.09.9.4 Mean-square convergence 410

3.09.9.5 Adaptive combination weights 412

3.09.10 Extensions and further considerations 414

3.09.10.1 Adaptive diffusion strategies with smoothing mechanisms 415

3.09.10.2 Diffusion recursive least-squares 419

3.09.10.3 Diffusion Kalman filtering 423

3.09.10.4 Diffusion distributed optimization 426

Appendices 430

A Properties of Kronecker products 430

B Graph Laplacian and network connectivity 430

C Stochastic matrices 433

xii Contents

D Block maximum norm 435

E Comparison with consensus strategies 442

E.1 Consensus recursion 442

E.2 Error recursion 443

Acknowledgments 449

References 450

SECTION II ARRAY SIGNAL PROCESSING

CHAPTER 10 Array Signal Processing: Overview of the Included Chapters 457Mats Viberg

3.10.1 Some history 457

3.10.2 Summary of the included chapters 457

3.10.2.1 Introduction to array processing 458

3.10.2.2 Broadband beamforming and optimization 458

3.10.2.3 Adaptive and Robust Beamforming 458

3.10.2.4 DOA Estimation Methods and Algorithms 458

3.10.2.5 Subspace Methods and Exploitation of Special Array Structures 459

3.10.2.6 Performance Bounds and Statistical Analysis of DOA Estimation 459

3.10.2.7 DOA Estimation of Nonstationary Signals 4593.10.2.8 Source Localization and Tracking 4603.10.2.9 Array Processing in the Face of Nonidealities 460

3.10.2.10 Applications of Array Signal Processing 460

3.10.3 Outlook 461

References 461

CHAPTER 11 Introduction to Array Processing 463Mats Viberg


3.11.2 Geometric data model 465

3.11.2.1 Wave propagation 465

3.11.2.2 Ideal data model 466

3.11.2.3 Non-ideal data models 470

3.11.3 Spatial filtering and beam patterns 4713.11.3.1 Spatial filtering 4713.11.3.2 One-dimensional arrays 472

3.11.3.3 Two-dimensional arrays 475

3.11.3.4 Wideband array response 477

3.11.4 Beam forming and signal detection 480

Contents xiii

3.11.4.1 Beamforming as spatial filter design 480

3.11.4.2 Adaptive beamforming 482

3.11.4.3 Signal detection 485

3.11.5 Direction-of-arrival estimation 486

3.11.5.1 Beamforming methods 487

3.11.5.2 Subspace methods 488

3.11.5.3 Parametric methods 489

3.11.5.4 Modeling errors and array calibration 492

3.11.6 Non-coherent array applications 493

3.11.6.1 Spread sources 493

3.11.6.2 Time series modeling 495

3.11.6.3 Source localization in sensor networks 497

3.11.6.4 Microwave and ultrasound imaging 497

3.11.7 Concluding remarks 498

References 499

CHAPTER 12 Adaptive and Robust Beamforming 503

SergiyA. Vorobyov


3.12.2 Data and beamforming models 504

3.12.2.1 Narrowband case 505

3.12.2.2 Wideband case • 507

3.12.3 Adaptive beamforming 508

3.12.3.1 Basic principles 508

3.12.3.2 MVDR beamforming with data covariance matrix 512

3.12.3.3 Optimal SINR 512

3.12.3.4 Adaptive beamforming for general-rank source 513

3.12.3.5 Gradient adaptive beamforming algorithms 513

3.12.3.6 Sample matrix inversion adaptive beamformer 514

3.12.3.7 Projection adaptive beamforming methods 515

3.12.3.8 Reduced complexity approaches to adaptive beamforming 516

3.12.3.9 Wideband adaptive beamforming 519

3.12.4 Robust adaptive beamforming 521

3.12.4.1 Motivations 521

3.12.4.2 Diagonally loaded SMI beamformer 522

3.12.4.3 Look direction mismatch (pointing error) problem 523

3.12.4.4 Generalized sidelobe canceler 527

3.12.4.5 Correlated (coherent) SOI and interferences: spatial smoothing 529

3.12.4.6 Forward-backward averaging and spatial smoothing 533

3.12.4.7 Rapidly moving interferences 535

xiv Contents

3.12.4.8 Unified principle to MVDR robust adaptive beamforming

design 536

3.12.4.9 Eigenspace-based beamformer 537

3.12.4.10 Worst-case-based robust adaptive beamforming 538

3.12.4.11 Relationship between the worst-case-based and the LSMI

adaptive beamformers 538

3.12.4.12 Doubly constrained robust adaptive beamforming 539

3.12.4.13 Probabilistically constrained robust adaptive beamforming 540

3.12.4.14 Sequential quadratic programming-based robust

adaptive beamforming 540

3.12.4.15 Eigenvalue beamforming using multi-rank MVDR

beamformer 541

3.12.4.16 Robust adaptive beamforming based on steering vector

estimation with as little as possible prior information 542

3.12.4.17 Comparison by simulation 544

3.12.4.18 Robust adaptive beamforming for the general-rank signal model 545

3.12.4.19 Wideband robust adaptive beamforming 546

3.12.4.20 Summary 547

Acknowledgments 548

References 548

CHAPTER 13 Broadband Beamforming and Optimization 553

Sven E. Nordholm, Hai H. Dam, Chiong C. Lai, and

Eric A. Lehmann


3.13.2 Environment and channel modeling 556

3.13.2.1 Aperture theory 556

3.13.2.2 Array geometries 557

3.13.3 Broadband beamformer design in element space 558

3.13.3.1 Weighted Least Squares design 561

3.13.3.2 Total Least Squares design and Eigen-Filters 562

3.13.3.3 Chebyshev design 563

3.13.3.4 Model and robust formulation 563

3.13.3.5 Robust WLS design 566

3.13.3.6 Robust Total Least Squares design 567

3.13.3.7 Robust Chebyshev design 567

3.13.3.8 Design examples 568

3.13.3.9 Steerable broadband beamformer 571

3.13.3.10 Discussion on optimization and design of broadband

beamformers 574

Contents xv

3.13.4 Broadband beamformer design using the wave equation 574

3.13.4.1 Broadband beamformer design based on the Wave equation 579

3.13.4.2 Time domain design of spherical broadband beamformer 581

3.13.4.3 Design examples 582

3.13.5 Optimum and adaptive broadband beamforming 584

3.13.5.1 Common signal modeling 584

3.13.5.2 Linearly Constrained Minimum Variance beamforming 584

3.13.5.3 LCMV in frequency domain 586

3.13.5.4 Generalized Sidelobe Canceler 587

3.13.5.5 Generalized Sidelobe Canceler in frequency domain 589

3.13.5.6 Wiener filter 590

3.13.5.7 Frequency domain Wiener filter 591

3.13.5.8 Optimal near-field Signal-to-Noise plus Interference

Beamformer (SNIB) 591

3.13.5.9 Examples for optimal beamformers 593


3.13.6.1 Further reading 596

References 596

CHAPTER 14 DOA Estimation Methods and Algorithms 599

Pei-Jung Chung, Mats Viberg, and Jia Yu

3.14.1 Background 599

3.14.2 Data model 600

3.14.2.1 Wave propagation 600

3.14.2.2 Frequency domain description 601

3.14.2.3 Uniqueness 604

3.14.3 Beamforming methods 604

3.14.3.1 Conventional beamformer 605

3.14.3.2 Minimum Variance Distortionless Response (MVDR)

beamformer 606

3.14.3.3 Sparse data representation based approach 607

3.14.3.4 Numerical examples 609

3.14.4 Subspace methods 611

3.14.4.1 MUSIC 612

3.14.4.2 ESPRIT 613

3.14.4.3 Signal coherence 614


3.14.5 Parametric methods 617

3.14.5.1 The maximum likelihood approach 618

3.14.5.2 Implementation 620

xvi Contents

3.14.5.3 Subspace fitting methods 625

3.14.5.4 Covariance matching estimation methods 626

3.14.5.5 Performance bound 627


3.14.6 WidebandDOA estimation 631

3.14.6.1 Wideband maximum likelihood estimation 632

3.14.6.2 Coherent signal subspace methods 633

3.14.7 Signal detection 634

3.14.7.1 Nonparametric methods 634

3.14.7.2 Parametric methods 636

3.14.7.3 Additional issues 636

3.14.8 Special topics 637

3.14.8.1 Tracking 637

3.14.8.2 Signals with known structures 637

3.14.8.3 Spatially correlated noise fields 638

3.14.8.4 Beamspace processing 638

3.14.8.5 Distributed sources 639

3.14.8.6 Polarization sensitivity 640

3.14.9 Discussion 640

Acknowledgments 641

References 641

CHAPTER 15 Subspace Methods and Exploitation of SpecialArray Structures 651

Martin Haardt, Marius Pesavento, Florian Roemer, and Mohammed

Nabil El Korso


3.15.2 Data model 654

3.15.2.1 Notation 654

3.15.2.2 General data model 655

3.15.2.3 Special array structures 657

3.15.2.4 Non-circular data 665

3.15.3 Subspace estimation 667

3.15.3.1 Matrix-based subspace estimation 667

3.15.3.2 Subspace estimation with a small number of snapshots 669

3.15.3.3 Forward-backward averaging and real-valued subspaceestimation 671

3.15.3.4 Tensor-based subspace estimation 672

Contents xvii

3.15.4 Subspace-based algorithms 674

3.15.4.1 One-dimensional algorithms using matrix-based subspaceestimates 674

3.15.4.2 Multi-dimensional algorithms using matrix-based subspace

estimates 690

3.15.4.3 Algorithms using tensor-based subspace estimates 698

3.15.4.4 Simulation results 703

3.15.5 Conclusions VI1

Acknowledgment 712

References 712

CHAPTER 16 Performance Bounds and Statistical Analysis ofDOA Estimation 719

Jean Pierre Delmas


3.16.2 Models and basic assumption 720

3.16.2.1 Parametric array model 720

3.16.2.2 Signal assumptions and problem formulation 721

3.16.2.3 Parameter identifiability 722

3.16.3 General statistical tools for performance analysis of DOA estimation 723

3.16.3.1 Performance analysis of a specific algorithm 723

3.16.3.2 Cramer-Rao Bounds (CRB) 729

3.16.3.3 Asymptotically Minimum Variance Bounds (AMVB) 734

3.16.3.4 Relations between AMVB and CRB: projector statistics 735

3.16.4 Asymptotic distribution of estimated DOA 736

3.16.4.1 Beamforming-based algorithms 737

3.16.4.2 Maximum likelihood algorithms 738

3.16.4.3 Second-order algorithms 743

3.16.4.4 Subspace-based algorithms 745

3.16.4.5 Robustness of algorithms 747

3.16.4.6 High-order algorithms 750

3.16.5 Detection of number of sources 752

3.16.5.1 MDL criterion 752

3.16.5.2 Performance analysis of MDL criterion 753

3.16.6 Resolution of two closely spaced sources 755

3.16.6.1 Angular resolution limit based on mean null spectra 755

3.16.6.2 Angular resolution limit based on the CRB 757

3.16.6.3 Angular resolution limit based on the detection theory 758

References 760

xviii Contents

CHAPTER 17 DOA Estimation of Nonstationary Signals 765

Moeness G. Amin and Yimin D. Zhang


3.17.2 Nonstationary signals and time-frequency representations 767

3.17.2.1 Nonstationary signals 767

3.17.2.2 Cohen's class of time-frequency representations 767

3.17.2.3 Wigner-Radon transform and fractional Fourier transform

for LFM signals 769

3.17.2.4 Polynomial phase signals and parameter estimations 772

3.17.3 Spatial time-frequency distribution 774

3.17.3.1 Spatial time-frequency distribution 774

3.17.3.2 SNR enhancement 775

3.17.3.3 Subspace analysis 777

3.17.4 DOA estimation techniques 779

3.17.4.1 Time-frequency MUSIC 780

3.17.4.2 Time-frequency maximum likelihood method 782

3.17.4.3 Effect of cross-terms 784

3.17.4.4 DOA estimation based on signal stationarization 787

3.17.4.5 DOA estimation based on spatial joint-variable domain

distributions 788

3.17.4.6 DOA estimation of wideband nonstationary signals 788

3.17.5 Joint DOD/DOA estimation in MIMO radar systems 789

3.17.5.1 Signal model 790

3.17.5.2 Joint DOD/DOA estimations 791


Glossary 794

References 794

CHAPTER 18 Source Localization and Tracking 799

Yu Hen Hu


3.18.2 Problem formulation 800

3.18.3 Triangulation 800

3.18.3.1 Distance based triangulation 800

3.18.3.2 Angle based triangulation 801

3.18.3.3 Triangulation: generalizations 802

3.18.4 Signal propagation models 802

3.18.4.1 Time delay estimation 805

3.18.4.2 Angle of arrival estimation 8063.18.5 Source localization algorithms 808

3.18.5.1 Bayesian source localization based on RSSI 808

Contents xix

3.18.5.2 Non-linear least square source localization using RSSI 809

3.18.5.3 Source localization using time difference of arrival 810

3.18.5.4 Source localization using angle of arrival 811

3.18.6 Target tracking algorithm 812

3.18.6.1 Dynamic and observation models 812

3.18.6.2 Sequential Bayesian estimation 813

3.18.6.3 Kalman filter 814


References 815

CHAPTER 19 Array Processing in the Face of Nonidealities 819

Mario Costa, Visa Koivunen, and Mats Viberg


3.19.2 Ideal array signal models 821

3.19.3 Examples of array nonidealities 825

3.19.3.1 Mutual coupling 825

3.19.3.2 Uncertainty in array elements' beampatterns and positions 826

3.19.3.3 Cross-polarization effects 827

3.19.3.4 Departures from narrowband assumption 828

3.19.3.5 Errors due to receiver front-end architectures 828

3.19.3.6 Effects of nonlinear elements 829

3.19.4 Array calibration 829

3.19.5 Model-driven techniques 830

3.19.5.1 Deterministic approach 831

3.19.5.2 Bayesian approach 832

3.19.6 Data-driven techniques 834

3.19.6.1 Local interpolation of the array calibration matrix 834

3.19.6.2 Array interpolation technique 836

3.19.6.3 Wavefield modeling principle and manifold separation

technique 837

3.19.7 Robust methods 842

3.19.7.1 Robust technique based on worst-case performance

optimization and uncertainty sets 843

3.19.8 Array processing examples 846

3.19.8.1 DoA estimation using an ideal uniform linear array and

manifold separation technique 846

3.19.8.2 Robust beamforming using array calibration 848

3.19.8.3 Polynomial rooting techniques for real-world arrays with

nonidealities 849

3.19.8.4 Azimuth, elevation, and polarization estimation 850


References 854

xx Contents

CHAPTER 20 Applications of Array Signal Processing 859

A. Lee Swindlehurst, Brian D. Jeffs, Gonzalo Seco-Granados, and Jian Li

3.20.1 Introduction and background 859

3.20.2 Radar applications 860

3.20.2.1 Space-time adaptive processing 862

3.20.2.2 MIMO radar 870

3.20.3 Radio astronomy 875

3.20.3.1 Synthesis imaging 876

3.20.3.2 Astronomical phased array feeds 885

3.20.3.3 Interference mitigation for radio astronomy 889

3.20.4 Positioning and navigation 893

3.20.4.1 Error sources and the benefits of antenna arrays in GNSS 894

3.20.4.2 Signal model for positioning applications 896

3.20.4.3 Beamforming 898

3.20.4.4 DOA estimation 903

3.20.4.5 Array-based parameter estimators 904

3.20.5 Wireless communications 907

3.20.5.1 Multiple antennas techniques in LTE 907

3.20.5.2 Multiple antennas techniques in WiMAX 913

3.20.5.3 Multiple antenna techniques in IEEE 802.11 915

3.20.6 Biomedical 917

3.20.6.1 Ultrasonic imaging 918

3.20.6.2 EEG and MEG signal processing 918

3.20.6.3 Multi-sensor extracellular probes 923

3.20.7 Sonar 928

3.20.7.1 Sonar arrays 929

3.20.7.2 The undersea acoustic channel 932

3.20.7.3 Matched field processing 935

3.20.7.4 Acoustic vector sensors 937

3.20.8 Microphone arrays 938

3.20.8.1 Aeroacoustic source localization 940

3.20.8.2 Wideband adaptive beamforming 941

3.20.9 Chemical sensor arrays 943


References and Further Reading 945

Index 955

Academic Press Library in Signal Processing - GBV · 2014. 2. 6. · Contents ix 3.06.8...

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