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Bayesian Signal Processing: Classical, Modern, and Particle Filtering Methods / Edition 1
     

Bayesian Signal Processing: Classical, Modern, and Particle Filtering Methods / Edition 1

5.0 1
by James V. Candy, Candy
 

ISBN-10: 0470180943

ISBN-13: 9780470180945

Pub. Date: 04/06/2009

Publisher: Wiley

New Bayesian approach helps you solve tough problems in signal processing with ease

Signal processing is based on this fundamental concept—the extraction of critical information from noisy, uncertain data. Most techniques rely on underlying Gaussian assumptions for a solution, but what happens when these assumptions are erroneous? Bayesian techniques

Overview

New Bayesian approach helps you solve tough problems in signal processing with ease

Signal processing is based on this fundamental concept—the extraction of critical information from noisy, uncertain data. Most techniques rely on underlying Gaussian assumptions for a solution, but what happens when these assumptions are erroneous? Bayesian techniques circumvent this limitation by offering a completely different approach that can easily incorporate non-Gaussian and nonlinear processes along with all of the usual methods currently available.

This text enables readers to fully exploit the many advantages of the "Bayesian approach" to model-based signal processing. It clearly demonstrates the features of this powerful approach compared to the pure statistical methods found in other texts. Readers will discover how easily and effectively the Bayesian approach, coupled with the hierarchy of physics-based models developed throughout, can be applied to signal processing problems that previously seemed unsolvable.

Bayesian Signal Processing features the latest generation of processors (particle filters) that have been enabled by the advent of high-speed/high-throughput computers. The Bayesian approach is uniformly developed in this book's algorithms, examples, applications, and case studies. Throughout this book, the emphasis is on nonlinear/non-Gaussian problems; however, some classical techniques (e.g. Kalman filters, unscented Kalman filters, Gaussian sums, grid-based filters, et al) are included to enable readers familiar with those methods to draw parallels between the two approaches.

Special features include:

  • Unified Bayesian treatment starting from the basics (Bayes's rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation techniques (sequential Monte Carlo sampling)
  • Incorporates "classical" Kalman filtering for linear, linearized, and nonlinear systems; "modern" unscented Kalman filters; and the "next-generation" Bayesian particle filters
  • Examples illustrate how theory can be applied directly to a variety of processing problems
  • Case studies demonstrate how the Bayesian approach solves real-world problems in practice
  • MATLAB notes at the end of each chapter help readers solve complex problems using readily available software commands and point out software packages available
  • Problem sets test readers' knowledge and help them put their new skills into practice

The basic Bayesian approach is emphasized throughout this text in order to enable the processor to rethink the approach to formulating and solving signal processing problems from the Bayesian perspective. This text brings readers from the classical methods of model-based signal processing to the next generation of processors that will clearly dominate the future of signal processing for years to come. With its many illustrations demonstrating the applicability of the Bayesian approach to real-world problems in signal processing, this text is essential for all students, scientists, and engineers who investigate and apply signal processing to their everyday problems.

Product Details

ISBN-13:
9780470180945
Publisher:
Wiley
Publication date:
04/06/2009
Series:
Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control Series , #54
Pages:
472
Product dimensions:
6.50(w) x 9.50(h) x 1.10(d)

Table of Contents

Preface xiii

References to the Preface xix

Acknowledgments xxiii

1 Introduction 1

1.1 Introduction 1

1.2 Bayesian Signal Processing 1

1.3 Simulation-Based Approach to Bayesian Processing 4

1.4 Bayesian Model-Based Signal Processing 8

1.5 Notation and Terminology 12

References 14

Problems 15

2 Bayesian Estimation 19

2.1 Introduction 19

2.2 Batch Bayesian Estimation 19

2.3 Batch Maximum Likelihood Estimation 22

2.3.1 Expectation-Maximization Approach to Maximum Likelihood 25

2.3.2 EM for Exponential Family of Distributions 30

2.4 Batch Minimum Variance Estimation 33

2.5 Sequential Bayesian Estimation 36

2.5.1 Joint Posterior Estimation 39

2.5.2 Filtering Posterior Estimation 41

2.6 Summary 43

References 44

Problems 45

3 Simulation-Based Bayesian Methods 51

3.1 Introduction 51

3.2 Probability Density Function Estimation 53

3.3 Sampling Theory 56

3.3.1 Uniform Sampling Method 58

3.3.2 Rejection Sampling Method 62

3.4 Monte Carlo Approach 64

3.4.1 Markov Chains 70

3.4.2 Metropolis-Hastings Sampling 71

3.4.3 Random Walk Metropolis-Hastings Sampling 73

3.4.4 Gibbs Sampling 75

3.4.5 Slice Sampling 78

3.5 Importance Sampling 81

3.6 Sequential Importance Sampling 84

3.7 Summary 87

References 87

Problems 90

4 State-Space Models for Bayesian Processing 95

4.1 Introduction 95

4.2 Continuous-Time State-Space Models 96

4.3 Sampled-Data State-Space Models 100

4.4 Discrete-Time State-Space Models 104

4.4.1 Discrete Systems Theory 107

4.5 Gauss-Markov State-Space Models 112

4.5.1 Continuous-Time/Sampled-Data Gauss-Markov Models 112

4.5.2 Discrete-Time Gauss-Markov Models 114

4.6 Innovations Model 120

4.7State-Space Model Structures 121

4.7.1 Time Series Models 121

4.7.2 State-Space and Time Series Equivalence Models 129

4.8 Nonlinear (Approximate) Gauss-Markov State-Space Models 135

4.9 Summary 139

References 140

Problems 141

5 Classical Bayesian State-Space Processors 147

5.1 Introduction 147

5.2 Bayesian Approach to the State-Space 147

5.3 Linear Bayesian Processor (Linear Kalman Filter) 150

5.4 Linearized Bayesian Processor (Linearized Kalman Filter) 160

5.5 Extended Bayesian Processor (Extended Kalman Filter) 167

5.6 Iterated-Extended Bayesian Processor (Iterated-Extended Kalman Filter) 174

5.7 Practical Aspects of Classical Bayesian Processors 182

5.8 Case Study: RLC Circuit Problem 186

5.9 Summary 191

References 191

Problems 193

6 Modern Bayesian State-Space Processors 197

6.1 Introduction 197

6.2 Sigma-Point (Unscented) Transformations 198

6.2.1 Statistical Linearization 198

6.2.2 Sigma-Point Approach 200

6.2.3 SPT for Gaussian Prior Distributions 205

6.3 Sigma-Point Bayesian Processor (Unscented Kalman Filter) 209

6.3.1 Extensions of the Sigma-Point Processor 218

6.4 Quadrature Bayesian Processors 218

6.5 Gaussian Sum (Mixture) Bayesian Processors 220

6.6 Case Study: 2D-Tracking Problem 224

6.7 Summary 230

References 231

Problems 233

7 Particle-Based Bayesian State-Space Processors 237

7.1 Introduction 237

7.2 Bayesian State-Space Particle Filters 237

7.3 Importance Proposal Distributions 242

7.3.1 Minimum Variance Importance Distribution 242

7.3.2 Transition Prior Importance Distribution 245

7.4 Resampling 246

7.4.1 Multinomial Resampling 249

7.4.2 Systematic Resampling 251

7.4.3 Residual Resampling 251

7.5 State-Space Particle Filtering Techniques 252

7.5.1 Bootstrap Particle Filter 253

7.5.2 Auxiliary Particle Filter 261

7.5.3 Regularized Particle Filter 264

7.5.4 MCMC Particle Filter 266

7.5.5 Linearized Particle Filter 270

7.6 Practical Aspects of Particle Filter Design 272

7.6.1 Posterior Probability Validation 273

7.6.2 Model Validation Testing 277

7.7 Case Study: Population Growth Problem 285

7.8 Summary 289

References 290

Problems 293

8 Joint Bayesian State/Parametric Processors 299

8.1 Introduction 299

8.2 Bayesian Approach to Joint State/Parameter Estimation 300

8.3 Classical/Modern Joint Bayesian State/Parametric Processors 302

8.3.1 Classical Joint Bayesian Processor 303

8.3.2 Modern Joint Bayesian Processor 311

8.4 Particle-Based Joint Bayesian State/Parametric Processors 313

8.5 Case Study: Random Target Tracking Using a Synthetic Aperture Towed Array 318

8.6 Summary 327

References 328

Problems 330

9 Discrete Hidden Markov Model Bayesian Processors 335

9.1 Introduction 335

9.2 Hidden Markov Models 335

9.2.1 Discrete-Time Markov Chains 336

9.2.2 Hidden Markov Chains 337

9.3 Properties of the Hidden Markov Model 339

9.4 HMM Observation Probability: Evaluation Problem 341

9.5 State Estimation in HMM: The Viterbi Technique 345

9.5.1 Individual Hidden State Estimation 345

9.5.2 Entire Hidden State Sequence Estimation 347

9.6 Parameter Estimation in HMM: The EM/Baum-Welch Technique 350

9.6.1 Parameter Estimation with State Sequence Known 352

9.6.2 Parameter Estimation with State Sequence Unknown 354

9.7 Case Study: Time-Reversal Decoding 357

9.8 Summary 362

References 363

Problems 365

10 Bayesian Processors for Physics-Based Applications 369

10.1 Optimal Position Estimation for the Automatic Alignment 369

10.1.1 Background 369

10.1.2 Stochastic Modeling of Position Measurements 372

10.1.3 Bayesian Position Estimation and Detection 374

10.1.4 Application: Beam Line Data 375

10.1.5 Results: Beam Line (KDP Deviation) Data 377

10.1.6 Results: Anomaly Detection 379

10.2 Broadband Ocean Acoustic Processing 382

10.2.1 Background 382

10.2.2 Broadband State-Space Ocean Acoustic Propagators 384

10.2.3 Broadband Bayesian Processing 389

10.2.4 Broadband BSP Design 393

10.2.5 Results 395

10.3 Bayesian Processing for Biothreats 397

10.3.1 Background 397

10.3.2 Parameter Estimation 400

10.3.3 Bayesian Processor Design 401

10.3.4 Results 403

10.4 Bayesian Processing for the Detection of Radioactive Sources 404

10.4.1 Background 404

10.4.2 Physics-Based Models 404

10.4.3 Gamma-Ray Detector Measurements 407

10.4.4 Bayesian Physics-Based Processor 410

10.4.5 Physics-Based Bayesian Deconvolution Processor 412

10.4.6 Results 415

References 417

Appendix A Probability & Statistics Overview 423

A.1 Probability Theory 423

A.2 Gaussian Random Vectors 429

A.3 Uncorrelated Transformation: Gaussian Random Vectors 430

References 430

Index 431

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