Bayesian Signal Processing : Classical, Modern, and Particle Filtering Methods

by Candy, James V.

• ISBN13: 9780470180945
• ISBN10: 0470180943
• Format: Hardcover
• Copyright: 2009-04-06
• Publisher: Wiley-Interscience
• More Book Details
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Summary

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

Author Biography

JAMES V. CANDY, PhD, is Chief Scientist for Engineering, founder, and former director of the Center for Advanced Signal & Image Sciences at the Lawrence Livermore National Laboratory. Dr. Candy is also an Adjunct Full Professor at the University of California, Santa Barbara, a Fellow of the IEEE, and a Fellow of the Acoustical Society of America. Dr. Candy has published more than 225 journal articles, book chapters, and technical reports. He is also the author of Signal Processing: Model-Based Approach, Signal Processing: A Modern Approach, and Model-Based Signal Processing (Wiley). Dr. Candy was awarded the IEEE Distinguished Technical Achievement Award for his development of model-based signal processing and the Acoustical Society of America Helmholtz-Rayleigh Interdisciplinary Silver Medal for his contributions to acoustical signal processing and underwater acoustics.

Table of Contents

Preface	p. xiii
References to the Preface	p. xix
Acknowledgments	p. xxiii
Introduction	p. 1
Introduction	p. 1
Bayesian Signal Processing	p. 1
Simulation-Based Approach to Bayesian Processing	p. 4
Bayesian Model-Based Signal Processing	p. 8
Notation and Terminology	p. 12
References	p. 14
Problems	p. 15
Bayesian Estimation	p. 19
Introduction	p. 19
Batch Bayesian Estimation	p. 19
Batch Maximum Likelihood Estimation	p. 22
Expectation-Maximization Approach to Maximum Likelihood	p. 25
EM for Exponential Family of Distributions	p. 30
Batch Minimum Variance Estimation	p. 33
Sequential Bayesian Estimation	p. 36
Joint Posterior Estimation	p. 39
Filtering Posterior Estimation	p. 41
Summary	p. 43
References	p. 44
Problems	p. 45
Simulation-Based Bayesian Methods	p. 51
Introduction	p. 51
Probability Density Function Estimation	p. 53
Sampling Theory	p. 56
Uniform Sampling Method	p. 58
Rejection Sampling Method	p. 62
Monte Carlo Approach	p. 64
Markov Chains	p. 70
Metropolis-Hastings Sampling	p. 71
Random Walk Metropolis-Hastings Sampling	p. 73
Gibbs Sampling	p. 75
Slice Sampling	p. 78
Importance Sampling	p. 81
Sequential Importance Sampling	p. 84
Summary	p. 87
References	p. 87
Problems	p. 90
State-Space Models for Bayesian Processing	p. 95
Introduction	p. 95
Continuous-Time State-Space Models	p. 96
Sampled-Data State-Space Models	p. 100
Discrete-Time State-Space Models	p. 104
Discrete Systems Theory	p. 107
Gauss-Markov State-Space Models	p. 112
Continuous-Time/Sampled-Data Gauss-Markov Models	p. 112
Discrete-Time Gauss-Markov Models	p. 114
Innovations Model	p. 120
State-Space Model Structures	p. 121
Time Series Models	p. 121
State-Space and Time Series Equivalence Models	p. 129
Nonlinear (Approximate) Gauss-Markov State-Space Models	p. 135
Summary	p. 139
References	p. 140
Problems	p. 141
Classical Bayesian State-Space Processors	p. 147
Introduction	p. 147
Bayesian Approach to the State-Space	p. 147
Linear Bayesian Processor (Linear Kalman Filter)	p. 150
Linearized Bayesian Processor (Linearized Kalman Filter)	p. 160
Extended Bayesian Processor (Extended Kalman Filter)	p. 167
Iterated-Extended Bayesian Processor (Iterated-Extended Kalman Filter)	p. 174
Practical Aspects of Classical Bayesian Processors	p. 182
Case Study: RLC Circuit Problem	p. 186
Summary	p. 191
References	p. 191
Problems	p. 193
Modern Bayesian State-Space Processors	p. 197
Introduction	p. 197
Sigma-Point (Unscented) Transformations	p. 198
Statistical Linearization	p. 198
Sigma-Point Approach	p. 200
SPT for Gaussian Prior Distributions	p. 205
Sigma-Point Bayesian Processor (Unscented Kalman Filter)	p. 209
Extensions of the Sigma-Point Processor	p. 218
Quadrature Bayesian Processors	p. 218
Gaussian Sum (Mixture) Bayesian Processors	p. 220
Case Study: 2D-Tracking Problem	p. 224
Summary	p. 230
References	p. 231
Problems	p. 233
Particle-Based Bayesian State-Space Processors	p. 237
Introduction	p. 237
Bayesian State-Space Particle Filters	p. 237
Importance Proposal Distributions	p. 242
Minimum Variance Importance Distribution	p. 242
Transition Prior Importance Distribution	p. 245
Resampling	p. 246
Multinomial Resampling	p. 249
Systematic Resampling	p. 251
Residual Resampling	p. 251
State-Space Particle Filtering Techniques	p. 252
Bootstrap Particle Filter	p. 253
Auxiliary Particle Filter	p. 261
Regularized Particle Filter	p. 264
MCMC Particle Filter	p. 266
Linearized Particle Filter	p. 270
Practical Aspects of Particle Filter Design	p. 272
Posterior Probability Validation	p. 273
Model Validation Testing	p. 277
Case Study: Population Growth Problem	p. 285
Summary	p. 289
References	p. 290
Problems	p. 293
Joint Bayesian State/Parametric Processors	p. 299
Introduction	p. 299
Bayesian Approach to Joint State/Parameter Estimation	p. 300
Classical/Modern Joint Bayesian State/Parametric Processors	p. 302
Classical Joint Bayesian Processor	p. 303
Modern Joint Bayesian Processor	p. 311
Particle-Based Joint Bayesian State/Parametric Processors	p. 313
Case Study: Random Target Tracking Using a Synthetic Aperture Towed Array	p. 318
Summary	p. 327
References	p. 328
Problems	p. 330
Discrete Hidden Markov Model Bayesian Processors	p. 335
Introduction	p. 335
Hidden Markov Models	p. 335
Discrete-Time Markov Chains	p. 336
Hidden Markov Chains	p. 337
Properties of the Hidden Markov Model	p. 339
HMM Observation Probability: Evaluation Problem	p. 341
State Estimation in HMM: The Viterbi Technique	p. 345
Individual Hidden State Estimation	p. 345
Entire Hidden State Sequence Estimation	p. 347
Parameter Estimation in HMM: The EM/Baum-Welch Technique	p. 350
Parameter Estimation with State Sequence Known	p. 352
Parameter Estimation with State Sequence Unknown	p. 354
Case Study: Time-Reversal Decoding	p. 357
Summary	p. 362
References	p. 363
Problems	p. 365
Bayesian Processors for Physics-Based Applications	p. 369
Optimal Position Estimation for the Automatic Alignment	p. 369
Background	p. 369
Stochastic Modeling of Position Measurements	p. 372
Bayesian Position Estimation and Detection	p. 374
Application: Beam Line Data	p. 375
Results: Beam Line (KDP Deviation) Data	p. 377
Results: Anomaly Detection	p. 379
Broadband Ocean Acoustic Processing	p. 382
Background	p. 382
Broadband State-Space Ocean Acoustic Propagators	p. 384
Broadband Bayesian Processing	p. 389
Broadband BSP Design	p. 393
Results	p. 395
Bayesian Processing for Biothreats	p. 397
Background	p. 397
Parameter Estimation	p. 400
Bayesian Processor Design	p. 401
Results	p. 403
Bayesian Processing for the Detection of Radioactive Sources	p. 404
Background	p. 404
Physics-Based Models	p. 404
Gamma-Ray Detector Measurements	p. 407
Bayesian Physics-Based Processor	p. 410
Physics-Based Bayesian Deconvolution Processor	p. 412
Results	p. 415
References	p. 417
Probability & Statistics Overview	p. 423
Probability Theory	p. 423
Gaussian Random Vectors	p. 429
Uncorrelated Transformation: Gaussian Random Vectors	p. 430
References	p. 430
Index	p. 431
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