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Bayesian Signal Processing: Classical, Modern and Particle Filtering Methods

Book Description

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.

    Table of Contents

    1. COVER
    2. TITLE PAGE
    3. COPYRIGHT
    4. DEDICATION
    5. PREFACE
      1. REFERENCES TO THE PREFACE
    6. ACKNOWLEDGMENTS
    7. 1: INTRODUCTION
      1. 1.1 INTRODUCTION
      2. 1.2 BAYESIAN SIGNAL PROCESSING
      3. 1.3 SIMULATION-BASED APPROACH TO BAYESIAN PROCESSING
      4. 1.4 BAYESIAN MODEL-BASED SIGNAL PROCESSING
      5. 1.5 NOTATION AND TERMINOLOGY
      6. References
    8. 2: BAYESIAN ESTIMATION
      1. 2.1 INTRODUCTION
      2. 2.2 BATCH BAYESIAN ESTIMATION
      3. 2.3 BATCH MAXIMUM LIKELIHOOD ESTIMATION
      4. 2.4 BATCH MINIMUM VARIANCE ESTIMATION
      5. 2.5 SEQUENTIAL BAYESIAN ESTIMATION
      6. 2.6 SUMMARY
      7. References
    9. 3: SIMULATION-BASED BAYESIAN METHODS
      1. 3.1 INTRODUCTION
      2. 3.2 PROBABILITY DENSITY FUNCTION ESTIMATION
      3. 3.3 SAMPLING THEORY
      4. 3.4 MONTE CARLO APPROACH
      5. 3.5 IMPORTANCE SAMPLING
      6. 3.6 SEQUENTIAL IMPORTANCE SAMPLING
      7. 3.7 SUMMARY
      8. References
    10. 4: STATE–SPACE MODELS FOR BAYESIAN PROCESSING
      1. 4.1 INTRODUCTION
      2. 4.2 CONTINUOUS-TIME STATE–SPACE MODELS
      3. 4.3 SAMPLED-DATA STATE–SPACE MODELS
      4. 4.4 DISCRETE-TIME STATE–SPACE MODELS
      5. 4.5 GAUSS-MARKOV STATE–SPACE MODELS
      6. 4.6 INNOVATIONS MODEL
      7. 4.7 STATE–SPACE MODEL STRUCTURES
      8. 4.8 NONLINEAR (APPROXIMATE) GAUSS-MARKOV STATE–SPACE MODELS
      9. 4.9 SUMMARY
      10. References
    11. 5: CLASSICAL BAYESIAN STATE–SPACE PROCESSORS
      1. 5.1 INTRODUCTION
      2. 5.2 BAYESIAN APPROACH TO THE STATE–SPACE
      3. 5.3 LINEAR BAYESIAN PROCESSOR (LINEAR KALMAN FILTER)
      4. 5.4 LINEARIZED BAYESIAN PROCESSOR (LINEARIZED KALMAN FILTER)
      5. 5.5 EXTENDED BAYESIAN PROCESSOR (EXTENDED KALMAN FILTER)
      6. 5.6 ITERATED-EXTENDED BAYESIAN PROCESSOR (ITERATED-EXTENDED KALMAN FILTER)
      7. 5.7 PRACTICAL ASPECTS OF CLASSICAL BAYESIAN PROCESSORS
      8. 5.8 CASE STUDY: RLC CIRCUIT PROBLEM
      9. 5.9 SUMMARY
      10. References
    12. 6: MODERN BAYESIAN STATE-SPACE PROCESSORS
      1. 6.1 INTRODUCTION
      2. 6.2 SIGMA-POINT (UNSCENTED) TRANSFORMATIONS
      3. 6.3 SIGMA-POINT BAYESIAN PROCESSOR (UNSCENTED KALMAN FILTER)
      4. 6.4 QUADRATURE BAYESIAN PROCESSORS
      5. 6.5 GAUSSIAN SUM (MIXTURE) BAYESIAN PROCESSORS
      6. 6.6 CASE STUDY: 2D-TRACKING PROBLEM
      7. 6.7 SUMMARY
      8. References
    13. 7: PARTICLE-BASED BAYESIAN STATE–SPACE PROCESSORS
      1. 7.1 INTRODUCTION
      2. 7.2 BAYESIAN STATE–SPACE PARTICLE FILTERS
      3. 7.3 IMPORTANCE PROPOSAL DISTRIBUTIONS
      4. 7.4 RESAMPLING
      5. 7.5 STATE–SPACE PARTICLE FILTERING TECHNIQUES
      6. 7.6 PRACTICAL ASPECTS OF PARTICLE FILTER DESIGN
      7. 7.7 CASE STUDY: POPULATION GROWTH PROBLEM
      8. 7.8 SUMMARY
      9. References
    14. 8: JOINT BAYESIAN STATE/PARAMETRIC PROCESSORS
      1. 8.1 INTRODUCTION
      2. 8.2 BAYESIAN APPROACH TO JOINT STATE/PARAMETER ESTIMATION
      3. 8.3 CLASSICAL/MODERN JOINT BAYESIAN STATE/PARAMETRIC PROCESSORS
      4. 8.4 PARTICLE-BASED JOINT BAYESIAN STATE/PARAMETRIC PROCESSORS
      5. 8.5 CASE STUDY: RANDOM TARGET TRACKING USING A SYNTHETIC APERTURE TOWED ARRAY
      6. 8.6 SUMMARY
      7. References
    15. 9: DISCRETE HIDDEN MARKOV MODEL BAYESIAN PROCESSORS
      1. 9.1 INTRODUCTION
      2. 9.2 HIDDEN MARKOV MODELS
      3. 9.3 PROPERTIES OF THE HIDDEN MARKOV MODEL
      4. 9.4 HMM OBSERVATION PROBABILITY: EVALUATION PROBLEM
      5. 9.5 STATE ESTIMATION IN HMM: THE VITERBI TECHNIQUE
      6. 9.6 PARAMETER ESTIMATION IN HMM: THE EM/BAUM-WELCH TECHNIQUE
      7. 9.7 CASE STUDY: TIME-REVERSAL DECODING
      8. 9.8 SUMMARY
      9. References
    16. 10: BAYESIAN PROCESSORS FOR PHYSICS-BASED APPLICATIONS
      1. 10.1 OPTIMAL POSITION ESTIMATION FOR THE AUTOMATIC ALIGNMENT
      2. 10.2 BROADBAND OCEAN ACOUSTIC PROCESSING
      3. 10.3 BAYESIAN PROCESSING FOR BIOTHREATS
      4. 10.4 BAYESIAN PROCESSING FOR THE DETECTION OF RADIOACTIVE SOURCES
      5. References
    17. Appendix A: PROBABILITY AND STATISTICS OVERVIEW
      1. A.1 PROBABILITY THEORY
      2. A.2 GAUSSIAN RANDOM VECTORS
      3. A.3 UNCORRELATED TRANSFORMATION: GAUSSIAN RANDOM VECTORS
    18. INDEX