Bayesian Signal Processing : Classical, Modern and Particle Filtering Methods

by James V. Candy (University of California, Lawrence Livermore National Laboratory )

• ISBN13: 9780470430576
• ISBN10: 0470430575
• Format: eBook
• Copyright: 2009-10-01
• Publisher: Wiley-Interscience
• More Book Details
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Summary

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

Preface

References

Acknowledgments

Introduction

Introduction

Bayesian Signal Processing

Simulation-Based Approach to Bayesian Processing

Bayesian Model-Based Signal Processing

Notation and Terminology

References

Problems

Bayesian Estimation

Introduction

Batch Bayesian Estimation

Batch Maximum Likelihood Estimation

Batch Minimum Variance Estimation

Sequential Bayesian Estimation

Summary

References

Problems

Simulation-Based Bayesian Methods

Introduction

Probability Density Function Estimation

Sampling Theory

Monte Carlo Approach

Importance Sampling

Sequential Importance Sampling

Summary

References

Problems

State-Space Models for Bayesian Processing

Introduction

Continuous-Time State-Space Models

Sampled-Data State-Space Models

Discrete-Time State-Space Models

Gauss-Markov State-Space Models

Innovations Model

State-Space Model Structures

Nonlinear (Approximate) Gauss-Markov State-Space Models

Summary

References

Problems

Classical Bayesian State-Space Processors

Introduction

Bayesian Approach to the State-Space

Linear Bayesian Processor

Linearized Bayesian Processor

Extended Bayesian Processor

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

Practical Aspects of Classical Bayesian Processors

Case Study: RLC Circuit Problem

Summary

References

Problems

Modern Bayesian State-Space Processors

Introduction

Sigma-Point (Unscented) Transformations

Sigma-Point Bayesian Processor

Quadrature Bayesian Processors

Gaussian Sum (Mixture) Bayesian Processors

Case Study: 2D-Tracking Problem

Summary

References

Problems

Particle-Based Bayesian State-Space Processors

Introduction

Bayesian State-Space Particle Filters

Importance Proposal Distributions

Resampling

State-Space Particle Filtering Techniques

Practical Aspects of Particle Filter Design

Case Study: Population Growth Problem

Summary

References

Problems

Joint Bayesian State/Parametric Processors

Introduction

Bayesian Approach to Joint State/Parameter Estimation

Classical/Modern Joint Bayesian State/Parametric Processors

Classical Joint Bayesian Processor

Modern Joint Bayesian Processor

Particle-Based Joint Bayesian State/Parametric Processors

Case Study: Random Target Tracking using a Synthetic Aperture Towed Array

Summary

References

Problems

Discrete Hidden Markov Model Bayesian Processors

Introduction

Hidden Markov Models

Properties of the Hidden Markov Model

HMM Observation Probability: Evaluation Problem

State Estimation in HMM: The Viterbi Technique

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

Case Study: Time-Reversal Decoding

Summary

References

Problems

Bayesian Processors for Physics-Based Applications

Optimal Position Estimation for the Automatic Alignment

Broadband Ocean Acoustic Processing

Bayesian Processing for Biothreats

Bayesian Processing for the Detection of Radioactive Sources

References

Probability & Statistics Overview

Probability Theory

Gaussian Random Vectors

Uncorrelated Transformation: Gaussian Random Vectors

Referencess

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