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Bayesian Signal Processing. Classical, Modern and Particle Filtering Methods. Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control

  • ID: 2170669
  • April 2009
  • 472 Pages
  • John Wiley and Sons Ltd
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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 READ MORE >

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1. Introduction.

1.1 Introduction.

1.2 Bayesian Signal Processing.

1.3 Simulation–Based Approach to Bayesian Processing.

1.4 Bayesian Model–Based Signal Processing.

1.5 Notation and Terminology.



2. Bayesian Estimation.

2.1 Introduction.

2.2 Batch Bayesian Estimation.

2.3 Batch Maximum Likelihood Estimation.

2.4 Batch Minimum Variance Estimation.

2.5 Sequential Bayesian Estimation.

2.6 Summary.



3. Simulation–Based Bayesian Methods.

3.1 Introduction.

3.2 Probability Density Function Estimation.

3.3 Sampling Theory.

3.4 Monte Carlo Approach.

3.5 Importance Sampling.

3.6 Sequential Importance Sampling.

3.7 Summary.



4. State–Space Models for Bayesian Processing.

4.1 Introduction.

4.2 Continuous–Time State–Space Models.

4.3 Sampled–Data State–Space Models.

4.4 Discrete–Time State–Space Models.

4.5 Gauss–Markov State–Space Models.

4.6 Innovations Model.

4.7 State–Space Model Structures.

4.8 Nonlinear (Approximate) Gauss–Markov State–Space Models.

4.9 Summary.



5. Classical Bayesian State–Space Processors.

5.1 Introduction.

5.2 Bayesian Approach to the State–Space.

5.3 Linear Bayesian Processor (Linear Kalman Filter).

5.4 Linearized Bayesian Processor (Linearized Kalman Filter).

5.5 Extended Bayesian Processor (Extended Kalman Filter).

5.6 Iterated–Extended Bayesian Processor (Iterated–Extended Kalman Filter).

5.7 Practical Aspects of Classical Bayesian Processors.

5.8 Case Study: RLC Circuit Problem.

5.9 Summary.



6. Modern Bayesian State–Space Processors.

6.1 Introduction.

6.2 Sigma–Point (Unscented) Transformations.

6.3 Sigma–Point Bayesian Processor (Unscented Kalman Filter).

6.4 Quadrature Bayesian Processors.

6.5 Gaussian Sum (Mixture) Bayesian Processors.

6.6 Case Study: 2D–Tracking Problem.

6.7 Summary.



7. Particle–Based Bayesian State–Space Processors.

7.1 Introduction.

7.2 Bayesian State–Space Particle Filters.

7.3 Importance Proposal Distributions.

7.4 Resampling.

7.5 State–Space Particle Filtering Techniques.

7.6 Practical Aspects of Particle Filter Design.

7.7 Case Study: Population Growth Problem.

7.8 Summary.



8. Joint Bayesian State/Parametric Processors.

8.1 Introduction.

8.2 Bayesian Approach to Joint State/Parameter Estimation.

8.3 Classical/Modern Joint Bayesian State/Parametric Processors.

8.3.1 Classical Joint Bayesian Processor.

8.3.2 Modern Joint Bayesian Processor.

8.4 Particle–Based Joint Bayesian State/Parametric Processors.

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

8.6 Summary.



9. Discrete Hidden Markov Model Bayesian Processors.

9.1 Introduction.

9.2 Hidden Markov Models.

9.3 Properties of the Hidden Markov Model.

9.4 HMM Observation Probability: Evaluation Problem.

9.5 State Estimation in HMM: The Viterbi Technique.

9.6 Parameter Estimation in HMM: The EM/Baum–Welch Technique.

9.7 Case Study: Time–Reversal Decoding.

9.8 Summary.



10. Bayesian Processors for Physics–Based Applications.

10.1 Optimal Position Estimation for the Automatic Alignment.

10.2 Broadband Ocean Acoustic Processing.

10.3 Bayesian Processing for Biothreats.

10.4 Bayesian Processing for the Detection of Radioactive Sources.


Appendix A. Probability & Statistics Overview.

A.1 Probability Theory.

A.2 Gaussian Random Vectors.

A.3 Uncorrelated Transformation: Gaussian Random Vectors.


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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.

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