Preface to Second Edition |
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xiii | |
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xv | |
Preface to First Edition |
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xvii | |
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xxiii | |
Acknowledgments |
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xxvii | |
List of Abbreviations |
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xxix | |
1 Introduction |
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1 | (19) |
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1 | (1) |
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1.2 Bayesian Signal Processing |
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1 | (3) |
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1.3 Simulation-Based Approach to Bayesian Processing |
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4 | (5) |
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1.3.1 Bayesian Particle Filter |
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8 | (1) |
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1.4 Bayesian Model-Based Signal Processing |
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9 | (4) |
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1.5 Notation and Terminology |
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13 | (2) |
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15 | (1) |
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16 | (4) |
2 Bayesian Estimation |
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20 | (32) |
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20 | (1) |
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2.2 Batch Bayesian Estimation |
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20 | (3) |
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2.3 Batch Maximum Likelihood Estimation |
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23 | (11) |
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2.3.1 Expectation—Maximization Approach to Maximum Likelihood |
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27 | (3) |
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2.3.2 EM for Exponential Family of Distributions |
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30 | (4) |
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2.4 Batch Minimum Variance Estimation |
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34 | (3) |
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2.5 Sequential Bayesian Estimation |
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37 | (8) |
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2.5.1 Joint Posterior Estimation |
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41 | (1) |
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2.5.2 Filtering Posterior Estimation |
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42 | (3) |
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2.5.3 Likelihood Estimation |
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45 | (1) |
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45 | (1) |
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46 | (1) |
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47 | (5) |
3 Simulation-Based Bayesian Methods |
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52 | (46) |
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52 | (2) |
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3.2 Probability Density Function Estimation |
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54 | (4) |
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58 | (8) |
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3.3.1 Uniform Sampling Method |
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60 | (4) |
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3.3.2 Rejection Sampling Method |
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64 | (2) |
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66 | (17) |
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71 | (3) |
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3.4.2 Metropolis—Hastings Sampling |
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74 | (1) |
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3.4.3 Random Walk Metropolis—Hastings Sampling |
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75 | (4) |
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79 | (2) |
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81 | (2) |
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83 | (4) |
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3.6 Sequential Importance Sampling |
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87 | (3) |
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90 | (1) |
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91 | (3) |
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94 | (4) |
4 State—Space Models for Bayesian Processing |
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98 | (52) |
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98 | (1) |
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4.2 Continuous-Time State—Space Models |
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99 | (4) |
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4.3 Sampled-Data State—Space Models |
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103 | (4) |
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4.4 Discrete-Time State—Space Models |
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107 | (8) |
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4.4.1 Discrete Systems Theory |
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109 | (6) |
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4.5 Gauss—Markov State—Space Models |
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115 | (8) |
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4.5.1 Continuous-Time/Sampled-Data Gauss—Markov Models |
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115 | (2) |
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4.5.2 Discrete-Time Gauss—Markov Models |
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117 | (6) |
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123 | (1) |
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4.7 State—Space Model Structures |
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124 | (13) |
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124 | (7) |
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4.7.2 State—Space and Time Series Equivalence Models |
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131 | (6) |
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4.8 Nonlinear (Approximate) Gauss—Markov State—Space Models |
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137 | (5) |
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142 | (1) |
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142 | (1) |
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143 | (7) |
5 Classical Bayesian State-Space Processors |
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150 | (51) |
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150 | (1) |
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5.2 Bayesian Approach to the State—Space |
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151 | (2) |
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5.3 Linear Bayesian Processor (Linear Kalman Filter) |
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153 | (9) |
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5.4 Linearized Bayesian Processor (Linearized Kalman Filter) |
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162 | (8) |
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5.5 Extended Bayesian Processor (Extended Kalman Filter) |
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170 | (9) |
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5.6 Iterated-Extended Bayesian Processor (Iterated-Extended Kalman Filter) |
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179 | (6) |
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5.7 Practical Aspects of Classical Bayesian Processors |
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185 | (5) |
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5.8 Case Study: RLC Circuit Problem |
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190 | (4) |
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194 | (1) |
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195 | (1) |
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196 | (5) |
6 Modern Bayesian State—Space Processors |
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201 | (52) |
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201 | (1) |
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6.2 Sigma-Point (Unscented) Transformations |
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202 | (11) |
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6.2.1 Statistical Linearization |
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202 | (3) |
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6.2.2 Sigma-Point Approach |
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205 | (5) |
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6.2.3 SPT for Gaussian Prior Distributions |
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210 | (3) |
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6.3 Sigma-Point Bayesian Processor (Unscented Kalman Filter) |
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213 | (10) |
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6.3.1 Extensions of the Sigma-Point Processor |
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222 | (1) |
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6.4 Quadrature Bayesian Processors |
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223 | (1) |
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6.5 Gaussian Sum (Mixture) Bayesian Processors |
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224 | (4) |
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6.6 Case Study: 2D-Tracking Problem |
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228 | (6) |
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6.7 Ensemble Bayesian Processors (Ensemble Kalman Filter) |
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234 | (11) |
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245 | (2) |
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247 | (2) |
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249 | (4) |
7 Particle-Based Bayesian State—Space Processors |
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253 | (74) |
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253 | (1) |
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7.2 Bayesian State—Space Particle Filters |
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253 | (5) |
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7.3 Importance Proposal Distributions |
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258 | (4) |
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7.3.1 Minimum Variance Importance Distribution |
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258 | (3) |
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7.3.2 Transition Prior Importance Distribution |
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261 | (1) |
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262 | (8) |
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7.4.1 Multinomial Resampling |
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267 | (1) |
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7.4.2 Systematic Resampling |
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268 | (1) |
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7.4.3 Residual Resampling |
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269 | (1) |
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7.5 State—Space Particle Filtering Techniques |
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270 | (20) |
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7.5.1 Bootstrap Particle Filter |
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270 | (4) |
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7.5.2 Auxiliary Particle Filter |
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274 | (7) |
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7.5.3 Regularized Particle Filter |
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281 | (2) |
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7.5.4 MCMC Particle Filter |
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283 | (3) |
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7.5.5 Linearized Particle Filter |
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286 | (4) |
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7.6 Practical Aspects of Particle Filter Design |
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290 | (21) |
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290 | (1) |
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7.6.2 Ensemble Estimation |
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291 | (2) |
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7.6.3 Posterior Probability Validation |
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293 | (11) |
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7.6.4 Model Validation Testing |
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304 | (7) |
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7.7 Case Study: Population Growth Problem |
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311 | (6) |
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317 | (1) |
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318 | (3) |
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321 | (6) |
8 Joint Bayesian State/Parametric Processors |
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327 | (40) |
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327 | (1) |
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8.2 Bayesian Approach to Joint State/Parameter Estimation |
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328 | (2) |
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8.3 Classical/Modern Joint Bayesian State/Parametric Processors |
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330 | (11) |
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8.3.1 Classical Joint Bayesian Processor |
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331 | (7) |
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8.3.2 Modern Joint Bayesian Processor |
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338 | (3) |
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8.4 Particle-Based Joint Bayesian State/Parametric Processors |
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341 | (8) |
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342 | (2) |
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8.4.2 Joint Bayesian State/Parameter Estimation |
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344 | (5) |
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8.5 Case Study: Random Target Tracking Using a Synthetic Aperture Towed Array |
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349 | (10) |
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359 | (1) |
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360 | (2) |
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362 | (5) |
9 Discrete Hidden Markov Model Bayesian Processors |
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367 | (34) |
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367 | (1) |
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367 | (5) |
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9.2.1 Discrete-Time Markov Chains |
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368 | (1) |
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9.2.2 Hidden Markov Chains |
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369 | (3) |
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9.3 Properties of the Hidden Markov Model |
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372 | (1) |
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9.4 HMM Observation Probability: Evaluation Problem |
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373 | (3) |
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9.5 State Estimation in HMM: The Viterbi Technique |
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376 | (8) |
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9.5.1 Individual Hidden State Estimation |
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377 | (3) |
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9.5.2 Entire Hidden State Sequence Estimation |
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380 | (4) |
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9.6 Parameter Estimation in HMM: The EM/Baum—Welch Technique |
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384 | (6) |
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9.6.1 Parameter Estimation with State Sequence Known |
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385 | (2) |
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9.6.2 Parameter Estimation with State Sequence Unknown |
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387 | (3) |
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9.7 Case Study: Time-Reversal Decoding |
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390 | (5) |
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395 | (1) |
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396 | (2) |
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398 | (3) |
10 Sequential Bayesian Detection |
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401 | (83) |
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401 | (1) |
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10.2 Binary Detection Problem |
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402 | (9) |
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10.2.1 Classical Detection |
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403 | (4) |
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10.2.2 Bayesian Detection |
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407 | (1) |
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10.2.3 Composite Binary Detection |
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408 | (3) |
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411 | (12) |
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10.3.1 Probability-of-Error Criterion |
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411 | (1) |
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10.3.2 Bayes Risk Criterion |
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412 | (2) |
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10.3.3 Neyman—Pearson Criterion |
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414 | (2) |
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10.3.4 Multiple (Batch) Measurements |
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416 | (2) |
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10.3.5 Multichannel Measurements |
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418 | (2) |
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10.3.6 Multiple Hypotheses |
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420 | (3) |
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423 | (17) |
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10.4.1 Receiver Operating Characteristic (ROC) Curves |
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424 | (16) |
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10.5 Sequential Detection |
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440 | (7) |
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10.5.1 Sequential Decision Theory |
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442 | (5) |
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10.6 Model-Based Sequential Detection |
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447 | (12) |
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10.6.1 Linear Gaussian Model-Based Processor |
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447 | (4) |
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10.6.2 Nonlinear Gaussian Model-Based Processor |
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451 | (3) |
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10.6.3 Non-Gaussian Model-Based Processor |
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454 | (5) |
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10.7 Model-Based Change (Anomaly) Detection |
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459 | (9) |
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10.7.1 Model-Based Detection |
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460 | (1) |
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10.7.2 Optimal Innovations Detection |
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461 | (2) |
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10.7.3 Practical Model-Based Change Detection |
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463 | (5) |
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10.8 Case Study: Reentry Vehicle Change Detection |
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468 | (4) |
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10.8.1 Simulation Results |
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471 | (1) |
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472 | (3) |
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475 | (2) |
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477 | (7) |
11 Bayesian Processors for Physics-Based Applications |
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484 | (92) |
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11.1 Optimal Position Estimation for the Automatic Alignment |
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484 | (13) |
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485 | (2) |
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11.1.2 Stochastic Modeling of Position Measurements |
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487 | (2) |
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11.1.3 Bayesian Position Estimation and Detection |
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489 | (1) |
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11.1.4 Application: Beam Line Data |
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490 | (2) |
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11.1.5 Results: Beam Line (KDP Deviation) Data |
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492 | (2) |
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11.1.6 Results: Anomaly Detection |
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494 | (3) |
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11.2 Sequential Detection of Broadband Ocean Acoustic Sources |
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497 | (23) |
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498 | (2) |
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11.2.2 Broadband State—Space Ocean Acoustic Propagators |
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500 | (4) |
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11.2.3 Discrete Normal-Mode State—Space Representation |
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504 | (1) |
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11.2.4 Broadband Bayesian Processor |
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504 | (1) |
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11.2.5 Broadband Particle Filters |
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505 | (2) |
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11.2.6 Broadband Bootstrap Particle Filter |
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507 | (2) |
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11.2.7 Bayesian Performance Metrics |
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509 | (1) |
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11.2.8 Sequential Detection |
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509 | (3) |
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11.2.9 Broadband BSP Design |
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512 | (8) |
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520 | (1) |
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11.3 Bayesian Processing for Biothreats |
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520 | (8) |
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521 | (3) |
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11.3.2 Parameter Estimation |
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524 | (1) |
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11.3.3 Bayesian Processor Design |
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525 | (1) |
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526 | (2) |
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11.4 Bayesian Processing for the Detection of Radioactive Sources |
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528 | (13) |
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11.4.1 Physics-Based Processing Model |
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528 | (3) |
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11.4.2 Radionuclide Detection |
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531 | (4) |
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535 | (4) |
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539 | (1) |
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540 | (1) |
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11.4.6 Radionuclide Detection |
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540 | (1) |
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541 | (1) |
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11.5 Sequential Threat Detection: An X-ray Physics-Based Approach |
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541 | (13) |
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11.5.1 Physics-Based Models |
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543 | (4) |
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11.5.2 X-ray State—Space Simulation |
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547 | (2) |
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11.5.3 Sequential Threat Detection |
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549 | (5) |
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554 | (1) |
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11.6 Adaptive Processing for Shallow Ocean Applications |
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554 | (18) |
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11.6.1 State—Space Propagator |
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555 | (7) |
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562 | (3) |
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11.6.3 Model-Based Ocean Acoustic Processing |
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565 | (7) |
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572 | (1) |
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572 | (4) |
Appendix: Probability and Statistics Overview |
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576 | (8) |
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576 | (6) |
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A.2 Gaussian Random Vectors |
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582 | (1) |
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A.3 Uncorrelated Transformation: Gaussian Random Vectors |
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583 | (1) |
References |
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584 | (1) |
Index |
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585 | |