| Preface to the Second Edition | p. v |
| Preface | p. vii |
| Introduction | |
| Hidden Markov Model Processing | p. 3 |
| Models, Objectives, and Methods | p. 3 |
| Book Outline | p. 3 |
| Discrete-Time HMM Estimation | |
| Discrete States and Discrete Observations | p. 15 |
| Introduction | p. 15 |
| Model | p. 16 |
| Change of Measure | p. 20 |
| Unnormalized Estimates and Bayes' Formula | p. 26 |
| A General Unnormalized Recursive Filter | p. 28 |
| States, Transitions, and Occupation Times | p. 30 |
| Parameter Reestimation | p. 33 |
| Recursive Parameter Estimation | p. 38 |
| Quantized Observations | p. 40 |
| The Dependent Case | p. 43 |
| Problems and Notes | p. 52 |
| Continuous-Range Observations | p. 55 |
| Introduction | p. 55 |
| State and Observation Processes | p. 55 |
| Conditional Expectations | p. 56 |
| Change of Measure | p. 58 |
| Filter-Based State Estimation | p. 61 |
| Smoother-Based State Estimation | p. 65 |
| Vector Observations | p. 72 |
| Recursive Parameter Estimation | p. 74 |
| HMMs with Colored Noise | p. 77 |
| Mixed-State HMM Estimation | p. 79 |
| Problems and Notes | p. 80 |
| Continuous-Range States and Observations | p. 83 |
| Introduction | p. 83 |
| Linear Dynamics and Parameters | p. 83 |
| The ARMAX Model | p. 87 |
| Nonlinear Dynamics | p. 90 |
| Kalman Filter | p. 98 |
| State and Mode Estimation for Discrete-Time Jump Markov Systems | p. 106 |
| Example | p. 139 |
| Problems and Notes | p. 139 |
| A General Recursive Filter | p. 143 |
| Introduction | p. 143 |
| Signal and Observations | p. 143 |
| Change of Measure | p. 144 |
| Recursive Estimates | p. 146 |
| Extended Kalman Filter | p. 148 |
| Parameter Identification and Tracking | p. 149 |
| Formulation in Terms of Transition Densities | p. 153 |
| Dependent Case | p. 155 |
| Recursive Prediction Error Estimation | p. 159 |
| Problems and Notes | p. 161 |
| Practical Recursive Filters | p. 163 |
| Introduction | p. 163 |
| Recursive Prediction Error HMM Algorithm | p. 166 |
| Example: Quadrature Amplitude Modulation | p. 171 |
| Example: Frequency Modulation | p. 179 |
| Coupled-Conditional Filters | p. 187 |
| Notes | p. 194 |
| Continuous-Time HMM Estimation | |
| Discrete-Range States and Observations | p. 197 |
| Introduction | p. 197 |
| Dynamics | p. 197 |
| A General Finite-Dimensional Filter | p. 203 |
| Parameter Estimation | p. 209 |
| Problems and Notes | p. 211 |
| Markov Chains in Brownian Motion | p. 213 |
| Introduction | p. 213 |
| The Model | p. 213 |
| A General Finite-Dimensional Filter | p. 214 |
| States, Transitions, and Occupation Times | p. 216 |
| Parameter Estimation | p. 219 |
| Finite-Dimensional Predictors | p. 220 |
| A Non-Markov Finite-Dimensional Filter | p. 225 |
| Problems and Notes | p. 232 |
| Two-Dimensional HMM Estimation | |
| Hidden Markov Random Fields | p. 237 |
| Discrete Signal and Observations | p. 237 |
| HMRF Observed in Gaussian Noise | p. 254 |
| Continuous-State HMRF | p. 260 |
| Example: A Mixed HMRF | p. 264 |
| Problems and Notes | p. 269 |
| HMM Optimal Control | |
| Discrete-Time HMM Control | p. 273 |
| Control of Finite-State Processes | p. 273 |
| More General Processes | p. 279 |
| A Dependent Case | p. 284 |
| Problems and Notes | p. 288 |
| Risk-Sensitive Control of HMM | p. 291 |
| Introduction | p. 291 |
| The Risk-Sensitive Control Problem | p. 292 |
| Connection with H∞ Control | p. 297 |
| Connection with H2 or Risk-Neutral Control | p. 299 |
| A Finite-Dimensional Example | p. 303 |
| Risk-Sensitive LQG Control | p. 309 |
| Problems and Notes | p. 313 |
| Continuous-Time HMM Control | p. 315 |
| Introduction | p. 315 |
| Robust Control of a Partially Observed Markov Chain | p. 315 |
| The Dependent Case | p. 328 |
| Hybrid Conditionally Linear Process | p. 340 |
| Problems and Notes | p. 348 |
| Basic Probability Concepts | p. 351 |
| Continuous-Time Martingale Representation | p. 359 |
| References | p. 365 |
| Author Index | p. 373 |
| Subject Index | p. 375 |
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