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Summary
More than a decade ago, world-renowned control systems authority Frank L.1 Lewis introduced what would become a standard reference on estimation, under the title Optimal Estimation. While the book is still being used by professionals and leading universities throughout the world, the time has come for a new edition of this classic work, and Lewis enlisted the aid of two accomplished experts to bring the book current with the estimation methods driving today's high-performance systems.
Table of Contents
| Preface | p. xv |
| Authors | p. xvii |
| Subject | p. xix |
| Audience | p. xxi |
| Optimal Estimation | p. 1 |
| Classical Estimation Theory | p. 3 |
| Mean-Square Estimation | p. 3 |
| Mean-Square Estimation of a Random Variable X by a Constant | p. 4 |
| Mean-Square Estimation of a Random Variable X Given a Random Variable Z: General Case | p. 5 |
| The Orthogonality Principle | p. 13 |
| Linear Mean-Square Estimation of a Random Variable X Given a Random Variable Z | p. 14 |
| Maximum-Likelihood Estimation | p. 19 |
| Nonlinear Maximum-Likelihood Estimation | p. 19 |
| Linear Gaussian Measurements | p. 20 |
| The Cramer-Rao Bound | p. 25 |
| Recursive Estimation | p. 28 |
| Sequential Processing of Measurements | p. 28 |
| Sequential Maximum-Likelihood Estimation | p. 31 |
| Prewhitening of Data | p. 33 |
| Wiener Filtering | p. 34 |
| The Linear Estimation Problem | p. 36 |
| Solution of the Wiener-Hopf Equation | p. 38 |
| Infinite-Delay Steady-State Smoothing | p. 38 |
| Causal Steady-State Filtering | p. 41 |
| Problems | p. 50 |
| Discrete-Time Kalman Filter | p. 59 |
| Deterministic State Observer | p. 59 |
| Linear Stochastic Systems | p. 64 |
| Propagation of Means and Covariances | p. 65 |
| Statistical Steady-State and Spectral Densities | p. 68 |
| The Discrete-Time Kalman Filter | p. 70 |
| Kalman Filter Formulations | p. 71 |
| Discrete Measurements of Continuous-Time Systems | p. 84 |
| Discretization of Continuous Stochastic Systems | p. 85 |
| Multiple Sampling Rates | p. 98 |
| Discretization of Time-Varying Systems | p. 101 |
| Error Dynamics and Statistical Steady State | p. 101 |
| The Error System | p. 101 |
| The Innovations Sequence | p. 102 |
| The Algebraic Riccati Equation | p. 103 |
| Time-Varying Plant | p. 110 |
| Frequency Domain Results | p. 112 |
| A Spectral Factorization Result | p. 112 |
| The Innovations Representation | p. 114 |
| Chang-Letov Design Procedure for the Kalman Filter | p. 115 |
| Deriving the Discrete Wiener Filter | p. 118 |
| Correlated Noise and Shaping Filters | p. 123 |
| Colored Process Noise | p. 124 |
| Correlated Measurement and Process Noise | p. 127 |
| Colored Measurement Noise | p. 130 |
| Optimal Smoothing | p. 132 |
| The Information Filter | p. 133 |
| Optimal Smoothed Estimate | p. 136 |
| Rauch-Tung-Striebel Smoother | p. 138 |
| Problems | p. 140 |
| Continuous-Time Kalman Filter | p. 151 |
| Derivation from Discrete Kalman Filter | p. 151 |
| Some Examples | p. 157 |
| Derivation from Wiener-Hope Equation | p. 166 |
| Introduction of a Shaping Filter | p. 167 |
| A Differential Equation for the Optimal Impulse Response | p. 168 |
| A Differential Equation for the Estimate | p. 169 |
| A Differential Equation for the Error Covariance | p. 170 |
| Discussion | p. 172 |
| Error Dynamics and Statistical Steady State | p. 177 |
| The Error System | p. 177 |
| The Innovations Sequence | p. 178 |
| The Algebraic Riccati Equation | p. 179 |
| Time-Varying Plant | p. 180 |
| Frequency Domain Results | p. 180 |
| Spectral Densities for Linear Stochastic Systems | p. 181 |
| A Spectral Factorization Result | p. 181 |
| Chang-Letov Design Procedure | p. 184 |
| Correlated Noise and Shaping Filters | p. 188 |
| Colored Process Noise | p. 188 |
| Correlated Measurement and Process Noise | p. 189 |
| Colored Measurement Noise | p. 190 |
| Discrete Measurements of Continuous-Time Systems | p. 193 |
| Optimal Smoothing | p. 197 |
| The Information Filter | p. 200 |
| Optimal Smoothed Estimate | p. 201 |
| Rauch-Ting-Striebel Smoother | p. 203 |
| Problems | p. 204 |
| Kalman Filter Design and Implementation | p. 213 |
| Modeling Errors, Divergence, and Exponential Data Weighting | p. 213 |
| Modeling Errors | p. 213 |
| Kalman Filter Divergence | p. 223 |
| Fictitious Process Noise Injection | p. 226 |
| Exponential Data Weighting | p. 230 |
| Reduced-Order Filters and Decoupling | p. 236 |
| Decoupling and Parallel Processing | p. 236 |
| Reduced-Order Filters | p. 242 |
| Using Suboptimal Gains | p. 249 |
| Scalar Measurement Updating | p. 253 |
| Problems | p. 254 |
| Estimation for Nonlinear Systems | p. 259 |
| Update of the Hyperstate | p. 259 |
| Discrete Systems | p. 259 |
| Continuous Systems | p. 263 |
| General Update of Mean and Covariance | p. 265 |
| Time Update | p. 266 |
| Measurement Update | p. 268 |
| Linear Measurement Update | p. 269 |
| Extended Kalman Filter | p. 271 |
| Approximate Time Update | p. 271 |
| Approximate Measurement Update | p. 272 |
| The Extended Kalman Filter | p. 273 |
| Application to Adaptive Sampling | p. 283 |
| Mobile Robot Localization in Sampling | p. 284 |
| The Combined Adaptive Sampling Problem | p. 284 |
| Closed-Form Estimation for a Linear Field without Localization Uncertainty | p. 286 |
| Closed-Form Estimation for a Linear Field with Localization Uncertainty | p. 290 |
| Adaptive Sampling Using the Extended Kalman Filter | p. 295 |
| Simultaneous Localization and Sampling Using a Mobile Robot | p. 297 |
| Problems | p. 305 |
| Robust Estimation | p. 313 |
| Robust Kalman Filter | p. 315 |
| Systems with Modeling Uncertainties | p. 315 |
| Robust Finite Horizon Kalman a Priori Filter | p. 317 |
| Robust Stationary Kalman a Priori Filter | p. 321 |
| Convergence Analysis | p. 326 |
| Feasibility and Convergence Analysis | p. 326 |
| [epsilon]-Switching Strategy | p. 329 |
| Linear Matrix Inequality Approach | p. 331 |
| Robust Filter for Systems with Norm-Bounded Uncertainty | p. 332 |
| Robust Filtering for Systems with Polytopic Uncertainty | p. 335 |
| Robust Kalman Filtering for Continuous-Time Systems | p. 341 |
| Proofs of Theorems | p. 343 |
| Problems | p. 350 |
| H[infinity] Filtering of Continuous-Time Systems | p. 353 |
| H[infinity] Filtering Problem | p. 353 |
| Relationship with Two-Person Zero-Sum Game | p. 356 |
| Finite Horizon H[infinity] Linear Filter | p. 357 |
| Characterization of All Finite Horizon H[infinity] Linear Filters | p. 361 |
| Stationary H[infinity] Filter-Riccati Equation Approach | p. 365 |
| Relationship between Guaranteed H[infinity] Norm and Actual H[infinity] Norm | p. 371 |
| Characterization of All Linear Time-Invariant H[infinity] Filters | p. 373 |
| Relationship with the Kalman Filter | p. 373 |
| Convergence Analysis | p. 374 |
| H[infinity] Filtering for a Special Class of Signal Models | p. 378 |
| Stationary H[infinity] Filter-Linear Matrix Inequality Approach | p. 382 |
| Problems | p. 383 |
| H[infinity] Filtering of Discrete-Time Systems | p. 387 |
| Discrete-Time H[infinity] Filtering Problem | p. 387 |
| H[infinity] a Priori Filter | p. 390 |
| Finite Horizon Case | p. 391 |
| Stationary Case | p. 397 |
| H[infinity] a Posteriori Filter | p. 400 |
| Finite Horizon Case | p. 400 |
| Stationary Case | p. 405 |
| Polynomial Approach to H[infinity] Estimation | p. 408 |
| J-Spectral Factorization | p. 410 |
| Applications in Channel Equalization | p. 414 |
| Problems | p. 419 |
| Optimal Stochastic Control | p. 421 |
| Stochastic Control for State Variable Systems | p. 423 |
| Dynamic Programming Approach | p. 423 |
| Discrete-Time Systems | p. 424 |
| Continuous-Time Systems | p. 435 |
| Continuous-Time Linear Quadratic Gaussian Problem | p. 443 |
| Complete State Information | p. 445 |
| Incomplete State Information and the Separation Principle | p. 449 |
| Discrete-Time Linear Quadratic Gaussian Problem | p. 453 |
| Complete State Information | p. 454 |
| Incomplete State Information | p. 455 |
| Problems | p. 457 |
| Stochastic Control for Polynomial Systems | p. 463 |
| Polynomial Representation of Stochastic Systems | p. 463 |
| Optimal Prediction | p. 465 |
| Minimum Variance Control | p. 469 |
| Polynomial Linear Quadratic Gaussian Regulator | p. 473 |
| Problems | p. 481 |
| Review of Matrix Algebra | p. 485 |
| Basic Definitions and Facts | p. 485 |
| Partitioned Matrices | p. 486 |
| Quadratic Forms and Definiteness | p. 488 |
| Matrix Calculus | p. 490 |
| References | p. 493 |
| Index | p. 501 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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