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. |