Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition

by Lewis; Frank L.

• ISBN13: 9780849390081
• ISBN10: 0849390087
• Edition: 2nd
• Format: Hardcover
• Copyright: 2007-09-17
• Publisher: CRC Press

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
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