Optimal and robust estimation : with an introduction to stochastic control theory

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More than a decade ago, world-renowned control systems authority Frank L. Lewis introduced what would become a standard textbook on estimation, under the title Optimal Estimation, used in top universities throughout the world. The time has come for a new edition of this classic text, and Lewis enlisted the aid of two accomplished experts to bring the book completely up to date with the estimation methods driving today's high-performance systems.

A Classic Revisited
Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition reflects new developments in estimation theory and design techniques. As the title suggests, the major feature of this edition is the inclusion of robust methods. Three new chapters cover the robust Kalman filter, H-infinity filtering, and H-infinity filtering of discrete-time systems.

Modern Tools for Tomorrow's Engineers
This text overflows with examples that highlight practical applications of the theory and concepts. Design algorithms appear conveniently in tables, allowing students quick reference, easy implementation into software, and intuitive comparisons for selecting the best algorithm for a given application. In addition, downloadable MATLAB® code allows students to gain hands-on experience with industry-standard software tools for a wide variety of applications.

This cutting-edge and highly interactive text makes teaching, and learning, estimation methods easier and more modern than ever.

Preface	p. xv
Authors	p. xvii
Subject	p. xix
Audience	p. xxi
I Optimal Estimation	p. 1
1 Classical Estimation Theory	p. 3
1.1 Mean-Square Estimation	p. 3
1.1.1 Mean-Square Estimation of a Random Variable X by a Constant	p. 4
1.1.2 Mean-Square Estimation of a Random Variable X Given a Random Variable Z: General Case	p. 5
1.1.3 The Orthogonality Principle	p. 13
1.1.4 Linear Mean-Square Estimation of a Random Variable X Given a Random Variable Z	p. 14
1.2 Maximum-Likelihood Estimation	p. 19
1.2.1 Nonlinear Maximum-Likelihood Estimation	p. 19
1.2.2 Linear Gaussian Measurements	p. 20
1.3 The Cramer-Rao Bound	p. 25
1.4 Recursive Estimation	p. 28
1.4.1 Sequential Processing of Measurements	p. 28
1.4.2 Sequential Maximum-Likelihood Estimation	p. 31
1.4.3 Prewhitening of Data	p. 33
1.5 Wiener Filtering	p. 34
1.5.1 The Linear Estimation Problem	p. 36
1.5.2 Solution of the Wiener-Hopf Equation	p. 38
1.5.2.1 Infinite-Delay Steady-State Smoothing	p. 38
1.5.2.2 Causal Steady-State Filtering	p. 41
Problems	p. 50
2 Discrete-Time Kalman Filter	p. 59
2.1 Deterministic State Observer	p. 59
2.2 Linear Stochastic Systems	p. 64
2.2.1 Propagation of Means and Covariances	p. 65
2.2.2 Statistical Steady-State and Spectral Densities	p. 68
2.3 The Discrete-Time Kalman Filter	p. 70
2.3.1 Kalman Filter Formulations	p. 71
2.4 Discrete Measurements of Continuous-Time Systems	p. 84
2.4.1 Discretization of Continuous Stochastic Systems	p. 85
2.4.2 Multiple Sampling Rates	p. 98
2.4.3 Discretization of Time-Varying Systems	p. 101
2.5 Error Dynamics and Statistical Steady State	p. 101
2.5.1 The Error System	p. 101
2.5.2 The Innovations Sequence	p. 102
2.5.3 The Algebraic Riccati Equation	p. 103
2.5.4 Time-Varying Plant	p. 110
2.6 Frequency Domain Results	p. 112
2.6.1 A Spectral Factorization Result	p. 112
2.6.2 The Innovations Representation	p. 114
2.6.3 Chang-Letov Design Procedure for the Kalman Filter	p. 115
2.6.4 Deriving the Discrete Wiener Filter	p. 118
2.7 Correlated Noise and Shaping Filters	p. 123
2.7.1 Colored Process Noise	p. 124
2.7.2 Correlated Measurement and Process Noise	p. 127
2.7.3 Colored Measurement Noise	p. 130
2.8 Optimal Smoothing	p. 132
2.8.1 The Information Filter	p. 133
2.8.2 Optimal Smoothed Estimate	p. 136
2.8.3 Rauch-Tung-Striebel Smoother	p. 138
Problems	p. 140
3 Continuous-Time Kalman Filter	p. 151
3.1 Derivation from Discrete Kalman Filter	p. 151
3.2 Some Examples	p. 157
3.3 Derivation from Wiener-Hope Equation	p. 166
3.3.1 Introduction of a Shaping Filter	p. 167
3.3.2 A Differential Equation for the Optimal Impulse Response	p. 168
3.3.3 A Differential Equation for the Estimate	p. 169
3.3.4 A Differential Equation for the Error Covariance	p. 170
3.3.5 Discussion	p. 172
3.4 Error Dynamics and Statistical Steady State	p. 177
3.4.1 The Error System	p. 177
3.4.2 The Innovations Sequence	p. 178
3.4.3 The Algebraic Riccati Equation	p. 179
3.4.4 Time-Varying Plant	p. 180
3.5 Frequency Domain Results	p. 180
3.5.1 Spectral Densities for Linear Stochastic Systems	p. 181
3.5.2 A Spectral Factorization Result	p. 181
3.5.3 Chang-Letov Design Procedure	p. 184
3.6 Correlated Noise and Shaping Filters	p. 188
3.6.1 Colored Process Noise	p. 188
3.6.2 Correlated Measurement and Process Noise	p. 189
3.6.3 Colored Measurement Noise	p. 190
3.7 Discrete Measurements of Continuous-Time Systems	p. 193
3.8 Optimal Smoothing	p. 197
3.8.1 The Information Filter	p. 200
3.8.2 Optimal Smoothed Estimate	p. 201
3.8.3 Rauch-Ting-Striebel Smoother	p. 203
Problems	p. 204
4 Kalman Filter Design and Implementation	p. 213
4.1 Modeling Errors, Divergence, and Exponential Data Weighting	p. 213
4.1.1 Modeling Errors	p. 213
4.1.2 Kalman Filter Divergence	p. 223
4.1.3 Fictitious Process Noise Injection	p. 226
4.1.4 Exponential Data Weighting	p. 230
4.2 Reduced-Order Filters and Decoupling	p. 236
4.2.1 Decoupling and Parallel Processing	p. 236
4.2.2 Reduced-Order Filters	p. 242
4.3 Using Suboptimal Gains	p. 249
4.4 Scalar Measurement Updating	p. 253
Problems	p. 254
5 Estimation for Nonlinear Systems	p. 259
5.1 Update of the Hyperstate	p. 259
5.1.1 Discrete Systems	p. 259
5.1.2 Continuous Systems	p. 263
5.2 General Update of Mean and Covariance	p. 265
5.2.1 Time Update	p. 266
5.2.2 Measurement Update	p. 268
5.2.3 Linear Measurement Update	p. 269
5.3 Extended Kalman Filter	p. 271
5.3.1 Approximate Time Update	p. 271
5.3.2 Approximate Measurement Update	p. 272
5.3.3 The Extended Kalman Filter	p. 273
5.4 Application to Adaptive Sampling	p. 283
5.4.1 Mobile Robot Localization in Sampling	p. 284
5.4.2 The Combined Adaptive Sampling Problem	p. 284
5.4.3 Closed-Form Estimation for a Linear Field without Localization Uncertainty	p. 286
5.4.4 Closed-Form Estimation for a Linear Field with Localization Uncertainty	p. 290
5.4.5 Adaptive Sampling Using the Extended Kalman Filter	p. 295
5.4.6 Simultaneous Localization and Sampling Using a Mobile Robot	p. 297
Problems	p. 305
II Robust Estimation	p. 313
6 Robust Kalman Filter	p. 315
6.1 Systems with Modeling Uncertainties	p. 315
6.2 Robust Finite Horizon Kalman a Priori Filter	p. 317
6.3 Robust Stationary Kalman a Priori Filter	p. 321
6.4 Convergence Analysis	p. 326
6.4.1 Feasibility and Convergence Analysis	p. 326
6.4.2 [epsilon]-Switching Strategy	p. 329
6.5 Linear Matrix Inequality Approach	p. 331
6.5.1 Robust Filter for Systems with Norm-Bounded Uncertainty	p. 332
6.5.2 Robust Filtering for Systems with Polytopic Uncertainty	p. 335
6.6 Robust Kalman Filtering for Continuous-Time Systems	p. 341
Proofs of Theorems	p. 343
Problems	p. 350
7 H[infinity] Filtering of Continuous-Time Systems	p. 353
7.1 H[infinity] Filtering Problem	p. 353
7.1.1 Relationship with Two-Person Zero-Sum Game	p. 356
7.2 Finite Horizon H[infinity] Linear Filter	p. 357
7.3 Characterization of All Finite Horizon H[infinity] Linear Filters	p. 361
7.4 Stationary H[infinity] Filter-Riccati Equation Approach	p. 365
7.4.1 Relationship between Guaranteed H[infinity] Norm and Actual H[infinity] Norm	p. 371
7.4.2 Characterization of All Linear Time-Invariant H[infinity] Filters	p. 373
7.5 Relationship with the Kalman Filter	p. 373
7.6 Convergence Analysis	p. 374
7.7 H[infinity] Filtering for a Special Class of Signal Models	p. 378
7.8 Stationary H[infinity] Filter-Linear Matrix Inequality Approach	p. 382
Problems	p. 383
8 H[infinity] Filtering of Discrete-Time Systems	p. 387
8.1 Discrete-Time H[infinity] Filtering Problem	p. 387
8.2 H[infinity] a Priori Filter	p. 390
8.2.1 Finite Horizon Case	p. 391
8.2.2 Stationary Case	p. 397
8.3 H[infinity] a Posteriori Filter	p. 400
8.3.1 Finite Horizon Case	p. 400
8.3.2 Stationary Case	p. 405
8.4 Polynomial Approach to H[infinity] Estimation	p. 408
8.5 J-Spectral Factorization	p. 410
8.6 Applications in Channel Equalization	p. 414
Problems	p. 419
III Optimal Stochastic Control	p. 421
9 Stochastic Control for State Variable Systems	p. 423
9.1 Dynamic Programming Approach	p. 423
9.1.1 Discrete-Time Systems	p. 424
9.1.2 Continuous-Time Systems	p. 435
9.2 Continuous-Time Linear Quadratic Gaussian Problem	p. 443
9.2.1 Complete State Information	p. 445
9.2.2 Incomplete State Information and the Separation Principle	p. 449
9.3 Discrete-Time Linear Quadratic Gaussian Problem	p. 453
9.3.1 Complete State Information	p. 454
9.3.2 Incomplete State Information	p. 455
Problems	p. 457
10 Stochastic Control for Polynomial Systems	p. 463
10.1 Polynomial Representation of Stochastic Systems	p. 463
10.2 Optimal Prediction	p. 465
10.3 Minimum Variance Control	p. 469
10.4 Polynomial Linear Quadratic Gaussian Regulator	p. 473
Problems	p. 481
Appendix Review of Matrix Algebra	p. 485
A.1 Basic Definitions and Facts	p. 485
A.2 Partitioned Matrices	p. 486
A.3 Quadratic Forms and Definiteness	p. 488
A.4 Matrix Calculus	p. 490
References	p. 493
Index	p. 501

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