Optimal and robust estimation

Cover......Page 1
Half Title Page......Page 5
Copyright......Page 6
Title Page......Page 7
Dedication......Page 8
Contents......Page 11
Preface......Page 17
Authors......Page 19
Subject......Page 21
Audience......Page 23
I: Optimal Estimation......Page 25
1.1 Mean-Square Estimation......Page 27
1.2 Maximum-Likelihood Estimation......Page 43
1.3 The Cramér–Rao Bound......Page 49
1.4 Recursive Estimation......Page 52
1.5 Wiener Filtering......Page 58
Problems......Page 74
2.1 Deterministic State Observer......Page 83
2.2 Linear Stochastic Systems......Page 88
2.3 The Discrete-Time Kalman Filter......Page 94
2.4 Discrete Measurements of Continuous-Time Systems......Page 108
2.5 Error Dynamics and Statistical Steady State......Page 125
2.6 Frequency Domain Results......Page 136
2.7 Correlated Noise and Shaping Filters......Page 147
2.8 Optimal Smoothing......Page 156
Problems......Page 164
3.1 Derivation from Discrete Kalman Filter......Page 175
3.2 Some Examples......Page 181
3.3 Derivation from Wiener–Hope Equation......Page 190
3.4 Error Dynamics and Statistical Steady State......Page 201
3.5 Frequency Domain Results......Page 204
3.6 Correlated Noise and Shaping Filters......Page 212
3.7 Discrete Measurements of Continuous-Time Systems......Page 217
3.8 Optimal Smoothing......Page 221
Problems......Page 228
4.1 Modeling Errors, Divergence, and Exponential Data Weighting......Page 237
4.2 Reduced-Order Filters and Decoupling......Page 260
4.3 Using Suboptimal Gains......Page 273
4.4 Scalar Measurement Updating......Page 277
Problems......Page 278
5.1 Update of the Hyperstate......Page 283
5.2 General Update of Mean and Covariance......Page 289
5.3 Extended Kalman Filter......Page 295
5.4 Application to Adaptive Sampling......Page 307
Problems......Page 329
II: Robust Estimation......Page 337
6.1 Systems with Modeling Uncertainties......Page 339
6.2 Robust Finite Horizon Kalman a Priori Filter......Page 341
6.3 Robust Stationary Kalman a Priori Filter......Page 345
6.4 Convergence Analysis......Page 350
6.5 Linear Matrix Inequality Approach......Page 355
6.6 Robust Kalman Filtering for Continuous-Time Systems......Page 365
Proofs of Theorems......Page 367
Problems......Page 374
7.1 H[sub(∞)] Filtering Problem......Page 377
7.2 Finite Horizon H[sub(∞)] Linear Filter......Page 381
7.3 Characterization of All Finite Horizon H[sub(∞)] Linear Filters......Page 385
7.4 Stationary H[sub(∞)] Filter—Riccati Equation Approach......Page 389
7.5 Relationship with the Kalman Filter......Page 397
7.6 Convergence Analysis......Page 398
7.7 H[sub(∞)] Filtering for a Special Class of Signal Models......Page 402
7.8 Stationary H[sub(∞)] Filter—Linear Matrix Inequality Approach......Page 406
Problems......Page 407
8.1 Discrete-Time H[sub(∞)] Filtering Problem......Page 411
8.2 H[sub(∞)] a Priori Filter......Page 414
8.3 H[sub(∞)] a Posteriori Filter......Page 424
8.4 Polynomial Approach to H[sub(∞)] Estimation......Page 432
8.5 J-Spectral Factorization......Page 434
8.6 Applications in Channel Equalization......Page 438
Problems......Page 443
III: Optimal Stochastic Control......Page 445
9.1 Dynamic Programming Approach......Page 447
9.2 Continuous-Time Linear Quadratic Gaussian Problem......Page 467
9.3 Discrete-Time Linear Quadratic Gaussian Problem......Page 477
Problems......Page 481
10.1 Polynomial Representation of Stochastic Systems......Page 487
10.2 Optimal Prediction......Page 489
10.3 Minimum Variance Control......Page 493
10.4 Polynomial Linear Quadratic Gaussian Regulator......Page 497
Problems......Page 505
A.1 Basic Definitions and Facts......Page 509
A.2 Partitioned Matrices......Page 510
A.3 Quadratic Forms and Definiteness......Page 512
A.4 Matrix Calculus......Page 514
References......Page 517
Index......Page 525