Stochastic Processes, Estimation, and Control (Advances in Design and Control)

Contents......Page 8
Book Content......Page 12
1.1 Probability Theory as a Set of Outcomes......Page 16
1.2 Set Theory......Page 21
1.3 Probability Space and the Probability Measure......Page 23
1.4 Algebras of Sets and Probability Space......Page 24
1.5 Key Concepts in Probability Theory......Page 28
1.6 Exercises......Page 33
2.1 Random Variables......Page 40
2.2 Probability Distribution Function......Page 43
2.3 Probability Density Function......Page 46
2.4 Probabilistic Concepts Applied to Random Variables......Page 50
2.5 Functions of a Random Variable......Page 52
2.6 Expectations and Moments of a Random Variable......Page 55
2.7 Characteristic Functions......Page 61
2.8 Conditional Expectations and Conditional Probabilities......Page 68
2.9 Stochastic Processes......Page 74
2.10 Gauss–Markov Processes......Page 78
2.11 Nonlinear Stochastic Difference Equations......Page 80
2.12 Exercises......Page 81
3.1 Minimum Variance Estimation......Page 96
3.2 Conditional Estimate of a Gaussian Random Vector with Additive Gaussian Noise......Page 103
3.3 Maximum Likelihood Estimation......Page 109
3.4 The Discrete-Time Kalman Filter: Conditional Mean Estimator......Page 110
3.5 “Tuning” a Kalman Filter......Page 121
3.6 Discrete-Time Nonlinear Filtering......Page 124
3.7 Exercises......Page 126
4.1 Linear Least Squares......Page 134
4.2 The Orthogonal Projection Lemma......Page 144
4.3 Extensions of Least Squares Theory......Page 149
4.4 Nonlinear Least Squares: Newton–Gauss Iteration......Page 151
4.5 Deriving the Kalman Filter via the Orthogonal Projection Lemma......Page 155
4.6 Exercises......Page 160
5.1 Random Walk and Brownian Motion......Page 168
5.2 Mean-Square Calculus......Page 175
5.3 Wiener Integrals......Page 183
5.4 Itô Integrals......Page 186
5.5 Second-Order Itô Integrals......Page 193
5.6 Stochastic Differential Equations and Exponentials......Page 195
5.7 The Itô Stochastic Differential......Page 197
5.8 Continuous-Time Gauss–Markov Processes......Page 201
5.9 Propagation of the Probability Density Function......Page 205
5.10 Exercises......Page 207
6.1 The Continuous-Time Kalman Filter (Kalman–Bucy Filter)......Page 212
6.2 Properties of the Continuous-Time Riccati Equation......Page 217
6.3 Stationarity......Page 219
6.4 Power Spectral Densities......Page 222
6.5 Continuous-Time Linear Systems Driven by Stationary Signals......Page 230
6.6 Discrete-Time Linear Systems Driven by Stationary Random Processes......Page 235
6.7 The Steady-State Kalman Filter: The Wiener Filter......Page 238
6.8 Exercises......Page 249
7.1 Linearized Kalman Filtering......Page 256
7.2 The Extended Kalman Filter......Page 259
7.3 The Iterative Extended Kalman Filter......Page 260
7.4 Filter Divergence......Page 264
7.5 Exercises......Page 270
8.1 Continuous-Time Colored-Noise Filter......Page 278
8.2 Optimal Smoothing and Filtering in Continuous Time......Page 282
8.3 Discrete-Time Smoothing and Maximum Likelihood Estimation......Page 286
8.4 Linear Exponential Gaussian Estimation......Page 288
8.5 Estimation with State-Dependent Noise......Page 292
8.6 Exercises......Page 299
9.1 Dynamic Programming: An Illustration......Page 304
9.2 Stochastic Dynamical System......Page 306
9.3 Dynamic Programming Algorithm......Page 307
9.4 Stochastic LQ Problems with Perfect Information......Page 310
9.5 Dynamic Programming with Partial Information......Page 312
9.6 The Discrete-Time LQG Problem with Partial Information......Page 315
9.7 The Continuous-Time LQG Problem......Page 320
9.8 Stationary Optimal Control......Page 332
9.9 LQG Control with Loop Transfer Recovery......Page 336
9.10 Exercises......Page 345
10.1 Discrete-Time LEG Control......Page 350
10.2 Terminal Guidance: A Special Continuous-Time LEG Problem......Page 370
10.3 Continuous-Time LEG Control......Page 377
10.4 LEG Controllers and......Page 379
10.5 Exercises......Page 387
Appendix A. Proof of Lemma 10.1......Page 388
Appendix B. Proof of Lemma 10.2......Page 389
Bibliography......Page 392
Index......Page 396