Stochastic Models, Estimation and Control Volume 1

✍ Scribed by Peter S. Maybeck

• Publisher: Academic Press
• Year: 1979
• Tongue: English
• Leaves: 445
• Series: Mathematics in Science and Engineering 141a
• Category: Library

✦ Synopsis

From Contents: Introduction; Deterministic System Models; Probability Theory and Static Models; Stochastic Processes and Linear Dynamic System Models; Optimal Filtering and Linear System Models; Design and Performance Analysis of Kalman Filters; Square Root Filtering. (Description by http-mart)

✦ Table of Contents

Front Cover......Page 1
Stochastic models, estimation, and control......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface......Page 12
Contents of Volume 2......Page 16
Notation......Page 18
1.1 Why Stochastic Models, Estimation, and Control?......Page 22
1.3 The Kalman Filter: An Introduction to Concepts......Page 24
1.4 Basic Assumptions......Page 28
1.5 A Simple Example......Page 30
General References......Page 36
Appendix and Problems......Page 37
References......Page 44
2.2 Continuous-Time Dynamic Models......Page 46
2.3 Solutions to State Differential Equations......Page 58
2.4 Discrete-Time Measurements......Page 63
2.5 Controllability and Observability......Page 64
References......Page 69
Problems......Page 70
3.1 Introduction......Page 80
3.2 Probability and Random Variables......Page 81
3.3 Probability Distributions and Densities......Page 91
3.4 Conditional Probability and Densities......Page 97
3.5 Functions of Random Variables......Page 105
3.6 Expectation and Moments of Random Variables......Page 109
3.7 Conditional Expectations......Page 116
3.8 Characteristic Functions......Page 120
3.9 Gaussian Random Vectors......Page 122
3.10 Linear Operations on Gaussian Random Variables......Page 132
3.11 Estimation with Static Linear Gaussian System Models......Page 135
References......Page 143
Problems......Page 144
4.2 Stochastic Processes......Page 154
4.3 Stationary Stochastic Processes and Power Spectral Density......Page 160
4.4 System Modeling: Objectives and Directions......Page 166
4.5 Foundations: White Gaussian Noise and Brownian Motion......Page 168
4.6 Stochastic Integrals......Page 177
4.7 Stochastic Differentials......Page 183
4.8 Linear Stochastic Differential Equations......Page 184
4.9 Linear Stochastic Difference Equations......Page 191
4.10 The Overall System Model......Page 195
4.11 Shaping Filters and State Augmentation......Page 201
4.12 Power Spectrum Concepts and Shaping Filters......Page 207
4.13 Generating Practical System Models......Page 211
4.14 Summary......Page 215
Problems......Page 216
5.2 Problem Formulation......Page 224
5.3 The Discrete-Time (Sampled Data) Optimal Estimator: The Kalman Filter......Page 227
5.4 Statistics of Processes within the Filter Structure......Page 247
5.5 Other Criteria of Optimality......Page 252
5.6 Covariance Measurement Update Computations......Page 257
5.7 Inverse Covariance Form......Page 259
5.8 Stability......Page 263
5.9 Correlation of Dynamic Driving Noise and Measurement Noise......Page 267
5.10 Time-Correlated Measurement Noise: Perfect Measurements......Page 269
5.11 Continuous-Time Filter......Page 278
5.12 Wiener Filtering and Frequency Domain Techniques......Page 288
5.13 Summary......Page 296
References......Page 297
Problems......Page 300
6.2 The Requisite of Engineering Judgment......Page 310
6.3 Application of Kalman Filtering to Inertial Navigation Systems......Page 312
6.4 INS Aided by Position Data: A Simple Example......Page 318
6.5 Doppler-Aided INS......Page 326
6.6 INS Calibration and Alignment Using Direct Kalman Filter......Page 338
6.7 Generating Alternative Designs......Page 343
6.8 Performance (Sensitivity) Analysis......Page 346
6.9 Systematic Design Procedure......Page 362
6.10 INS Aided by Navigation Satellites......Page 363
6.11 Practical Aspects of Implementation......Page 372
6.12 Summary......Page 379
References......Page 380
Problems......Page 383
7.1 Introduction......Page 389
7.2 Matrix Square Roots......Page 391
7.3 Covariance Square Root Filter for Qd = 0......Page 394
7.4 Vector-Valued Measurements......Page 395
7.5 Covariance Square Root Filter for Qd ≠ 0......Page 398
7.6 Inverse Covariance Square Root Filter......Page 409
7.7 U–D Covariance Factorization Filter......Page 413
7.8 Filter Performance and Requirements......Page 420
References......Page 426
Problems......Page 427
Index......Page 432