Stochastic Models, Estimation and Control Peter S. Maybeck Volumes 1, 2 & 3 Tables of Contents

Transcription

1 Navtech Part #s Volume 1 #1277 Volume 2 #1278 Volume 3 # Volume Set #1280 Stochastic Models, Estimation and Control Peter S. Maybeck Volumes 1, 2 & 3 Tables of Contents Volume 1 Preface Contents of Other Volumes Notation xi xv xvii Chapter 1 Introduction 1.1 Why Stochastic Models, Estimation, and Control? Overview of the Text The Kalman Filter: An Introduction to Concepts Basic Assumptions A Simple Example A Preview 15 General References 15 Appendix and Problems 16 References 23 Chapter 2 Deterministic system models 2.1 Introduction Continuous-Time Dynamic Models Solutions to State Differential Equations Discrete-Time Measurements Controllability and Observability Summary 48 References 48 Problems 49 Chapter 3 Probability theory and static models 3.1 Introduction Probability and Random Variables Probability Distributions and Densities Conditional Probability and Densities 76

2 3.5 Functions of Random Variables Expectation and Moments of Random Variables Conditional Expectations Characteristic Functions Gaussian Random Vectors Linear Operations on Gaussian Random Variables Estimation with Static Linear Gaussian System Models Summary 122 References 122 problems 123 Chapter 4 Stochastic processes and linear dynamic system models 4.1 Introduction Stochastic Processes Stationary Stochastic Processes and Power Spectral Density System Modeling: Objectives and Directions Foundations: White Gaussian Noise and Brownie, Motion Stochastic Integrals Stochastic Differentials Linear Stochastic Differential Equations Linear Stochastic Difference Equations The Overall System Model Shaping Filters and State Augmentation Power Spectrum Concepts and Shaping Filters Generating Practical System Models Summary 194 References 195 Problems 195 Chapter 5 Optimal filtering with linear system models 5.1 Introduction Problem Formulation The Discrete-Time (Sampled Data) Optimal Estimator: The Kalman Filter Statistics of Processes within the Filter Structure Other Criteria of Optimality, Covariance Measurement Update Computations Inverse Covariance Form Stability Correlation of Dynamic Driving Noise end Measurement Noise Time-Correlated Measurement Noise: Perfect Measurements Continuous-Time Filter Wiener Filtering and Frequency Domain Techniques Summary 275 References 276 problems 279

3 Chapter 6 Design and performance analysis of Kalman filters 6.1 Introduction The Requisite of Engineering Judgment Application of Kalman Filtering to Inertial Navigation Systems 29I 6.4 INS Aided by Position Data: A Simple Example Doppler-Aided INS INS Calibration and Alignment Using Direct Kalman Filter Generating Allemative Designs Performance (Sensitivity) Analysis Systematic Design Procedure INS Aided by Navigation Satellites Practical Aspects of Implementation Summary 358 References 359 Problems 362 Chapter 7 Square root filtering 7.1 Introduction Matrix Square Roots Covariance Square Root Filter for Qa Vector-Valued Measurements Covariance Square Root Filter for Q~ IE Inverse Covariance Square Raw Filter U-D Covariance Factorization Filter Filter Performance and Requirements Summary 405 References 405 Problems 406 Index 411 Volume 2 Chapter 8 Optimal smoothing 8.1 Introduction Basic Structure Three Classes of Smoothing Problems Fixed-Interval Smoothing Fixed-Point Smoothing Faced-Lag Smoothing Summary 17 References 18 Problems 19

4 Chapter 9 Compensation of linear model inadequacies 9.1 Introduction Pseudonoise Addition and Artificial Lower Bounding of P Limiting Effective Filter Memory and Overweighting Most Recent Data Finite Memory Filtering Linearized and Extended Kalman Filters Summary 59 References 59 Problems 62 Chapter 10 Parameter uncertainties and adaptive estimation 10.1 Introduction Problem Formulation Uncertainties in Φ and B d : Likelihood Equations Uncertainties in Φ and B d : Full-Scale Estimator Uncertainties in Φ and B d : Performance Analysis Uncertainties in Φ and B d : Attaining Online Applicability Uncertainties in Qa and R Bayesian and Multiple Model Filtering Algorithms Correlation Methods for Self-Tuning: Residual Whitening Covariance Matching and Other Techniques Summary 143 References 144 Problems 151 Chapter 11 Nonlinear stochastic system models 11.1 Introduction Extensions of Linear System Modeling Markov Process Fundamentals Itô Stochastic Integrals and Differentials Itô Stochastic Differential Equations Forward Kolmogorov Equation Summary, 202 References 202 Problems 205 Chapter 12 Nonlinear estimation 12.1 Introduction Nonlinear Filtering with Discrete-Time Measurements Conceptually Conditional Moment Estimator, Conditional Quasi-Moments and Hermite Polynomial Series Conditional Mode Estimator Statistically Linearized Filter 243

5 12.7 Nonlinear Filtering with Continuous-Time Measurements Summary 257 References 259 Problems 265 Index 273 Volume 3 Chapter 13 Dynamic programming and stochastic control 13.1 Introduction Basic Problem Formulation 13.3 Introduction to Concepts. Overview of Simple LQG Problem The Backward Kolmogrov Equation Optimal Stochastic Control with Perfect Knowledge of the State Optimal Stochastic Control with Noise-Corrupted Measurements Summary 58 Reference 60 Problems 62 Chapter 14 Linear stochastic controller design and performance analysis 14.1 Introduction The LQG Stochastic Regulator Stability Stability of LQG Regulators Stability Robustness of LQG Regulators The LQG Synthesis of Trackers Nonzero Setpoint Controllers Rejection of Time Correlated Disturbances the LQG Synthesis of PI Controllers Command Generator Tracking Performance Evaluation of Linear Sampled Data Controllers Systematic Design Procedure The LQG Controller for Continuous Time Measurements Summary 190 References 193 Problems 202 Chapter 15 Nonlinear stochastic controllers 15.1 Introduction Basic Problem Formulation and Controller Characteristics Linear Perturbation Control Laws for Nonlinear System, Direct Application of LQG Synthesis 230

6 15.4 Assumed Certainty Equivalence Design Closed Loop Law Approximations and Dual Effect Stochastic Adaptive Control Design Philosophy Summary and Perspective 257 References 260 Problems 266 INDEX END