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    Stochastic Models Estimation and Control Volume 1
    Front Cover
    Stochastic models, estimation, and control
    Copyright Page
    Contents
    Preface
    Contents of Volume 2
    Notation
    Chapter 1. Introduction
    1.1 Why Stochastic Models, Estimation, and Control?
    1.2 Overview of the Text
    1.3 The Kalman Filter: An Introduction to Concepts
    1.4 Basic Assumptions
    1.5 A Simple Example
    1.6 A Preview
    General References
    Appendix and Problems
    References
    Chapter 2. Deterministic system models
    2.1 Introduction
    2.2 Continuous-Time Dynamic Models
    2.3 Solutions to State Differential Equations
    2.4 Discrete-Time Measurements
    2.5 Controllability and Observability
    2.6 Summary
    References
    Problems
    Chapter 3. Probability theory and static models
    3.1 Introduction
    3.2 Probability and Random Variables
    3.3 Probability Distributions and Densities
    3.4 Conditional Probability and Densities
    3.5 Functions of Random Variables
    3.6 Expectation and Moments of Random Variables
    3.7 Conditional Expectations
    3.8 Characteristic Functions
    3.9 Gaussian Random Vectors
    3.10 Linear Operations on Gaussian Random Variables
    3.11 Estimation with Static Linear Gaussian System Models
    3.12 Summary
    References
    Problems
    Chapter 4. Stochastic processes and linear dynamic system models
    4.1 Introduction
    4.2 Stochastic Processes
    4.3 Stationary Stochastic Processes and Power Spectral Density
    4.4 System Modeling: Objectives and Directions
    4.5 Foundations: White Gaussian Noise and Brownian Motion
    4.6 Stochastic Integrals
    4.7 Stochastic Differentials
    4.8 Linear Stochastic Differential Equations
    4.9 Linear Stochastic Difference Equations
    4.10 The Overall System Model
    4.11 Shaping Filters and State Augmentation
    4.12 Power Spectrum Concepts and Shaping Filters
    4.13 Generating Practical System Models
    4.14 Summary
    References
    Problems
    Chapter 5. Optimal filtering with linear system models
    5.1 Introduction
    5.2 Problem Formulation
    5.3 The Discrete-Time (Sampled Data) Optimal Estimator: The Kalman Filter
    5.4 Statistics of Processes within the Filter Structure
    5.5 Other Criteria of Optimality
    5.6 Covariance Measurement Update Computations
    5.7 Inverse Covariance Form
    5.8 Stability
    5.9 Correlation of Dynamic Driving Noise and Measurement Noise
    5.10 Time-Correlated Measurement Noise: Perfect Measurements
    5.11 Continuous-Time Filter
    5.12 Wiener Filtering and Frequency Domain Techniques
    5.13 Summary
    References
    Problems
    Chapter 6. Design and performance analysis of Kalman filters
    6.1 Introduction
    6.2 The Requisite of Engineering Judgment
    6.3 Application of Kalman Filtering to Inertial Navigation Systems
    6.4 INS Aided by Position Data: A Simple Example
    6.5 Doppler-Aided INS
    6.6 INS Calibration and Alignment Using Direct Kalman Filter
    6.7 Generating Alternative Designs
    6.8 Performance (Sensitivity) Analysis
    6.9 Systematic Design Procedure
    6.10 INS Aided by Navigation Satellites
    6.11 Practical Aspects of Implementation
    6.12 Summary
    References
    Problems
    Chapter 7. Square root filtering
    7.1 Introduction
    7.2 Matrix Square Roots
    7.3 Covariance Square Root Filter for Qd = 0
    7.4 Vector-Valued Measurements
    7.5 Covariance Square Root Filter for Qd ≠ 0
    7.6 Inverse Covariance Square Root Filter
    7.7 U–D Covariance Factorization Filter
    7.8 Filter Performance and Requirements
    7.9 Summary
    References
    Problems
    Index
    Stochastic Models Estimation and Control Volume 2
    Front Page
    Stochastic Models, Estimation, and Control
    Copyright Page
    Contents
    Preface
    Notation
    VOLUME 2
    Chapter 8. Optimal smoothing
    8.1 Introduction
    8.2 Basic Structure
    8.3 Three Classes of Smoothing Problems
    8.4 Fixed-Interval Smoothing
    8.5 Fixed-Point Smoothing
    8.6 Fixed-Lag Smoothing
    8.7 Summary
    References
    Problems
    Chapter 9. Compensation of linear model inadequacies
    9.1 Introduction
    9.2 Pseudonoise Addition and Artificial Lower Bounding of P
    9.3 Limiting Effective Filter Memory and Overweighting Most Recent Data
    9.4 Finite Memory Filtering
    9.5 Linearized and Extended Kalman Filters
    9.6 Summary
    References
    Problems
    Chapter 10. Parameter uncertainties and adaptive estimation
    10.1 Introduction
    10.2 Problem Formulation
    10.3 Uncertainties in Φ and Bd: Lkelihood Equations
    10.4 Uncertainties in Φ and Bd : Full-Scale Estimator
    10.5 Uncertainties in Φ and Bd : Performance Analysis
    10.6 Uncertainties in Φ and Bd : Attaining Online Applicability
    10.7 Uncertainties in Qd and R
    10.8 Bayesian and Multiple Model Filtering Algorithms
    10.9 Correlation Methods for Self-Tuning: Residual "Whitening"
    10.10 Covariance Matching and Other Techniques
    10.11 Summary
    References
    Problems
    Chapter 11. Nonlinear stochastic system models
    11.1 Introduction
    11.2 Extensions of Linear System Modeling
    11.3 Markov Process Fundamentals
    11.4 Itô Stochastic Integrals and Differentials
    11.5 Itô Stochastic Differential Equations
    11.6 Forward Kolmogorov Equation
    11.7 Summary
    References
    Problems
    Chapter 12. Nonlinear estimation
    12.1 Introduction
    12.2 Nonlinear Filtering with Discrete-Time Measurements: Conceptually
    12.3 Conditional Moment Estimators
    12.4 Conditional Quasi-Moments and Hermite Polynomial Series
    12.5 Conditional Mode Estimators
    12.6 Statistically Linearized Filter
    12.7 Nonlinear Filtering with Continuous-Time Measurements
    12.8 Summary
    References
    Problems
    Index
    绝版
    Stochastic models, estimation, and control
    Copyright Page
    Contents
    Preface
    Notation
    Chapter 13. Dynamic programming and stochastic control
    13.1 Introduction
    13.2 Basic Problem Formulation
    13.3 Introduction to Concepts: Overview of Simple LQG Problem
    13.4 The Backward Kolmogorov Equation
    13.5 Optimal Stochastic Control with Perfect Knowledge of the State
    13.6 Optimal Stochastic Control with Noise-Corrupted Measurements
    13.7 Summary
    References
    Problems
    Chapter 14. Linear stochastic controller design and performance analysis
    14.1 Introduction
    14.2 The LQG Stochastic Regulator
    14.3 Stability
    14.4 Stability of LQG Regulators
    14.5 Stability Robustness of LQG Regulators
    14.6 The LQG Synthesis of Trackers
    14.7 Nonzero Setpoint Controllers
    14.8 Rejection of Time-Correlated Disturbances
    14.9 The LQG Synthesis of PI Controllers
    14.10 Command Generator Tracking
    14.11 Performance Evaluation of Linear Sampled-Data Controllers
    14.12 Systematic Design Procedure
    14.13 The LQG Controller for Continuous-Time Measurements
    14.14 Summary
    References
    Problems
    Chapter 15. Nonlinear stochastic controllers
    15.1 Introduction
    15.2 Basic Problem Formulation and Controller Characteristics
    15.3 Linear Perturbation Control Laws for Nonlinear Systems: Direct Application of LQG Synthesis
    15.4 Assumed Certainty Equivalence Design
    15.5 Closed-Loop Law Approximations and Dual Effect
    15.6 Stochastic Adaptive Control
    15.7 Design Philosophy
    15.8 Summary and Perspective
    References
    Problems
    Index
    Stochastic models, estimation, and control VOLUME 1
    This is Volume 14 1 in MATHEMATICS IN SCIENCE AND ENGINEERING A Series of Monographs and Textbooks Edited by RICHARD BELLMAN, University of Southern California The complete listing of books in this series is available from the Publisher upon request.
    Stochastic models, estimation, and control VOLUME 1 PETER S. MAYBECK DEPARTMENT OF ELECTRICAL ENGINEERING AIR FORCE INSTITUTE OF TECHNOLOGY WRIGHT-PATTERSON AIR FORCE BASE OHIO ACADEMIC PRESS New York San Francisco London 1979 A Subsidiary of Harcourt Brace Jovanovich, Publishers
    COPYRIGHT @ 1979, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART O F THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. 111 Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NW1 7DX Library of Congress Cataloging in Publication Data Maybeck, Peter S Stochastic models, estimation and control. (Mathematics in science and engineering ; v. ) Includes bibliographies. 1. System analysis. 2. Control theory. 3. Estimation theory. I. Title. 11. Series. QA402.M37 ISBN 0-12-480701-1 519.2 78-8836 (v. 1) PRINTED IN THE UNITED STATES OF AMERICA 7 9 8 0 8 1 8 2 9 8 7 6 5 4 3 2 1
    TO Beverly
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    Prefuce Contents of Volume 2 Notation Chapter 1 Introduction Why Stochastic Models, Estimation, and Control? The Kalman Filter: An Introduction to Concepts 1 . 1 1.2 Overview of the Text 1.3 1.4 Basic Assumptions 1.5 A Simple Example 1.6 A Preview General References Appendix and Problems References Chapter 2 Deterministic system models Solutions to State Differential Equations Introduction 2.1 2.2 Continuous-Time Dynamic Models 2.3 2.4 Discrete-Time Measurements 2.5 Controlla’bility and Observability 2.6 Summary References Problems Chapter 3 Probability theory and static models Introduction 3.1 3.2 Probability and Random Variables 3.3 Probability Distributions and Densities 3.4 Conditional Probability and Densities Contents xi xv xvii 1 3 3 7 9 15 15 16 23 25 25 37 42 43 48 48 49 59 60 70 76 vii
    viii CONTENTS 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 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 References Problems Chapter 4 Stochastic processes and linear dynamic system models 4. I 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4. I4 Introduction Stochastic Processes Stationary Stochastic Processes and Power Spectral Density System Modeling: Objectives and Directions Foundations: White Gaussian Noise and Brownian 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 References Problems Chapter 5 Optimal filtering with linear system models 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 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 and Measurement Noise Time-Correlated Measurement Noise: Perfect Measurements Continuous-Time Filter Wiener Filtering and Frequency Domain Techniques Summary References Problems 84 88 95 99 101 1 1 1 114 122 122 123 133 133 139 145 147 156 162 163 170 174 180 186 190 1 94 195 195 203 203 206 226 23 1 236 238 242 246 248 257 267 215 276 279
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