Stochastic models, estimation and control, Vol.2

307 Pages·1982·4.679 MB·English

by  Peter S. Maybeck

Stochastic models,
estimation, and control
VOLUME 2
ThisisVolume 141-2 in
MATHEMATICS IN SCIENCE AND ENGINEERING
A Series of Monographs and Textbooks
Edited by RICHARD BELLMAN, University of Southern California
"{he"om\lletel\'i.t\t\'g,otboo¥..'i.\\\\\\\'1> '1>e!\e'1>\'1> a'la\lab\e homt\\e\lub\\'!>\\et
upon request.
Stochastic models,
estimation,
and control
VOLUME 2
PETER S. MAYBECK
DEPARTMENT OF ELECTRICAL ENGINEERING
AIR FORCE INSTITUTE OF TECHNOLOGY
WRIGHT-PATTERSON AIR FORCE BASE
OHIO
@
1982
ACADEMIC PRESS
ASubsidiaryofHarcourtBrace Jovanovich, Publishers
New York London
Paris San Diego SanFrancisco Sao Paulo Sydney Tokyo Toronto
COPYRIGHT© 1982, BYACADEMIC PRESS,INC.
ALLRIGHTSRESERVED.
NO PART OFTHISPUBLICATIONMAYBEREPRODUCEDOR
TRANSMITTEDIN ANYFORMORBYANYMEANS, ELECTRONIC
ORMECHANICAL,INCLUDINGPHOTOCOPY, RECORDING, ORANY
INFORMATIONSTORAGE'ANDRETRIEVAL SYSTEM,WITHOUT
PERMISSIONIN WRITINGFROM THE PUBLISHER.
ACADEMIC PRESS, INC.
111FifthAvenue,NewYork,NewYork10003
United Kingdom Edition publishedby
ACADEMIC PRESS, INC. (LONDON) LTD.
24/28OvalRoad,LondonNWI 7DX
Library of corgress Catalogirg in Publication Data
Maybeck, Peter S.
Stochastic models, estimation, and control.
(Mathematicsin science and engineering)
Includes bibliographies and index.
1. System analysis. 2. Control theory.
3. Estimation theory. 4. Stochastic processes.
I. Title. II. Series.
QA4D2.toG7 519.2 78-8836
ISBN D-12-48D7D2-X (v. 2) AACRl
PRINTEDIN THEUNITEDSTATES OF AMERICA
82 83 84 85 9 8 7 6 543 2 1
To Kristen and Keryn . . .
the "other women" in my life
Thispage intentionallyleftblank
Contents
Preface • xi
Notation xiii
VOLUME 1
Chapter 1 Introduction
Chapter 2 Deterministic system models
Chapter 3 Probability theory and static models
Chapter 4 Stochastic processes and linear dynamic system models
Chapter 5 Optimal filtering with linear system models
Chapter 6 Designand performance analysis of Kalman filters
Chapter 7 Square root filtering
VOLUME 2
Chapter 8 Optimal smoothing
8.1 Introduction I
8.2 Basic Structure 2
8.3 ThreeClasses of Smoothing Problems 3
8.4 Fixed-Interval Smoothing 5
8.5 Fixed-Point Smoothing 15
8.6 Fixed-Lag Smoothing 16
8.7 Summary 17
References 18
Problems 19
vii
viii CONTENTS
Chapter 9 Compensation of linear model inadequacies
9.1 Introduction 23
9.2 Pseudonoise Addition and Artificial LowerBoundingofP 24
9.3 Limiting Effective FilterMemory and OverweightingMost Recent
Data 28
904 Finite Memory Filtering 33
9.5 Linearizedand Extended Kalman Filters 39
9.6 Summary 59
References 59
Problems 62
Chapter 10 Parameter uncertainties and adaptive estimation
10.1 Introduction 68
10.2 Problem Formulation 70
10.3 Uncertaintiesincitand Bd: Likelihood Equations 74
lOA Uncertaintiesincitand Bd: Full-Scale Estimator 80
10.5 Uncertaintiesincitand Bd: Performance Analysis 96
10.6 Uncertaintiesincitand Bd: AttainingOnline Applicability lot
10.7 Uncertaintiesin Qdand R 120
10.8 Bayesianand Multiple Model FilteringAlgorithms 129
10.9 Correlation Methodsfor Self-Tuning: Residual "Whitening" 136
10.10 Covariance Matchingand OtherTechniques 141
10.11 Summary 143
References 144
Problems 151
Chapter 11 Nonlinear stochastic system models
11.1 Introduction 159
11.2 Extensionsof LinearSystem Modeling 160
11.3 Markov Process Fundamentals 167
1104 ItOStochasticIntegralsand Differentials 175
11.5 ItOStochasticDifferentialEquations 181
11.6 ForwardKolmogorov Equation 192
11.7 Summary 202
References 202
Problems 205
Chapter 12 Nonlinear estimation
12.1 Introduction 212
12.2 Nonlinear Filteringwith Discrete-Time Measurements: Conceptually 213
12.3 ConditionalMomentEstimators 215
1204 Conditional Quasi-Momentsand Hermite Polynomial Series 239
12.5 Conditional Mode Estimators 241
12.6 Statistically LinearizedFilter 243
CONTENTS ix
12.7 Nonlinear Filtering with Continuous-Time Measurements 245
12.8 Summary 257
References 259
Problems 265
Index 273
VOLUME 3
Chapter 13 Dynamic programming and stochastic control
Chapter 14 Linear stochastic controller design and
performance analysis
Chapter 15 Nonlinear stochastic controllers