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
li*®
liktmry
*
Petrotoum
l
Mln«r«l
•
S*ucfi
ACADEMIC
PRESS
New
York
San Francisco London 1979
A Subsidiary
of Harcourt Brace
Jovanovich,
Publishers
To
Beverly
Contents
Preface
xi
Contents
of
Volume
2
xv
Notation
xvii
Chapter
1
Introduction
1.1
Why
Stochastic
Models,
Estimation,
and Control?
1
1.2
Overview of
the Text
3
1.3 The
Kalman
Filter:
An Introduction
to Concepts
3
1.4 Basic Assumptions
7
1.5 A
Simple Example
9
1.6 A
Preview
15
General
References
15
Appendix
and Problems
16
References
23
Chapter
2 Deterministic
system
models
2.1 Introduction
25
2.2 Continuous-Time
Dynamic Models
25
2.3
Solutions to
State
Differential
Equations
37
2.4 Discrete-Time
Measurements
42
2.5
Controllability
and
Observability
43
2.6
Summary
48
References
48
Problems
49
Chapter 3
Probability
theory and
static
models
3.1
Introduction
59
3.2
Probability and
Random
Variables
60
3.3 Probability
Distributions and
Densities
70
3.4
Conditional
Probability and
Densities
76
vii
Vlll
CONTENTS
3.5 Functions of
Random
Variables
84
3.6 Expectation and
Moments
of
Random
Variables
88
3.7
Conditional
Expectations
95
3.8
Characteristic
Functions
99
3.9
Gaussian
Random Vectors
101
3.10
Linear
Operations
on
Gaussian
Random
Variables
111
3.11
Estimation with
Static
Linear
Gaussian System
Models
114
3.12 Summary
122
References
122
Problems
123
Chapter 4 Stochastic
processes
and
linear
dynamic
system models
4.1 Introduction
133
4.2 Stochastic
Processes
133
4.3 Stationary
Stochastic
Processes
and
Power
Spectral
Density 139
4.4
System
Modeling:
Objectives
and
Directions
145
4.5 Foundations:
White
Gaussian Noise
and
Brownian
Motion
147
4.6 Stochastic
Integrals
156
4.7 Stochastic
Differentials
162
4.8 Linear Stochastic
Differential
Equations
163
4.9
Linear
Stochastic
Difference
Equations
170
4.10
The
Overall System
Model
174
4.11 Shaping
Filters and
State
Augmentation
180
4.12 Power Spectrum
Concepts
and
Shaping
Filters
186
4.13 Generating
Practical
System
Models
190
4.14
Summary
194
References
195
Problems
195
Chapter
5
Optimal
filtering
with
linear
system
models
5.1
Introduction
203
5.2
Problem
Formulation
203
5.3
The
Discrete-Time
(Sampled
Data)
Optimal
Estimator:
The
Kalman
Filter
206
5.4
Statistics of
Processes
within
the
Filter
Structure
226
5.5
Other
Criteria
of
Optimality
231
5.6
Covariance
Measurement
Update
Computations
236
5.7
Inverse
Covariance
Form
238
5.8
Stability
242
5.9
Correlation
of
Dynamic
Driving
Noise
and
Measurement
Noise
246
5.10
Time-Correlated
Measurement
Noise;
Perfect
Measurements
248
5.11
Continuous-Time
Filter
257
5.12
Wiener
Filtering
and
Frequency
Domain
Techniques
267
5.13
Summary
275
References
276
Problems
279
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