Optimal Filtering,9780486439389

Optimal Filtering

by ;
ISBN13: 9780486439389
ISBN10: 0486439380
Format: Paperback
Pub. Date: 2005-01-05
Publisher(s): Dover Publications
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Summary

This graduate-level text augments and extends studies of signal processing, particularly in regard to communication systems and digital filtering theory. Topics include filtering, linear systems, and estimation; the discrete-time Kalman filter; time-invariant filters; properties of Kalman filters; computational aspects; smoothing of discrete-time signals; and more. 24 figures. 1979 edition.

Table of Contents

Preface ix
Introduction
1(8)
Filtering
1(1)
History of Signal Filtering
2(2)
Subject Matter of this Book
4(2)
Outline of the Book
6(3)
References
7(2)
Filtering, Linear Systems, and Estimation
9(27)
Systems, Noise, Filtering, Smoothing, and Prediction
9(3)
The Gauss-Markov Discrete-time Model
12(11)
Estimation Criteria
23(13)
References
34(2)
The Discrete-Time Kalman Filter
36(26)
The Kalman Filter
36(10)
Best Linear Estimator Property of the Kalman Filter
46(4)
Identification as a Kalman Filtering Problem
50(3)
Application of Kalman Filters
53(9)
References
59(3)
Time-Invariant Filters
62(28)
Background to Time Invariance of the Filter
62(1)
Stability Properties of Linear, Discrete-time Systems
63(5)
Stationary Behaviour of Linear Systems
68(8)
Time Invariance and Asymptotic Stability of the Filter
76(9)
Frequency Domain Formulas
85(5)
References
88(2)
Kalman Filter Properties
90(39)
Introduction
90(2)
Minimum Variance and Linear Minimum Variance Estimation; Orthogonality and Projection
92(8)
The Innovations Sequence
100(5)
The Kalman Kilter
105(10)
True Filtered Estimates and the Signal-to-Noise Ratio Improvement Property
115(7)
Inverse Problems: When is a Filter Optimal?
122(7)
References
127(2)
Computational Aspects
129(36)
Signal Model Errors, Filter Divergence, and Data Saturation
129(6)
Exponential Data Weighting---A Filter with Prescribed Degree of Stability
135(3)
The Matrix Inversion Lemma and the Information Filter
138(4)
Sequential Processing
142(5)
Square Root Filtering
147(6)
The High Measurement Noise Case
153(2)
Chandrasekhar-Type, Doubling, and Nonrecursive Algorithms
155(10)
References
162(3)
Smoothing of Discrete-Time Signals
165(28)
Introduction to Smoothing
165(5)
Fixed-point Smoothing
170(6)
Fixed-lag Smoothing
176(11)
Fixed-interval Smoothing
187(6)
References
190(3)
Applications in Nonlinear Filtering
193(30)
Nonlinear Filtering
193(2)
The Extended Kalman Filter
195(10)
A Bound Optimal Filter
205(6)
Gaussian Sum Estimators
211(12)
References
221(2)
Innovations Representations, Spectral Factorization, Wiener and Levinson Filtering
223(44)
Introduction
223(4)
Kalman Filter Design from Covariance Data
227(3)
Innovations Representations with Finite Initial Time
230(8)
Stationary Innovations Representations and Spectral Factorization
238(16)
Wiener Filtering
254(4)
Levinson Filters
258(9)
References
264(3)
Parameter Identification and Adaptive Estimation
267(21)
Adaptive Estimation via Parallel Processing
267(12)
Adaptive Estimation via Extended Least Squares
279(9)
References
286(2)
Colored Noise and Suboptimal Reduced Order Filters
288(63)
General Approaches to Dealing with Colored Noise
288(2)
Filter Design with Markov Output Noise
290(2)
Filter Design with Singular or Near-singular Output Noise
292(4)
Suboptimal Design Given Colored Input or Measurement Noise
296(5)
Suboptimal Filter Design by Model Order Reduction
301(6)
References
304(3)
APPENDIXES
A Brief Review of Results of Probability Theory
307(17)
A.1 Pure Probability Theory
308(8)
A.2 Stochastic Processes
316(4)
A.3 Gaussian Random Variables, Vectors, and Processes
320(3)
References
323(1)
B Brief Review of Some Results of Matrix Theory
324(16)
References
339(1)
C Brief Review of Several Major Results of Linear System Theory
340(7)
References
346(1)
D Lyapunov Stability
347(4)
References
349(2)
Author Index 351(3)
Subject Index 354

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