Introduction to Optimal Estimation / Edition 1

Introduction to Optimal Estimation / Edition 1

by Edward W. Kamen, Jonathan K. Su, E. W. Kamen
     
 

ISBN-10: 185233133X

ISBN-13: 9781852331337

Pub. Date: 10/29/1999

Publisher: Springer London

This book provides an introductory, yet comprehensive, treatment of bo th Wiener and Kalman filtering along with a development of least-squar es estimation, maximum likelihood estimation, and maximum a posteriori estimation based on discrete-time measurements. Although this is a fa irly broad range of estimation techniques, it is possible to cover all of them in

Overview

This book provides an introductory, yet comprehensive, treatment of bo th Wiener and Kalman filtering along with a development of least-squar es estimation, maximum likelihood estimation, and maximum a posteriori estimation based on discrete-time measurements. Although this is a fa irly broad range of estimation techniques, it is possible to cover all of them in some depth in a single textbook, which is what is attempte d here. Emphasis is also placed on showing how these different approac hes to estimation fit together to form a systematic development of opt imal estimation. MATLAB is used in the development of a number of the book's examples and required for many of the homework problems.

Product Details

ISBN-13:
9781852331337
Publisher:
Springer London
Publication date:
10/29/1999
Series:
Advanced Textbooks in Control and Signal Processing Series
Edition description:
1999
Pages:
380
Product dimensions:
0.82(w) x 6.14(h) x 9.21(d)

Table of Contents

1 Introduction.- 1.1 Signal Estimation.- 1.2 State Estimation.- 1.3 Least Squares Estimation.- Problems.- 2 Random Signals and Systems with Random Inputs.- 2.1 Random Variables.- 2.2 Random Discrete-Time Signals.- 2.3 Discrete-Time Systems with Random Inputs.- Problems.- 3 Optimal Estimation.- 3.1 Formulating the Problem.- 3.2 Maximum Likelihood and Maximum a posteriori Estimation.- 3.3 Minimum Mean-Square Error Estimation.- 3.4 Linear MMSE Estimation.- 3.5 Comparison of Estimation Methods.- Problems.- 4 The Wiener Filter.- 4.1 Linear Time-Invariant MMSE Filters.- 4.2 The FIR Wiener Filter.- 4.3 The Noncausal Wiener Filter.- 4.4 Toward the Causal Wiener Filter.- 4.5 Derivation of the Causal Wiener Filter.- 4.6 Summary of Wiener Filters.- Problems.- 5 Recursive Estimation and the Kaiman Filter.- 5.1 Estimation with Growing Memory.- 5.2 Estimation of a Constant Signal.- 5.3 The Recursive Estimation Problem.- 5.4 The Signal/Measurement Model.- 5.5 Derivation of the Kaiman Filter.- 5.6 Summary of Kaiman Filter Equations.- 5.7 Kaiman Filter Properties.- 5.8 The Steady-state Kaiman Filter.- 5.9 The SSKF as an Unbiased Estimator.- 5.10 Summary.- Problems.- 6 Further Development of the Kaiman Filter.- 6.1 The Innovations.- 6.2 Derivation of the Kaiman Filter from the Innovations.- 6.3 Time-varying State Model and Nonstationary Noises.- 6.4 Modeling Errors.- 6.5 Multistep Kaiman Prediction.- 6.6 Kaiman Smoothing.- Problems.- 7 Kaiman Filter Applications.- 7.1 Target Tracking.- 7.2 Colored Process Noise.- 7.3 Correlated Noises.- 7.4 Colored Measurement Noise.- 7.5 Target Tracking with Polar Measurements.- 7.6 System Identification.- Problems.- 8 Nonlinear Estimation.- 8.1 The Extended Kalman Filter.- 8.2 An Alternate Measurement Update.- 8.3 Nonlinear System Identification Using Neural Networks.- 8.4 Frequency Demodulation.- 8.5 Target Tracking Using the EKF.- 8.6 Multiple Target Tracking.- Problems.- A The State Representation.- A.1 Discrete-Time Case.- A.2 Construction of State Models.- A.3 Dynamical Properties.- A.4 Discretization of Noise Covariance Matrices.- B The z-transform.- B.1 Region of Convergence.- B.2 z-transform Pairs and Properties.- B.3 The Inverse z-transform.- C Stability of the Kaiman Filter.- C.1 Observability.- C.2 Controllability.- C.3 Types of Stability.- C.4 Positive-Definiteness of P(n).- C.5 An Upper Bound for P(n).- C.6 A Lower Bound for P(n).- C.7 A Useful Control Lemma.- C.8 A Kaiman Filter Stability Theorem.- C.9 Bounds for P(n).- D The Steady-State Kaiman Filter.- D.2 A Stabilizability Lemma.- D.3 Preservation of Ordering.- D.5 Existence and Stability.- E Modeling Errors.- E.1 Inaccurate Initial Conditions.- E.2 Nonlinearities and Neglected States.- References.

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