Introduction to optimal estimation
type: Item
instance of: scholarly article
title: Introduction to optimal estimation
zbMATH Open document ID: 0988.93001
author: J. K. Su
author: E. W. Kamen
published in: Advanced Textbooks in Control and Signal Processing
publication date: 2000-02-06T00:00:00Z
review text: This book grew out of a series of lecture notes into an introductory but comprehensive treatment of Kalman and Wiener filtering, together with the consideration of least-squares estimation, maximum likelihood estimation, and maximum a posteriori estimation based on discrete-time measurements. Emphasis is also placed here on the relation of these different methods to a systematic development of optimal estimation. The background needed for the reading of the book is stated as being `a standard course on probability and random variables and one or more courses on signals and systems including a development of the state space theory of linear systems'. Summaries of other material needed are provided by the authors. There are unfortunately a fair number of typographical errors (even in the Series Editors' Foreword!) that detract from the appeal of the book. These would, however, probably be correctable by the reader without much difficulty. The mathematical statistician who reads this book will be jolted by a number of things that presumably would not bother the expert in filtering theory [cf. \textit{A. H. Jazwinski}, Stochastic processes and filtering theory, Academic Press (1970; Zbl 0203.50101)]. Let me mention a few of these here: 1. the defining, on page 28, of a probability space as \(S\) rather than a triple \((S, {\mathcal A},P)\); 2. the specifying of two random variables as independent if their joint p.d.f. factorizes into the product of the marginals without noting that this is required to hold for all values of the variables; 3. the defining, on page 71, of \(\widehat s(n)\) as an unbiased estimate (of \(s(n)?)\) when \(E[s(n)-\widehat s(n)]=0\). An on this point, it is wrong to write, in (3.6), \(\lim_{n\to \infty}E [\widehat s(n)]= E[s(n)]\). The Bayesian statistician will also be surprised to find maximum a posteriori estimation carried out in \S 3.2 with no parameters, though this might be seen as sanctioned by work like \textit{S. Geisser}, ``The futur…
Mathematics Subject Classification ID: 93-01
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93E25
zbMATH DE Number: 1399376
zbMATH Keywords: Wiener filtering
zbMATH Keywords: least-squares estimation
zbMATH Keywords: maximum likelihood estimation
zbMATH Keywords: maximum a posteriori estimation
zbMATH Keywords: optimal estimation
zbMATH Keywords: Kalman filters
reviewed by: Andrew Dale
describes a project that uses: Matlab
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1399376