Recursive Nonlinear Estimation : A Geometric Approach

By: Rudolph Kulhavy

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In a close analogy to matching data in Euclidean space, this monograph views parameter estimation as matching of the empirical distribution of data with a model-based distribution. Using an appealing Pythagorean-like geometry of the empirical and model distributions, the book brings a new solution to the problem of recursive estimation of non-Gaussian and nonlinear models which can be regarded as a specific approximation of Bayesian estimation. The cases of independent observations and controlled dynamic systems are considered in parallel; the former case giving initial insight into the latter case which is of primary interest to the control community. A number of examples illustrate the key concepts and tools used. This unique monograph follows some previous results on the Pythagorean theory of estimation in the literature (e.g., Chentsov, Csiszar and Amari) but extends the results to the case of controlled dynamic systems.

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Inference Under Constraints	p. 1
From Matching Data to Matching Probabilities	p. 13
Optimal Estimation with Compressed Data	p. 63
Approximate Estimation with Compressed Data	p. 129
Numerical Implementation	p. 179
Concluding Remarks	p. 191
Selected Topics from Probability Theory	p. 199
Selected Topics from Convex Optimization	p. 209
References	p. 213
Index	p. 223
Table of Contents provided by Blackwell. All Rights Reserved.

Recursive Nonlinear Estimation : A Geometric Approach

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