Posterior cramér-rao bounds for discrete-time nonlinear filtering

Petr Tichavský; Carlos H. Muravchik; Arye Nehorai

doi:10.1109/9780470544198.ch69

Posterior cramér-rao bounds for discrete-time nonlinear filtering

Petr Tichavský, Carlos H. Muravchik, Arye Nehorai

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

A mean-square error lower bound for the discretetime nonlinear filtering problem is derived based on the Van Trees (posterior) version of the Cramér-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.

Original language	English
Title of host publication	Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Publisher	Wiley-IEEE Press
Pages	686-696
Number of pages	11
ISBN (Electronic)	9780470544198
ISBN (Print)	0470120959, 9780470120958
DOIs	https://doi.org/10.1109/9780470544198.ch69
State	Published - Jan 1 2007

Keywords

Covariance matrix
Equations
Filtering
Joints
Mathematical model
Maximum likelihood detection
Zinc

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10.1109/9780470544198.ch69

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KW - Equations

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KW - Joints

KW - Mathematical model

KW - Maximum likelihood detection

KW - Zinc

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Posterior cramér-rao bounds for discrete-time nonlinear filtering

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