Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than...

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Bibliographic Details
Published in:IEEE transactions on signal processing 1998-05, Vol.46 (5), p.1386-1396
Main Authors: Tichavsky, P., Muravchik, C.H., Nehorai, A.
Format: Article
Language:English
Subjects:
Adaptive control
Adaptive filters
Applied sciences
Autoregressive processes
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Filtering
Frequency estimation
Information, signal and communications theory
Multidimensional systems
Phase modulation
Phase noise
Recursive estimation
Signal and communications theory
Signal, noise
Telecommunications and information theory
Time varying systems
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Summary:A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-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.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.668800