Filtering, predictive, and smoothing Cramér–Rao bounds for discrete-time nonlinear dynamic systems

Cramér–Rao lower bounds for the discrete-time nonlinear state estimation problem are treated. The Cramér–Rao bound for the mean-square error matrix of a state estimate is particularly important for quality evaluation of nonlinear state estimators as it represents a limit of cognizability of the stat...

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Bibliographic Details
Published in:Automatica (Oxford) 2001-11, Vol.37 (11), p.1703-1716
Main Authors: Šimandl, Miroslav, Královec, Jakub, Tichavský, Petr
Format: Article
Language:English
Subjects:
Cramér–Rao bound
Filtering
Mean-square error
Nonlinear state estimation
Nonlinear systems
Prediction
Smoothing
Stochastic systems
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Summary:Cramér–Rao lower bounds for the discrete-time nonlinear state estimation problem are treated. The Cramér–Rao bound for the mean-square error matrix of a state estimate is particularly important for quality evaluation of nonlinear state estimators as it represents a limit of cognizability of the state. Recursive relations for filtering, predictive, and smoothing Cramér–Rao bounds are derived to establish a unifying framework for several previously published derivation procedures and results. Lower bounds for systems with unknown parameters are newly provided. Computation of filtering, predictive, and smoothing Cramér–Rao bounds, their mutual comparison and utilization for quality evaluation of some nonlinear filters are shown in numerical examples.
ISSN:0005-1098
1873-2836
DOI:10.1016/S0005-1098(01)00136-4