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

Authors:
Miroslav ŠImandl;Jakub KráLovec;Petr Tichavský
Affiliations:
Department of Cybernetics, Faculty of Applied Sciences, University of West Bohemia, Univerzitnı 8, 30614 Pilsen, Czech Republic;Department of Cybernetics, Faculty of Applied Sciences, University of West Bohemia, Univerzitnı 8, 30614 Pilsen, Czech Republic;Institute for Information Theory and Automation, Academy of Sciences of the Czech Republic, Box 18, 18208 Prague, Czech Republic
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

Cramer-Rao lower bounds for the discrete-time nonlinear state estimation problem are treated. The Cramer-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 Cramer-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 Cramer-Rao bounds, their mutual comparison and utilization for quality evaluation of some nonlinear filters are shown in numerical examples.