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Journal of Applied Mathematics and Stochastic Analysis - Volume 2004 2004, Issue 4, Pages 371-384



Haskayne School of Business, University of Calgary, 2500 University Drive NW, Alberta, Calgary, Canada T2N 1N4

School of Mathematical Sciences, The University of Adelaide, 5005, SA, Australia

Received 11 November 2003; Revised 2 June 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the numerical stabilityof discretisation schemes for continuous-time state estimation filters. The dynamical systemswe consider model the indirect observationof a continuous-time Markov chain. Two candidateobservation models are studied. These models are a the observation of the state through a Brownian motion,and b the observation of the state through a Poisson process. It is shown that for robust filters via Clark-s transformation,one can ensure nonnegative estimated probabilities by choosing amaximum grid step to be no greater than a given bound. Theimportance of this result is that one can choose an a priori grid step maximum ensuring nonnegative estimated probabilities. Incontrast, no such upper bound is available for the standardapproximation schemes. Further, this upper bound also applies tothe corresponding robust smoothing scheme, in turn ensuringstability for smoothed state estimates.





Author: W. P. Malcolm, R. J. Elliott, and J. van der Hoek

Source: https://www.hindawi.com/



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