A deterministic discretisation-step upper bound for state estimation via Clark transformations
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2004-01-01
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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.
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W. P. Malcolm, R. J. Elliott, and J. van der Hoek, “A deterministic discretisation-step upper bound for state estimation via Clark transformations,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2004, no. 4, pp. 371-384, 2004. doi:10.1155/S1048953304311032