A deterministic discretisation-step upper bound for state estimation via Clark transformations
Date
2004
Authors
Malcolm, W.
Elliott, R.
Van Der Hoek, J.
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Journal article
Citation
Journal of Applied Mathematics and Stochastic Analysis, 2004; 2004(4):371-384
Statement of Responsibility
W. P. Malcolm, R. J. Elliott, and J. van der Hoek
Conference Name
Abstract
We consider the numerical stability of discretisation schemes for continuous-time state estimation filters. The dynamical systems we consider model the indirect observation of a continuous-time Markov chain. Two candidate observation 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 a maximum grid step to be no greater than a given bound. The importance of this result is that one can choose an a priori grid step maximum ensuring nonnegative estimated probabilities. In contrast, no such upper bound is available for the standard approximation schemes. Further, this upper bound also applies to the corresponding robust smoothing scheme, in turn ensuring stability for smoothed state estimates.
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Copyright © 2004 Hindawi Publishing Corporation