Browsing by Author "Malcolm, W. P."
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- ItemOpen AccessA deterministic discretisation-step upper bound for state estimation via Clark transformations(2004-01-01) Malcolm, W. P.; Elliott, R. J.; van der Hoek, J.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.
- ItemOpen AccessDiscrete-Time Expectation Maximization Algorithms for Markov-Modulated Poisson Processes(IEEE Control Systems Society, 2008) Elliott, Robert; Malcolm, W. P.In this paper, we consider parameter estimation Markov-modulated Poisson processes via robust filtering and smoothing techniques. Using the expectation maximization algorithm framework, our filters and smoothers can be applied to estimate the parameters of ourmodel in either an online configuration or an offline configuration. Further, our estimator dynamics do not involve stochastic integrals and our new formulas, in terms of time integrals, are easily discretized, and are written in numerically stable forms inW. P.Malcolm, R. J. Elliott, and J. van der Hoek, “On the numerical stability of time-discretized state estimation via clark transformations,” presented at the IEEE Conf. Decision Control, Mauii, HI, Dec. 2003.