Robust continuous-time smoothers-without two-sided stochastic integrals

TitleRobust continuous-time smoothers-without two-sided stochastic integrals
Publication TypeConference Paper
Year of Publication2000
AuthorsKrishnamurthy, V., and R. Elliott
Conference NameDecision and Control, 2000. Proceedings of the 39th IEEE Conference on
Pagination286 -291 vol.1
Keywordscontinuous time systems, continuous-time partially observed nonlinear stochastic dynamical system, fixed-interval smoothing, hidden Markov model smoothers, hidden Markov models, maximum likelihood estimation, nonlinear dynamical systems, nonstochastic parabolic partial differential equations, observers, parabolic equations, partial differential equations, robust continuous-time smoothers, robust smoothed state estimates, smoothing methods, stochastic systems
Abstract

We consider the problem of fixed-interval smoothing of a continuous-time partially observed nonlinear stochastic dynamical system. Existing results for such smoothers require the use of two sided stochastic calculus. The main contribution of this paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the smoothing equations are non-stochastic parabolic partial differential equations (with random coefficients)-and hence the technical machinery associated with two sided stochastic calculus is not required. Furthermore, the robust smoothed state estimates are locally Lipschitz in the observations-which is useful for numerical simulation. As examples, finite dimensional robust versions of the hidden Markov model smoothers are derived-these finite dimensional smoothers do not involve stochastic integrals

URLhttp://dx.doi.org/10.1109/CDC.2000.912774
DOI10.1109/CDC.2000.912774

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