Robust continuous-time smoothers without two-sided stochastic integrals

TitleRobust continuous-time smoothers without two-sided stochastic integrals
Publication TypeJournal Article
Year of Publication2002
AuthorsKrishnamurthy, V., and R. Elliott
JournalAutomatic Control, IEEE Transactions on
Volume47
Pagination1824 - 1841
Date Publishednov.
ISSN0018-9286
KeywordsBenes smoother, continuous time systems, continuous-time partially observed nonlinear stochastic dynamical system, finite-dimensional smoothers, fixed-interval smoothing, hidden Markov model smoother, hidden Markov models, locally Lipschitz observations, maximum likelihood estimation, nonlinear smoothing, nonlinear systems, observers, parabolic equations, partial differential equations, piecewise linear dynamics, piecewise linear models, robust continuous-time smoothers, robust smoothed state estimates, smoothing methods, stochastic differential equations, 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 the paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the smoothing equations are nonstochastic 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 Benes and hidden Markov model smoothers and smoothers for piecewise linear dynamics are derived; these finite-dimensional smoothers do not involve stochastic integrals.

URLhttp://dx.doi.org/10.1109/TAC.2002.804481
DOI10.1109/TAC.2002.804481

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