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Type: Journal article
Title: Robust continuous-time smoothers without two-sided stochastic integrals
Author: Krishnamurthy, V.
Elliott, R.
Citation: IEEE Transactions on Automatic Control, 2002; 47(11):1824-1841
Publisher: IEEE-Inst Electrical Electronics Engineers Inc
Issue Date: 2002
ISSN: 0018-9286
Statement of
Vikram Krishnamurthy and Robert Elliott
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.
Keywords: Continuous time
hidden Markov models (HMMs)
maximum likelihood estimation
nonlinear smoothing
piecewise linear models
stochastic differential equations
Description: Copyright © 2002 IEEE
DOI: 10.1109/TAC.2002.804481
Appears in Collections:Applied Mathematics publications
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