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Exponential stability of discrete-time filters for bounded observation noise. (English) Zbl 0901.93066

Summary: This paper proves exponential asymptotic stability of discrete-time filters for the estimation of solutions to stochastic difference equations, when the observation noise is bounded. No assumption is made on the ergodicity of the signal. The proof uses the Hilbert projective metric, introduced into filter stability analysis by R. Atar and O. Zeitouni [SIAM J. Control Optimization 35, 36-55 (1997)]. It is shown that when the signal noise is sufficiently regular, boundedness of the observation noise implies that the filter update operation is, on average, a strict contraction with respect to the Hilbert metric. Asymptotic stability then follows.

MSC:

93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93E15 Stochastic stability in control theory
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