Discrete-time risk-sensitive filters with non-Gaussian initial conditions and their ergodic properties
Date
1999Publisher
IEEESource
Proceedings of the American Control ConferenceProceedings of the American Control Conference
Volume
6Pages
4403-4407Google Scholar check
Keyword(s):
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In this paper, we study asymptotic stability properties of risk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risk-sensitive filter asymptotically converges to any suboptimal filter initialized with an incorrect covariance matrix for the Initial state vector in the mean square sense provided the incorrect initializing value for the covariance matrix results in a risk-sensitive filter that is asymptotically stable. For non-Gaussian initial conditions, we show that under certain conditions, a suboptimal risk-sensitive filter initialized with Gaussian initial conditions asymptotically approaches the optimal risk-sensitive filter for non-Gaussian initial conditions in the mean square sense.