Optimal filtering for linear systems with state and multiple observation delays. (English) Zbl 1167.93400

Basin, M.; Alcorta-Garcia, M. A.; Alanis-Duran, A.

Int. J. Syst. Sci. 39, No. 5, 547-555 (2008).

Summary: This article solves the optimal filtering problem for linear systems with state and multiple observation delays. An optimal estimate equation similar to the traditional Kalman-Bucy one is derived, and the system of equations for determining the filter gain matrix consists of an infinite set of equations. It is then demonstrated that a finite set of the filtering equations can be obtained in case of commensurable delays. In the example, the designed optimal filter is compared to the traditional Kalman-Bucy filter.

MSC:

93E11	Filtering in stochastic control theory
93C05	Linear systems in control theory
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
93E20	Optimal stochastic control

Keywords:

filtering; stochastic system; time-delay system

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