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Mean-square filtering problem for discrete Volterra equations. (English) Zbl 1072.93025

Classical mean-square filtering problems for a discrete Volterra equation are studied. The well-known Kalman filtering technique can be used, but if the measurements are large then the matrices are of high dimension and this is difficult to deal with. Here an approximate model is proposed, described by a difference equation of a moderate dimension.
The reduced Kalman filter is an approximate but efficient estimator. Using the duality theory of convex variational problems, a level of nonoptimality for the chosen filter is obtained. The level can be efficiently computed without exactly solving the full filtering problem.

MSC:

93E11 Filtering in stochastic control theory
93C55 Discrete-time control/observation systems
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References:

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