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IMA Journal of Mathematical Control and Information 2002 19(1 and 2):25-48; doi:10.1093/imamci/19.1_and_2.25
© 2002 by Institute of Mathematics and its Applications
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Mean-square filtering problem in hereditary systems with nonzero initial conditions

V. Kolmanovskii1, A. Matasov2 and P. Borne3

1 Moscow State Institute of Electronics and Mathematics, Space Research Institute (IKI), Russian Academy of Sciences, Russia 2 Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Space Research Institute (IKI), Russian Academy of Sciences, Russia 3 Ecole Centrale de Lille, France

The optimal mean-square filtering problem for linear hereditary dynamic systems with nonzero initial conditions is considered. In contrast to the resolved classical problem with zero initial conditions, the filtering problem under consideration reduces to a non-classical linear-quadratic optimal problem. The solution of the latter problem is unknown. We replace this non-classical problem by a simplified classical one, which has a known solution. The solution of this approximate problem is used instead of the solution for the exact original problem. By applying the duality theory we obtain an estimate for the nonoptimality level of the simplified solution. It is essential that this estimate can be computed without exactly solving the initial complex filtering problem.

Keywords: linear hereditary dynamic systems; stochastic mean-square filtering problem; duality theory.


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