Geodesic
Approximation of a guaranteed estimation problem with mixed constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 4, pp. 48-63

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Questions of finite-dimensional approximation for a guaranteed estimation problem are considered for linear nonstationary systems with disturbances subject to mixed integral and geometric constraints, where the geometric constraints are not assumed to be compact. The parameters of the system and the measurement equation are formed in such a way that the state vector of the system is not subject to geometric constraints. Under these assumptions, one can reduce the estimation problem to an optimal control problem without state constraints and use Pontryagin's maximum principle. A discrete multistep system is proposed for which the information set converges in the Hausdorff metric to the corresponding information set of a continuous system as the partition step of the observation interval vanishes. Estimates characterizing the convergence rate are derived and an example is given.
Keywords: guaranteed estimation, filtering, variational inequalities, normal cone, maximum principle
Mots-clés : information set. 
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B. I. Anan'ev; P. A. Yurovskikh. Approximation of a guaranteed estimation problem with mixed constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 4, pp. 48-63. http://geodesic.mathdoc.fr/item/TIMM_2020_26_4_a2/