The Confidence Approach in the Dynamic System State Estimation Problem

Abstract

The report considers the problem of determining dynamic plant state estimates under the influence of random and uncertain factors acting separately or jointly. The quality criterion of the estimates obtained is a probability of an estimate error not exceeding a certain pre-set threshold.In oraer to obtain these estimates, the authors sug-gest the generalized minimax (confidence) approach developed by them; the essence of this approach consists in reducing the original probability problem to an equivalent minimax problem of deterministic structure. In terms of this approach the authors present a formulation of the conditions which make it possible to generate data processing algorithms with the properties mentioned above. The authors also suggest using the optimization of the measurement procedure according to the probability criterion as an additional way of improving the estimation accuracy. In order to solve this problem, an approach has been developed which uses the analytical properties of the Riccati type equation and makes it possible to reduce the nonlinear problem of optimization of the measurement procedure in a dynamic system to a linear one with respect to phase variables. In order to obtain the optimal schedules of navigation measurement in specific engineering problems, an effective modified Krylov-Chernousko-method-based numerical procedure has been developed.