Синтез квазіоптимальних швидкодіючих фільтрів з позицій критерію найменших квадратів

Abstract

The subject of the article research is special signal processing methods based on the optimal discrete filtering theory. The goal is to increase the efficiency of model-based methods for processing information signals by reducing computational costs and increasing the speed of optimal discrete filtering algorithms. Applied methods: description of dynamic processes in terms of state space using elements of vector-matrix algebra, weighted least squares method, elements of Kalman's theory of optimal discrete filtering, basic concepts of the O'Reilly–Luenberger theory of functional observers, elements of probability theory, statistical modeling by the Monte Carlo method. Results: a new method for reducing computational costs is proposed, which uses the approximation of the Kalman filter transfer matrix time dependence by given piecewise linear functions according to the least squares criterion. The effectiveness of the method was evaluated on the example of a second-order dynamical system. On the basis of a comparative analysis, several acceptable variants of the considered approximation are proposed. The practical significance of the work lies in the further development of methods for the synthesis of quasi-optimal high-speed filters. The operability of the proposed modifications is confirmed by the example of a second-order linear dynamic system. The efficiency of the algorithms was evaluated by the statistical modeling method according to the criterion "accuracy-computational costs". It is shown that the total savings in the number of multiplication and addition operations can reach tens of times due to insignificant losses in the accuracy of the filtering process.