Approximation of the Expanded Filter of Kalman Parallel Two-cascade Structure

Abstract

The given paper considers the problem of linear dynamic system state estimation in the presence of possible perturbations. Generally, perturbation is considered to be a constituent of linear dynamic system state vector. Assessment, in this case, is carried out in the same way. At such interpretation the standard decision is the Kalman filter with expanded state vector. Implementation of such filter is connected with considerable difficulties of computing character. For their overcoming Friedland suggested to use structure which consists of two, independent, smaller dimension parallel filters instead of an expanded Kalman filter. The method of parallel separate estimation is used as an effective remedy of reduction of the computing expenses connected with implementation of an expanded Kalman filter which dimension considerably exceeds dimension of controlled system. In this case linear combination of exits of such structure, approximates an exit of an expanded Kalman filter. The computing efficiency of parallel structure with two cascades, long time, is very popular in such directions as problems of tracking it is high-speed purposes or a perspective of nonlinear assessment in the presence of possible malfunctions. It is known that the decomposition recommended by Friedland is optimum only for perturbations of the determined type. In a situation of completely accidental vector of perturbation this structure is suboptimal. The practical difficulties connected with complexity of calculations of certain algebraic algorithms are the reason of it. As these restrictions are rigidly imposed, it is possible to overcome them seldom or never. The purpose of this work is researches of one of possible options of modification Friedland structure for the purpose of its reduction to an expanded Kalman filter with less strict restrictions. As the basis, for the considered modernization use of a orthogonal transformation method of matrixes for the purpose of receiving two standard Kallman filters of special type is necessary. Linear combination of these filters exits will also approximate an exit of the expanded Kalman filter, and introduction of the additional adjusting inputs considerably will weaken, considered in other works, restrictions.

In the conclusion, the method of mathematical modeling showed efficiency of the modified structure. Comparative analysis with the results received in other works is carried out.