Алгоритмы дискретной фильтрации на основе модифицированной взвешенной ортогонализации Грама –Шмидта для дискретных стохастических систем с мультипликативными и аддитивными шумами

Abstract

Discrete-time stochastic systems with multiplicative and additive noises describe a wide class of mathematical models of complex systems, for example, industrial-technological, energy, economic, telecommunication, aerospace systems, etc. An important class of algorithms for processing measure ment information in complex systems are Kalman-type discrete-time filtering algorithms. Purpose. Construction of new discrete-time filtering algorithms for discrete-time linear systems with multiplicative and additive noises based on numerically stable modified weighted Gram – Schmidt orthogonalization (MWGS). Methodology. The methods of computational linear algebra were used, namely, the direct procedu re of MWGS-orthogonalization, the theory of Kalman filtering, methods of scientific programming in MATLAB. Findings. New LD-algorithms for discrete-time filtering in covariance and informational form for discrete-time stochastic systems with multiplicative and additive noises are constructed. The algorithms have an extended array form allowing updates for all necessary filter values. The method employs numerically stable modified weighted Gram – Schmidt orthogonalization. Algebraic equiva lence of LD-filters to Kalman-type covariance and informational algorithms for linear discrete time stochastic systems with multiplicative and additive noises is proved. The conducted numerical experiments have shown the effectiveness of the proposed algorithms using the example of solving the problem of parametric estimation of a model of almost rectilinear motion, as well as their savings in computation time compared to previously constructed UD filters. Value. New discrete-time filtering LD-algorithms can be used as a reliable computational alterna tive to the Kalman-type “standard algorithms” since they have the property being numerically stable to machine round-off errors due to the use of the MWGS orthogonalization computational procedure at each iteration of the algorithm. The results can be used to solve problems of measurement information processing in discrete-time systems with multiplicative and additive noise.