V. G. Naidenov, V. I. Polyakov, Yu. V. Snytkin
Now at synthesis of discrete Kalman filters there is a problem of a finding of correct values of matrix factors for the base equations describing partially stochastic processes.
In this article the method is developed and the algorithm for the decision of this problem is synthesised.
The developed method uses properties of the stochastic differential equations and matrix exponent, and also specially constructed block matrix.
For achievement of demanded accuracy of calculations in algorithm two basic procedures are provided. The first procedure provides the decision of the differential equations for matrix exponent and Lyapunov's matrix equation at specially chosen time interval by calculation of the sums of final matrix numbers.
The second procedure provides a finding of decisions of the specified matrix equations for the set period of repetition of investigated discrete process by use of iterative procedures with doubling of an initial time interval.
Algorithm have the guaranteed accuracy and provide adequate formations of matrix factors of the recurrent stochastic equations describing discrete stochastic processes for any demanded periods of their repetition.
The developed method of formation of matrix factors of the recurrent stochastic equations in algorithms of a dynamic filtration of trajectory measurements has been approved at realisation of concrete measuring experiment and has shown the working capacity