Cite this article as:

Pristavko V. T., Litvin A. Y. Optimal filtration of matrix gaussian random processes in planes lateral motion problem . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 2, pp. 78-85. DOI: https://doi.org/10.18500/1816-9791-2013-13-2-1-78-85

Language:

Russian

Heading:

Mechanics

Optimal filtration of matrix gaussian random processes in planes lateral motion problem

Authors:

Pristavko Vladislav Tarasovich, Saint Petersburg State University, Russia, 199034, St. Petersburg, Universitetskaya nab., 7-9 , pvt1@yandex.ru

Litvin Aleksei Yur'evich, Saint Petersburg State University, Russia, 199034, St. Petersburg, Universitetskaya nab., 7-9 , alybey@mail.ru

Abstract:

In practice, observation problem is more complex because of random influences (noises): wind effects plane course, sensor errors distort object position view. In order to reduce noise filters are used. Proposed to carry out a simultaneous filtering of identical objects motion by defining problem in matrix variables. To achieve phisical realizability controlled matrix filter was proposed. Statements that allow to find the optimal solution was proved.

Key words:

matrix filtration, n-covariance matrix, square-law functional.

DOI:

https://doi.org/10.18500/1816-9791-2013-13-2-1-78-85

References

1. Lipcer R. S., Sirjaev A. N. Statistika sluchainykh

protsessov (nelineinaya filtratsiya i smezhnye voprosy)

[Statistics of random processes (Nonlinear filtering and

related problems)]. Probability Theory and Mathematical

Statistics, vol. 15. Moscow, Nauka, 1974, 696 pp. (in

Russian).

2. Pristavko V. T. Matpichnye modeli uppavleniia [Matrix