Filtering of Multidimensional Stationary Processes with Missing Observations

Oleksandr Masyutka; Mikhail Moklyachuk; Maria Sidei

doi:10.32323/ujma.472929

EN

Filtering of Multidimensional Stationary Processes with Missing Observations

Abstract

The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process from observations of the process with a stationary noise is considered. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of the functionals are derived under the condition of spectral certainty, where spectral densities of the signal and the noise processes are exactly known. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities of the processes are not known exactly, while some sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics of the optimal estimates are derived for some special sets of admissible spectral densities.

Keywords

Minimax-Robust estimate,Least favourable spectral density

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Oleksandr Masyutka This is me
0000-0002-7301-8813
Ukraine

Mikhail Moklyachuk ^*
0000-0002-0605-0012
Ukraine

Maria Sidei This is me
0000-0003-1765-0969
Ukraine

Publication Date

March 20, 2019

Submission Date

October 22, 2018

Acceptance Date

March 4, 2019

Published in Issue

Year 2019 Volume: 2 Number: 1

DOI

https://doi.org/10.32323/ujma.472929

IZ

https://izlik.org/JA29DD69RY

APA

Masyutka, O., Moklyachuk, M., & Sidei, M. (2019). Filtering of Multidimensional Stationary Processes with Missing Observations. Universal Journal of Mathematics and Applications, 2(1), 24-32. https://doi.org/10.32323/ujma.472929

AMA

1.Masyutka O, Moklyachuk M, Sidei M. Filtering of Multidimensional Stationary Processes with Missing Observations. Univ. J. Math. Appl. 2019;2(1):24-32. doi:10.32323/ujma.472929

Chicago

Masyutka, Oleksandr, Mikhail Moklyachuk, and Maria Sidei. 2019. “Filtering of Multidimensional Stationary Processes With Missing Observations”. Universal Journal of Mathematics and Applications 2 (1): 24-32. https://doi.org/10.32323/ujma.472929.

EndNote

Masyutka O, Moklyachuk M, Sidei M (March 1, 2019) Filtering of Multidimensional Stationary Processes with Missing Observations. Universal Journal of Mathematics and Applications 2 1 24–32.

IEEE

[1]O. Masyutka, M. Moklyachuk, and M. Sidei, “Filtering of Multidimensional Stationary Processes with Missing Observations”, Univ. J. Math. Appl., vol. 2, no. 1, pp. 24–32, Mar. 2019, doi: 10.32323/ujma.472929.

ISNAD

Masyutka, Oleksandr - Moklyachuk, Mikhail - Sidei, Maria. “Filtering of Multidimensional Stationary Processes With Missing Observations”. Universal Journal of Mathematics and Applications 2/1 (March 1, 2019): 24-32. https://doi.org/10.32323/ujma.472929.

JAMA

1.Masyutka O, Moklyachuk M, Sidei M. Filtering of Multidimensional Stationary Processes with Missing Observations. Univ. J. Math. Appl. 2019;2:24–32.

MLA

Masyutka, Oleksandr, et al. “Filtering of Multidimensional Stationary Processes With Missing Observations”. Universal Journal of Mathematics and Applications, vol. 2, no. 1, Mar. 2019, pp. 24-32, doi:10.32323/ujma.472929.

Vancouver

1.Oleksandr Masyutka, Mikhail Moklyachuk, Maria Sidei. Filtering of Multidimensional Stationary Processes with Missing Observations. Univ. J. Math. Appl. 2019 Mar. 1;2(1):24-32. doi:10.32323/ujma.472929