Research output: Contribution to journal › Article › peer-review
Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise. / Tovstik, T. M.
In: Vestnik St. Petersburg University: Mathematics, Vol. 54, No. 1, 01.2021, p. 86-94.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise
AU - Tovstik, T. M.
N1 - Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/1
Y1 - 2021/1
N2 - We consider the linear Kalman-Bucy filter problem for a system in which a signal and a noise are independent vector stationary autoregressive processes with orders higher than 1. Recurrent equations for the filtration and its error are derived. The optimal definition of the initial data is proposed. We describe an example in which the algorithm leads to a stationary mode at infinity, as well as an example in which the Kalman-Bucy filter is impossible since the filtration error tends to infinity. The behavior of the signal and its filter is illustrated by the simulation of the signal and the noise as Gaussian vector stationary autoregressive processes. These examples support the theoretical conclusions.
AB - We consider the linear Kalman-Bucy filter problem for a system in which a signal and a noise are independent vector stationary autoregressive processes with orders higher than 1. Recurrent equations for the filtration and its error are derived. The optimal definition of the initial data is proposed. We describe an example in which the algorithm leads to a stationary mode at infinity, as well as an example in which the Kalman-Bucy filter is impossible since the filtration error tends to infinity. The behavior of the signal and its filter is illustrated by the simulation of the signal and the noise as Gaussian vector stationary autoregressive processes. These examples support the theoretical conclusions.
KW - Kalman–Bucy filter
KW - vector autoregressive stationary process of high order
KW - Bucy filter
KW - Kalman–
UR - http://www.scopus.com/inward/record.url?scp=85102680101&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/b52e9b1c-b6d7-31e5-b025-797fa58fb99f/
U2 - 10.1134/S1063454121010118
DO - 10.1134/S1063454121010118
M3 - Article
AN - SCOPUS:85102680101
VL - 54
SP - 86
EP - 94
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 1
ER -
ID: 76383486