Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise

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Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise. / Tovstik, T. M.

в: Vestnik St. Petersburg University: Mathematics, Том 54, № 1, 01.2021, стр. 86-94.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

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Tovstik, T. M. / Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise. в: Vestnik St. Petersburg University: Mathematics. 2021 ; Том 54, № 1. стр. 86-94.

BibTeX

@article{eba0dd55222a46078c81d986d56cd403,

title = "Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise",

abstract = "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.",

keywords = "Kalman–Bucy filter, vector autoregressive stationary process of high order, Bucy filter, Kalman&#8211",

author = "Tovstik, {T. M.}",

year = "2021",

month = jan,

doi = "10.1134/S1063454121010118",

language = "English",

volume = "54",

pages = "86--94",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Linear Kalman–Bucy Filter with Vector Autoregressive Signal and Noise

AU - Tovstik, T. M.

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&#8211

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

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