title: Linear Kalman—Bucy filter with an autoregressive signal and noise
metadata.name: dc.contributor.author
metadata.value: Tovstik, Tatiana M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:47:09Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:47:09Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Tovstik T.M. Linear Kalman—Bucy filter with an autoregressive signal and noise. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 452–463.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.309
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14888
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the Kalman—Bucy filter problem the observed process consists of a sum of a signal and
  of a noise. The filter begins simultaneously with the beginning of observation, and it is
  necessary to estimate a signal. As a rule, this problem is studied both for scalar and for
  vector Markovian processes. In this paper, the scalar linear problem is considered, but a
  signal and a noise are independent stationary autoregressive processes with orders larger
  than unit. The recurrent equations for the filter process, for its error, and for its condition correlations are obtained. These recurrent equations contain the previous estimates and
  some last observed data. The optimal definition of initial data is proposed. The algebraic
  equations for the limit values of the filter error and for the limit cross-correlations are
  delivered. The roots of these equations lead to a criterion of the filter process convergence.
  Some examples at that the filter process converges or not converges are given. The Monte-
  Carlo method is used for a control of theoretical formulas for the filter and its error.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант 17-01-00267а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: Kalman—Bucy filter
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: autoregressive processes of high order
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Linear Kalman—Bucy filter with an autoregressive signal and noise
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 09-Tovstik.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14888/1/09-Tovstik.pdf
resources.format: Adobe PDF
resources.size: 698,93 kB