On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

Jinya Su; Baibing Li; Wen Hua Chen

doi:10.1016/j.automatica.2014.12.044

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

Jinya Su, Baibing Li, Wen Hua Chen

Computing Science

Loughborough University

Research output: Contribution to journal › Article › peer-review

61 Citations (Scopus)

Abstract

For linear stochastic time-varying systems, we investigate the properties of the Kalman filter with partially observed inputs. We first establish the existence condition of a general linear filter when the unknown inputs are partially observed. Then we examine the optimality of the Kalman filter with partially observed inputs. Finally, on the basis of the established existence condition and optimality result, we investigate asymptotic stability of the filter for the corresponding time-invariant systems. It is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases, including the classical Kalman filter and state estimation with unknown inputs.

Original language	English
Pages (from-to)	149-154
Number of pages	6
Journal	Automatica
Volume	53
DOIs	https://doi.org/10.1016/j.automatica.2014.12.044
Publication status	Published - 1 Mar 2015

Bibliographical note

Funding Information:
This work was jointly funded by UK Engineering and Physical Sciences Research Council (EPSRC) and BAE Systems ( EP/H501401/1 ). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen.

Publisher Copyright:
© 2014 The Authors.

Keywords

Asymptotic stability
Existence
Kalman filter
Optimality
Unknown inputs

Access to Document

10.1016/j.automatica.2014.12.044Licence: CC BY

Cite this

@article{0e46102c5e79458384a9e179b817f51e,

title = "On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs",

abstract = "For linear stochastic time-varying systems, we investigate the properties of the Kalman filter with partially observed inputs. We first establish the existence condition of a general linear filter when the unknown inputs are partially observed. Then we examine the optimality of the Kalman filter with partially observed inputs. Finally, on the basis of the established existence condition and optimality result, we investigate asymptotic stability of the filter for the corresponding time-invariant systems. It is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases, including the classical Kalman filter and state estimation with unknown inputs.",

keywords = "Asymptotic stability, Existence, Kalman filter, Optimality, Unknown inputs",

author = "Jinya Su and Baibing Li and Chen, {Wen Hua}",

note = "Funding Information: This work was jointly funded by UK Engineering and Physical Sciences Research Council (EPSRC) and BAE Systems ( EP/H501401/1 ). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen. Publisher Copyright: {\textcopyright} 2014 The Authors.",

year = "2015",

month = mar,

day = "1",

doi = "10.1016/j.automatica.2014.12.044",

language = "English",

volume = "53",

pages = "149--154",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier",

}

TY - JOUR

T1 - On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

AU - Su, Jinya

AU - Li, Baibing

AU - Chen, Wen Hua

N1 - Funding Information: This work was jointly funded by UK Engineering and Physical Sciences Research Council (EPSRC) and BAE Systems ( EP/H501401/1 ). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen. Publisher Copyright: © 2014 The Authors.

PY - 2015/3/1

Y1 - 2015/3/1

N2 - For linear stochastic time-varying systems, we investigate the properties of the Kalman filter with partially observed inputs. We first establish the existence condition of a general linear filter when the unknown inputs are partially observed. Then we examine the optimality of the Kalman filter with partially observed inputs. Finally, on the basis of the established existence condition and optimality result, we investigate asymptotic stability of the filter for the corresponding time-invariant systems. It is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases, including the classical Kalman filter and state estimation with unknown inputs.

AB - For linear stochastic time-varying systems, we investigate the properties of the Kalman filter with partially observed inputs. We first establish the existence condition of a general linear filter when the unknown inputs are partially observed. Then we examine the optimality of the Kalman filter with partially observed inputs. Finally, on the basis of the established existence condition and optimality result, we investigate asymptotic stability of the filter for the corresponding time-invariant systems. It is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases, including the classical Kalman filter and state estimation with unknown inputs.

KW - Asymptotic stability

KW - Existence

KW - Kalman filter

KW - Optimality

KW - Unknown inputs

UR - http://www.scopus.com/inward/record.url?scp=84924117026&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2014.12.044

DO - 10.1016/j.automatica.2014.12.044

M3 - Article

AN - SCOPUS:84924117026

SN - 0005-1098

VL - 53

SP - 149

EP - 154

JO - Automatica

JF - Automatica

ER -

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this