Probabilistic convergence of Kalman filtering with nonstationary intermittent observations

Junfeng Wu; Guodong Shi; Karl Henrik  Johansson

doi:10.1109/CDC.2014.7039978

Probabilistic convergence of Kalman filtering with nonstationary intermittent observations

Junfeng Wu, Guodong Shi, Karl Henrik Johansson

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we consider state estimation using a Kalman filter of a linear time-invariant process with nonstationary intermittent observations caused by packet losses. The packet loss process is modeled as a sequence of independent, but not necessarily identical Bernoulli random variables. Under this model, we show how the probabilistic convergence of the trace of the prediction error covariance matrices, which is denoted as Tr(P<inf>k</inf>), depends on the statistical property of the nonstationary packet loss process. A series of sufficient and/or necessary conditions for the convergence of sup<inf>k=n</inf> Tr(P<inf>k</inf>) and inf<inf>k=n</inf> Tr(P<inf>k</inf>) are derived. In particular, for one-step observable linear system, a sufficient and necessary condition for the convergence of inf<inf>k=n</inf> Tr(P<inf>k</inf>) is provided.

Original language	English
Title of host publication	Critical Observations in a Diagnostic Problem
Place of Publication	Piscataway, New Jersey, US
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3783-3788
Edition	Peer Reviewed
ISBN (Print)	9781479977451
DOIs	https://doi.org/10.1109/CDC.2014.7039978
Publication status	Published - 2014
Event	53rd IEEE Conference on Decision and Control - Los Angeles, USA, United States Duration: 1 Jan 2014 → …

Conference

Conference	53rd IEEE Conference on Decision and Control
Country/Territory	United States
Period	1/01/14 → …
Other	December 15-17 2014

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10.1109/CDC.2014.7039978

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title = "Probabilistic convergence of Kalman filtering with nonstationary intermittent observations",

abstract = "In this paper, we consider state estimation using a Kalman filter of a linear time-invariant process with nonstationary intermittent observations caused by packet losses. The packet loss process is modeled as a sequence of independent, but not necessarily identical Bernoulli random variables. Under this model, we show how the probabilistic convergence of the trace of the prediction error covariance matrices, which is denoted as Tr(Pk), depends on the statistical property of the nonstationary packet loss process. A series of sufficient and/or necessary conditions for the convergence of supk=n Tr(Pk) and infk=n Tr(Pk) are derived. In particular, for one-step observable linear system, a sufficient and necessary condition for the convergence of infk=n Tr(Pk) is provided.",

author = "Junfeng Wu and Guodong Shi and Johansson, {Karl Henrik}",

year = "2014",

doi = "10.1109/CDC.2014.7039978",

language = "English",

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pages = "3783--3788",

booktitle = "Critical Observations in a Diagnostic Problem",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

address = "United States",

edition = "Peer Reviewed",

note = "53rd IEEE Conference on Decision and Control ; Conference date: 01-01-2014",

}

Wu, J, Shi, G & Johansson , KH 2014, Probabilistic convergence of Kalman filtering with nonstationary intermittent observations. in Critical Observations in a Diagnostic Problem. Peer Reviewed edn, Institute of Electrical and Electronics Engineers Inc., Piscataway, New Jersey, US, pp. 3783-3788, 53rd IEEE Conference on Decision and Control, United States, 1/01/14. https://doi.org/10.1109/CDC.2014.7039978

Probabilistic convergence of Kalman filtering with nonstationary intermittent observations. / Wu, Junfeng; Shi, Guodong; Johansson , Karl Henrik .
Critical Observations in a Diagnostic Problem. Peer Reviewed. ed. Piscataway, New Jersey, US: Institute of Electrical and Electronics Engineers Inc., 2014. p. 3783-3788.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Probabilistic convergence of Kalman filtering with nonstationary intermittent observations

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AU - Shi, Guodong

AU - Johansson , Karl Henrik

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N2 - In this paper, we consider state estimation using a Kalman filter of a linear time-invariant process with nonstationary intermittent observations caused by packet losses. The packet loss process is modeled as a sequence of independent, but not necessarily identical Bernoulli random variables. Under this model, we show how the probabilistic convergence of the trace of the prediction error covariance matrices, which is denoted as Tr(Pk), depends on the statistical property of the nonstationary packet loss process. A series of sufficient and/or necessary conditions for the convergence of supk=n Tr(Pk) and infk=n Tr(Pk) are derived. In particular, for one-step observable linear system, a sufficient and necessary condition for the convergence of infk=n Tr(Pk) is provided.

AB - In this paper, we consider state estimation using a Kalman filter of a linear time-invariant process with nonstationary intermittent observations caused by packet losses. The packet loss process is modeled as a sequence of independent, but not necessarily identical Bernoulli random variables. Under this model, we show how the probabilistic convergence of the trace of the prediction error covariance matrices, which is denoted as Tr(Pk), depends on the statistical property of the nonstationary packet loss process. A series of sufficient and/or necessary conditions for the convergence of supk=n Tr(Pk) and infk=n Tr(Pk) are derived. In particular, for one-step observable linear system, a sufficient and necessary condition for the convergence of infk=n Tr(Pk) is provided.

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DO - 10.1109/CDC.2014.7039978

M3 - Conference contribution

SN - 9781479977451

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BT - Critical Observations in a Diagnostic Problem

PB - Institute of Electrical and Electronics Engineers Inc.

CY - Piscataway, New Jersey, US

T2 - 53rd IEEE Conference on Decision and Control

Y2 - 1 January 2014

ER -

Probabilistic convergence of Kalman filtering with nonstationary intermittent observations

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