Kalman filtering with Markovian packet losses and stability criteria

Minyi Huang; Subhrakanti Dey

doi:10.1109/cdc.2006.376710

Kalman filtering with Markovian packet losses and stability criteria

Minyi Huang^*, Subhrakanti Dey

^*Corresponding author for this work

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

16 Citations (Scopus)

Abstract

We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. We analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, which describes the upper envelope of the sequence of error covariance matrices {P_t, t > 1} for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case; for the scalar case we obtain a sufficient and necessary condition, and derive upper and lower bounds for the tail distribution of the peak variance. For practically verifying the stability condition, we further introduce a suboptimal estimator and develop a numerical procedure to generate tighter estimate for the constants involved in the stability criterion.

Original language	English
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5621-5626
Number of pages	6
ISBN (Print)	1424401712, 9781424401710
DOIs	https://doi.org/10.1109/cdc.2006.376710
Publication status	Published - 2006
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: 13 Dec 2006 → 15 Dec 2006

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	45th IEEE Conference on Decision and Control 2006, CDC
Country/Territory	United States
City	San Diego, CA
Period	13/12/06 → 15/12/06

Access to Document

10.1109/cdc.2006.376710

Cite this

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title = "Kalman filtering with Markovian packet losses and stability criteria",

abstract = "We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. We analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, which describes the upper envelope of the sequence of error covariance matrices \{Pt, t > 1\} for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case; for the scalar case we obtain a sufficient and necessary condition, and derive upper and lower bounds for the tail distribution of the peak variance. For practically verifying the stability condition, we further introduce a suboptimal estimator and develop a numerical procedure to generate tighter estimate for the constants involved in the stability criterion.",

author = "Minyi Huang and Subhrakanti Dey",

year = "2006",

doi = "10.1109/cdc.2006.376710",

language = "English",

isbn = "1424401712",

series = "Proceedings of the IEEE Conference on Decision and Control",

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

pages = "5621--5626",

booktitle = "Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC",

address = "United States",

note = "45th IEEE Conference on Decision and Control 2006, CDC ; Conference date: 13-12-2006 Through 15-12-2006",

}

Huang, M & Dey, S 2006, Kalman filtering with Markovian packet losses and stability criteria. in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177590, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5621-5626, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 13/12/06. https://doi.org/10.1109/cdc.2006.376710

Kalman filtering with Markovian packet losses and stability criteria. / Huang, Minyi; Dey, Subhrakanti.
Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. p. 5621-5626 4177590 (Proceedings of the IEEE Conference on Decision and Control).

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

TY - GEN

T1 - Kalman filtering with Markovian packet losses and stability criteria

AU - Huang, Minyi

AU - Dey, Subhrakanti

PY - 2006

Y1 - 2006

N2 - We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. We analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, which describes the upper envelope of the sequence of error covariance matrices {Pt, t > 1} for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case; for the scalar case we obtain a sufficient and necessary condition, and derive upper and lower bounds for the tail distribution of the peak variance. For practically verifying the stability condition, we further introduce a suboptimal estimator and develop a numerical procedure to generate tighter estimate for the constants involved in the stability criterion.

AB - We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. We analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, which describes the upper envelope of the sequence of error covariance matrices {Pt, t > 1} for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case; for the scalar case we obtain a sufficient and necessary condition, and derive upper and lower bounds for the tail distribution of the peak variance. For practically verifying the stability condition, we further introduce a suboptimal estimator and develop a numerical procedure to generate tighter estimate for the constants involved in the stability criterion.

UR - https://www.scopus.com/pages/publications/34249020324

U2 - 10.1109/cdc.2006.376710

DO - 10.1109/cdc.2006.376710

M3 - Conference Paper

SN - 1424401712

SN - 9781424401710

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5621

EP - 5626

BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 45th IEEE Conference on Decision and Control 2006, CDC

Y2 - 13 December 2006 through 15 December 2006

ER -

Kalman filtering with Markovian packet losses and stability criteria

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