Kalman Filtering with Partial Markovian Packet Losses

Bao-Feng Wang; Ge Guo

doi:10.1007/s11633-009-0395-x

November 2009

Article Contents

Bao-Feng Wang and Ge Guo. Kalman Filtering with Partial Markovian Packet Losses. International Journal of Automation and Computing, vol. 6, no. 4, pp. 395-400, 2009. doi: 10.1007/s11633-009-0395-x

Cite as: Bao-Feng Wang and Ge Guo. Kalman Filtering with Partial Markovian Packet Losses. International Journal of Automation and Computing, vol. 6, no. 4, pp. 395-400, 2009. doi: 10.1007/s11633-009-0395-x

Kalman Filtering with Partial Markovian Packet Losses

1.
School of Information Science and Technology, Dalian Maritime University, Dalian 116026, PRC

Received: 2009-02-01

Fund Project:

supported by National Natural Science Foundation of China (No.60504017);Fok Ying Tong Education Foundation(No.111066);Program for New Century Excellent Talents in University (No.NCET-04-0982)

Abstract

We consider the Kalman filtering problem in a networked environment where there are partial or entire packet losses described by a two state Markovian process. Based on random packet arrivals of the sensor measurements and the Kalman filter updates with partial packet, the statistical properties of estimator error covariance matrix iteration and stability of the estimator are studied. It is shown that to guarantee the stability of the Kalman filter, the communication network is required to provide for each of the sensor measurements an associated throughput, which captures all the rates of the successive sensor measurements losses. We first investigate a general discrete-time linear system with the observation partitioned into two parts and give suffcient conditions of the stable estimator. Furthermore, we extend the results to a more general case where the observation is partitioned into n parts. The results are illustrated with some simple numerical examples.
- Networked control systems,
- partial packet losses,
- Markovian packet losses,
- stability

References

[1]	C.Y.Gao,G.R.Duan,X.Y.Meng.Robust H_∞ Filter Design for 2D Discrete Systems in Roesser Model.International Journal of Automation and Computing,vol.5,no.4,pp.413-418,2008.
[2]	L.Yaug,X.P.Gush,C.N.Long,X.Y.Luo.Feedback Stabilization over Wireless Network Using Adaptive Coded Modulation.International Journal of Automation and Computing,vol.5,no.4,pp.381-388,2008.
[3]	W.S.Wong,R.W.Brochett.Systems with Finite Communication Bandwidth Constraints-Part Ⅰ:State Estimation Problems.IEEE Transactions on Automatic Control,vol.42,no.9,pp.1294-1299,1997.
[4]	W.S.Wong,R.W.Brochett.Systems with Finite Communication Bandwidth Constraints-Part Ⅱ:Stabilization with Limited Information Feedback.IEEE Transactions on Automatic Control,vol.44,no.5,pp.1049-1053,1999.
[5]	R.W.Brockett,D.Liberzon.Quantized Feedback Stabi lization of Linear Systems.IEEE Transactions on Auto matic Control,vol.45,no.7,pp.1279-1289,2000.
[6]	G.N.Nair,R.J.Evans.Communication-limited Stabilization of Linear Systems.In Proceedings of the 39th Conference on Decision and Control,IEEE Press,Sydney,Australia,vol.1,pp.1005-1010,2000.
[7]	I.R.Petersen,A.V.Savkin.Multi-rate Stabilization of Multivariable Discrete-time Linear Systems via a Limited Capacity Communication Channel.In Proceedings of the 40th Conference on Decision and Control,IEEE Press,Orlando,USA,vol.1,pp.304-309,2001.
[8]	M.Micheli,M.I.Jordan.Random Sampling of a Continuous-time Stochastic Dynamical System,[Online] ,Available:http://www.dam.brown.edu/ptg/REPORTS/ 02-8.pdf.
[9]	B.Sinopoli,L.Schenato,M.Franceschetti,K.Poolla,M.I.Jordan,S.S.Sastry.Kalman Filtering with Intermittent Observations.IEEE Transactions on Automatic Control,vol.49,no.9,pp.1453-1464,2004.
[10]	X.H.Liu,A.Goldsmith.Kalman Filtering with Partial Observation Losses.In Proceedings of the 43rd IEEE Conference on Decision and Control,IEEE Press,Atlantis,Bahamas,vol.4,pp.4180-4186,2004.
[11]	M.Y.Huang,S.Dey.Stability of Kalman filtering with Markovian Packet Losses.Automatica,vol.43,no.4,pp.598-607,2007.
[12]	L.Shi,M.Epstein,A.Tiwari,R.M.Murray.Estimation with Information Loss:Asymptotic Analysis and Error Bounds.In Proceedings of the 44th IEEE Conference on Decision and Control,IEEE Press,Seville,Spain,pp.1215-1221,2005.
[13]	M.Epstein,A.Tiwari,L.Shi,R.M.Murray.Estimation of Linear Stochastic Systems over a Queueing Network.In Proceedings of Systems Communications,IEEE Press,California,USA,pp.389-394,2005.
[14]	Z.Gajia,M.T.J.Qureshi.Lyapunov Matrix Equation in System Stability and Control,Dover Publications,1995.

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Kalman Filtering with Partial Markovian Packet Losses

1. School of Information Science and Technology, Dalian Maritime University, Dalian 116026, PRC

Received: 2009-02-01

Fund Project:

supported by National Natural Science Foundation of China (No.60504017);Fok Ying Tong Education Foundation(No.111066);Program for New Century Excellent Talents in University (No.NCET-04-0982)

Key words:

Abstract: We consider the Kalman filtering problem in a networked environment where there are partial or entire packet losses described by a two state Markovian process. Based on random packet arrivals of the sensor measurements and the Kalman filter updates with partial packet, the statistical properties of estimator error covariance matrix iteration and stability of the estimator are studied. It is shown that to guarantee the stability of the Kalman filter, the communication network is required to provide for each of the sensor measurements an associated throughput, which captures all the rates of the successive sensor measurements losses. We first investigate a general discrete-time linear system with the observation partitioned into two parts and give suffcient conditions of the stable estimator. Furthermore, we extend the results to a more general case where the observation is partitioned into n parts. The results are illustrated with some simple numerical examples.

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Reference (14)

[1]	C.Y.Gao,G.R.Duan,X.Y.Meng.Robust H_∞ Filter Design for 2D Discrete Systems in Roesser Model.International Journal of Automation and Computing,vol.5,no.4,pp.413-418,2008.
[2]	L.Yaug,X.P.Gush,C.N.Long,X.Y.Luo.Feedback Stabilization over Wireless Network Using Adaptive Coded Modulation.International Journal of Automation and Computing,vol.5,no.4,pp.381-388,2008.
[3]	W.S.Wong,R.W.Brochett.Systems with Finite Communication Bandwidth Constraints-Part Ⅰ:State Estimation Problems.IEEE Transactions on Automatic Control,vol.42,no.9,pp.1294-1299,1997.
[4]	W.S.Wong,R.W.Brochett.Systems with Finite Communication Bandwidth Constraints-Part Ⅱ:Stabilization with Limited Information Feedback.IEEE Transactions on Automatic Control,vol.44,no.5,pp.1049-1053,1999.
[5]	R.W.Brockett,D.Liberzon.Quantized Feedback Stabi lization of Linear Systems.IEEE Transactions on Auto matic Control,vol.45,no.7,pp.1279-1289,2000.
[6]	G.N.Nair,R.J.Evans.Communication-limited Stabilization of Linear Systems.In Proceedings of the 39th Conference on Decision and Control,IEEE Press,Sydney,Australia,vol.1,pp.1005-1010,2000.
[7]	I.R.Petersen,A.V.Savkin.Multi-rate Stabilization of Multivariable Discrete-time Linear Systems via a Limited Capacity Communication Channel.In Proceedings of the 40th Conference on Decision and Control,IEEE Press,Orlando,USA,vol.1,pp.304-309,2001.
[8]	M.Micheli,M.I.Jordan.Random Sampling of a Continuous-time Stochastic Dynamical System,[Online] ,Available:http://www.dam.brown.edu/ptg/REPORTS/ 02-8.pdf.
[9]	B.Sinopoli,L.Schenato,M.Franceschetti,K.Poolla,M.I.Jordan,S.S.Sastry.Kalman Filtering with Intermittent Observations.IEEE Transactions on Automatic Control,vol.49,no.9,pp.1453-1464,2004.
[10]	X.H.Liu,A.Goldsmith.Kalman Filtering with Partial Observation Losses.In Proceedings of the 43rd IEEE Conference on Decision and Control,IEEE Press,Atlantis,Bahamas,vol.4,pp.4180-4186,2004.
[11]	M.Y.Huang,S.Dey.Stability of Kalman filtering with Markovian Packet Losses.Automatica,vol.43,no.4,pp.598-607,2007.
[12]	L.Shi,M.Epstein,A.Tiwari,R.M.Murray.Estimation with Information Loss:Asymptotic Analysis and Error Bounds.In Proceedings of the 44th IEEE Conference on Decision and Control,IEEE Press,Seville,Spain,pp.1215-1221,2005.
[13]	M.Epstein,A.Tiwari,L.Shi,R.M.Murray.Estimation of Linear Stochastic Systems over a Queueing Network.In Proceedings of Systems Communications,IEEE Press,California,USA,pp.389-394,2005.
[14]	Z.Gajia,M.T.J.Qureshi.Lyapunov Matrix Equation in System Stability and Control,Dover Publications,1995.

Kalman Filtering with Partial Markovian Packet Losses

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