Mean square stability for Kalman filtering with Markovian packet losses
This paper studies the stability of Kalman filtering over a network subject to random packet losses, which are modeled by a time-homogeneous ergodic Markov process. For second-order systems, necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derive...
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| Published in: | Automatica (Oxford) Vol. 47; no. 12; pp. 2647 - 2657 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Kidlington
Elsevier Ltd
01.12.2011
Elsevier |
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| ISSN: | 0005-1098, 1873-2836 |
| Online Access: | Get full text |
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| Abstract | This paper studies the stability of Kalman filtering over a network subject to random packet losses, which are modeled by a time-homogeneous ergodic Markov process. For second-order systems, necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure. While for certain classes of higher-order systems, necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices. All stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the Markov process. Their implications and relationships with related results in the literature are discussed. |
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| AbstractList | This paper studies the stability of Kalman filtering over a network subject to random packet losses, which are modeled by a time-homogeneous ergodic Markov process. For second-order systems, necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure. While for certain classes of higher-order systems, necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices. All stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the Markov process. Their implications and relationships with related results in the literature are discussed. |
| Author | You, Keyou Fu, Minyue Xie, Lihua |
| Author_xml | – sequence: 1 givenname: Keyou surname: You fullname: You, Keyou email: youk0001@ntu.edu.sg organization: EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore – sequence: 2 givenname: Minyue surname: Fu fullname: Fu, Minyue email: minyue.fu@newcastle.edu.au organization: Department of Control Science and Engineering, Zhejiang University, Hangzhou, China – sequence: 3 givenname: Lihua surname: Xie fullname: Xie, Lihua email: elhxie@ntu.edu.sg, ELHXIE@ntu.edu.sg organization: EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore |
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| Keywords | Error covariance matrices Kalman filtering Stability Stopping time Stochastic linear systems Markovian packet losses Markov process Ergodic theory Error estimation Necessary and sufficient condition Kalman filter Stability criterion Modeling Stochastic system Transition matrix Uncertain system Transition probability Eigenvalue problem Second order equation Estimation error Ergodicity Covariance matrix Homogeneous process Mean estimation Open loop Mean error Transmission loss Non deterministic system |
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| SubjectTerms | Applied sciences Computer science; control theory; systems Computer systems and distributed systems. User interface Control theory. Systems Covariance Error covariance matrices Errors Exact sciences and technology Fluctuation phenomena, random processes, noise, and brownian motion Kalman filtering Markov processes Markovian packet losses Mathematical analysis Mathematics Matrices Matrix methods Modelling and identification Physics Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Software Stability Statistical physics, thermodynamics, and nonlinear dynamical systems Stochastic linear systems Stopping time |
| Title | Mean square stability for Kalman filtering with Markovian packet losses |
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