Mean square stability for Kalman filtering with Markovian packet losses

• Published in: Automatica (Oxford) Vol. 47; no. 12; pp. 2647 - 2657
• Main Authors: You, Keyou, Fu, Minyue, Xie, Lihua
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.12.2011; Elsevier
• Subjects: 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; 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
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2011.09.015

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.