Kalman filtering with state-dependent packet losses

• Published in: IET control theory & applications Vol. 13; no. 2; pp. 306 - 312
• Main Authors: Thapliyal, Omanshu, Nandiganahalli, Jayaprakash Suraj, Hwang, Inseok
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 29.01.2019
• Subjects: baseline packet loss algorithm; Brief Paper; covariance matrices; discrete time systems; estimation problem; iterative methods; Kalman filters; least mean squares methods; linear systems; linear time invariant systems subject; mean square error methods; minimum mean square error state estimates; observation packets; practical estimation problems; probabilistic packet arrival process; Riccati equations; state estimation; state space; state‐dependent hybrid measurement model; state‐dependent packet loss; probabilistic packet arrival process; covariance matrices; iterative methods; least mean squares methods; practical estimation problems; discrete time systems; state space; minimum mean square error state estimates; linear systems; estimation problem; baseline packet loss algorithm; state-dependent hybrid measurement model; Riccati equations; state-dependent packet loss; observation packets; state estimation; linear time invariant systems subject; Kalman filters; mean square error methods
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2018.5425

This study addresses the problem of state estimation for discrete-time, linear time invariant systems subject to packet losses, which occur in specific regions of the state space. Most practical estimation problems are characterised by occurrences of loss of observation packets, which makes the packet arrival process a non-stationary statistic, making the analysis and design of such an estimator challenging. This estimation problem subject to state-dependent packet losses is formulated using a state-dependent hybrid measurement model and solved using the projection theorem-based approach to obtain minimum mean square error state estimates. By systematically utilising the a priori information of the regions where the packet loss is likely to occur, the proposed estimator takes the Kalman filter structure with the modified algebraic Riccati iteration for the error covariance matrix being stochastic due to the probabilistic packet arrival process. Finally, the proposed estimator is demonstrated using an illustrative two-dimensional aircraft tracking example with state-dependent packet loss and is shown to have improved performance over the baseline packet loss algorithm.