Optimal Filtering Over Uncertain Wireless Communication Channels

• Published in: IEEE signal processing letters Vol. 18; no. 6; pp. 359 - 362
• Main Authors: Xiao Ma, Djouadi, S M, Charalambous, C D
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bernoulli; Channels; Delay; Estimates; Estimation; Estimators; Filtering; Filtering theory; Filtration; Kalman filters; linear optimal estimator; Markov processes; Mathematical analysis; Maximum likelihood detection; optimal filtering; Optimization; packet loss; Sensors; Wireless communication
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2011.2138134

In this letter, filtering over wireless communication channels subject to packet losses is considered. The packet losses are assumed to follow a Bernoulli distribution. The latter is interpreted as a special case of a Markov process for which hybrid filtering theory is shown to provide an exact solution. Unlike existing works where only the linear optimal state estimate is derived as a linear function of measurements, this paper shows that the optimal state estimate is in fact a nonlinear function of measurements. In addition, the optimal estimator is derived explicitly. Illustrative examples compare the performance of the linear optimal estimator and the optimal estimator, and show that the latter offer superior performance, in particular for unstable systems.