An Alternative Look at the Constant-Gain Kalman Filter for State Estimation Over Erasure Channels

• Published in: IEEE transactions on automatic control Vol. 58; no. 12; pp. 3259 - 3265
• Main Authors: Silva, Eduardo I., Solis, Miguel A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2013; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channel estimation; Covariance matrices; Data-dropouts; erasure channel; Kalman filters; optimal estimation; Signal to noise ratio; signal-to-noise ratio (SNR) constraints; State estimation; Steady-state
• ISSN: 0018-9286; 1558-2523; 2334-3303; 1558-2523
• DOI: 10.1109/TAC.2013.2263647

This technical note studies state estimation problems subject to data loss. We consider a class of switched estimators, where missing data is replaced by optimal estimates. The considered class of estimators encompasses a number of estimation schemes proposed in the literature. We show that the estimator that minimizes the steady-state estimation error covariance within that class, is given by a constant-gain Kalman filter which was previously proposed as an alternative to the Kalman filter with intermittent observations. As a by-product of our results, we derive expressions that allow one to compare, analytically, popular suboptimal data-dropout compensation mechanisms.