Protocol-Based Tobit Kalman Filter Under Integral Measurements and Probabilistic Sensor Failures

This paper is concerned with the Tobit Kalman filtering problem for a class of discrete time-varying systems subject to censored observations, integral measurements and probabilistic sensor failures under the Round-Robin protocol (RRP). The censored observations are characterized by the Tobit observation model, the integral measurements are described as functions of system states over a certain time interval required for data acquisition, and the sensor failures are governed by a set of uncorrelated random variables. The RRP is employed to decide the transmission sequence of sensors in order to alleviate undesirable data collisions. By resorting to the augmentation technique and the orthogonality projection principle, a protocol-based Tobit Kalman filter (TKF) is developed with the coexistence of integral measurements and sensor failures that lead to a couple of augmentation-induced terms. Moreover, the performance of the proposed filter is analyzed through examining the statistical property of the error covariance of the state estimation. Further analysis shows the existence of self-propagating upper and lower bounds on the estimation error covariance. A case study on ballistic roll rate estimation is presented to illustrate the efficacy of the developed filter.

Automated summary

This paper addresses the Tobit Kalman filtering problem for discrete time-varying systems under the Round-Robin protocol, considering censored observations, integral measurements, and sensor failures. By utilizing the augmentation technique and orthogonality projection principle, a protocol-based TKF is developed to handle the challenges caused by integral measurements and sensor failures. The performance of the proposed filter is analyzed through examining the statistical properties of the estimation error covariance, showing the existence of self-propagating upper and lower bounds.