Tobit Kalman filtering: Conditional expectation approach

This paper is concerned with the Tobit Kalman filtering for a class of discrete-time linear systems. A set of Bernoulli random variables is introduced to describe the randomly occurring censored measurements, which are dependent on the measurement outputs. Such dependence among random variables leads to the largest challenge encountered in this paper. The conditional expectation as a basic tool is utilized to address this challenge. Within the framework of the traditional Kalman filtering, the obtained filter includes not only the information from the system parameters but also the censored measurements. Finally, an illustrative simulation is presented to demonstrate the effectiveness and applicability of the proposed algorithm.