Improved Tobit Kalman filtering for systems with random parameters via conditional expectation

This paper is concerned with the Tobit Kalman filtering problem for a class of linear discrete-time system with random parameters. The elements of both the system matrix and the measurement matrix are allowed to be random variables in order to reflect the reality. The information matrix is employed to 1) derive the covariance between any two random variables; and 2) establish a novel weighting covariance formula to address the quadratic terms associated with the random matrices. A set of Bernoulli random variables is introduced to govern the censoring phenomenon on the measurement output. The conditional expectation, as a basic tool, is utilized to deal with the dependence among the random variables. Within the framework of the traditional Kalman filtering, the proposed filtering algorithm includes the information from both the random parameters and the censored measurements. A simulation example is presented to illustrate the effectiveness and applicability of the designed algorithm.