Tobit Kalman filter with fading measurements

•The Tobit Kalman filtering problem is investigated for discrete time-varying systems.•Both censored and fading measurements are considered.•The Tobit Kalman filter is designed by using the orthogonality projection principle.•Applications on the estimation of ballistic roll rates are provided.

This paper is concerned with the Tobit Kalman filtering problem for a class of discrete time-varying systems with both censored and fading measurements. The censored measurements are described by the Tobit measurement model and the fading measurements are characterized by the Lth-order Rice fading channel model capable of accounting for not only the packet dropout but also the communication phenomenon. The measurement fading occurs in a random way where the fading probabilities are regulated by a set of mutually independent Gaussian random variables. By resorting to the state augmentation technique and the orthogonality projection principle, the Tobit Kalman filter (TKF) is designed in the presence of fading measurements. In the course of filter design, several state-augmentation-induced terms are introduced, all of which can be calculated recursively or off-line. A numerical example concerning the estimation of ballistic roll rates is provided to illustrate the usefulness of the proposed filter.