Tobit Kalman filter with channel fading and dead-zone-like censoring

In complex control systems, the channel fading and the measurement censoring are often unavoidable due to sudden environmental changes, intermittent transmission congestions, random failures and repairs of components. To this end, the Tobit Kalman filtering problem for discrete-time systems with the dead-zone-like censoring and channel fading is studied where the censoring and fading phenomena are, respectively, described by the Tobit measurement model and the $ L_{th} $ Lth-order Rice fading channel model. The design of the filter is carried out in two stages: (1) the state augmentation technique is firstly adopted to remove the time-delay effect caused by the fading channel; and (2) the statistical information of censored measurements is used to determine the optimal filter structure in the minimum mean-square error sense, where the orthogonal projection principle is utilised to avoid the deep correlations among the multiple random variables induced by measurement censoring and channel fading. Besides, the desired filter is also devised based on the approach of the conditional expectation. For the convenience of calculation, the filter with the dead-zone-like censoring is converted into an equivalent one with one-side censoring. Finally, a numerical example of estimating the ballistic ball rates is given to verify the effectiveness of the proposed filters.