Resilient Filtering for Linear Time-Varying Repetitive Processes Under Uniform Quantizations and Round-Robin Protocols

In this paper, the resilient filtering problem is investigated for a class of linear time-varying repetitive processes with communication constraints. The communication between the sensors and the remote filter, which is subject to uniform quantizations, is carried out through a shared communication medium where only one sensor has access to the network at each transmission time. To prevent data from collisions, the Round-Robin (R-R) protocol scheduling is applied to orchestrate the transmission order of sensor nodes in a periodic manner. Moreover, stochastic perturbations on the gain parameters are taken into account in the course of the actual filter implementation. The main purpose of the addressed problem is to design a resilient filter such that, in the presence of the uniform quantization, the R-R protocol, and the filter gain perturbation, a certain upper bound is guaranteed on the filtering error variance and subsequently minimized at each time instant. By means of intensive stochastic analysis and mathematical induction, sufficient condition is provided to ensure the local minimization of certain upper bound on the filtering error variance. Furthermore, the boundedness issue is also discussed with respect to the filtering error variance. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed filter strategy.