A Recursive Algorithm for Secure Filtering for Two-Dimensional State-Saturated Systems Under Network-Based Deception Attacks

This paper addresses the recursive secure filtering problem for an array of two-dimensional shift-varying systems subject to state saturation under deception attacks. The network-based deception attacks, which occur in a probabilistic manner, are modulated by random variables obeying the Bernoulli distributions. The intention of the addressed problem is to design a recursive filter for estimating the system states with a satisfactory performance against state saturations and probabilistic attacks. By utilizing the inductive method and the matrix techniques, a feasible upper bound is attained on the filtering error variance and then minimized in the trace sense at each iteration. The coveted filter gain is recursively calculated by solving three sets of difference equations. Additionally, for the established filtering algorithm, the performance analysis is conducted to show the uniform boundedness of the minimum upper bound and the monotonicity regarding the deception attacks. An illustrative simulation is also implemented to verify the usefulness of the proposed filtering scheme.