Quadratic filtering for discrete time-varying non-Gaussian systems under binary encoding schemes

Abstract

This paper is concerned with the recursive quadratic filtering problem for a class of linear discrete-time systems subject to non-Gaussian noises. Considering its robustness against channel noises, the binary encoding scheme is utilized in the process of data transmission from sensors to the filter. Under such a scheme, the original signal is first encoded into a bit string, and then transmitted via memoryless binary symmetric channels (with certain crossover probabilities). Subsequently, the received bit string is recovered by a decoder at the receiver end. The primary purpose of this paper is to design a recursive quadratic filter for the underlying non-Gaussian systems with a minimized upper bound on the filtering error covariance. For this purpose, an augmented system is first constructed by aggregating the original vectors and their second-order Kronecker powers. Accordingly, an upper bound on the filtering error covariance is obtained in the form of solutions to certain Riccati-like difference equations, and the obtained bound is then minimized by properly choosing the filter parameter. Moreover, sufficient conditions are established to guarantee the boundedness of filtering error covariance. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed quadratic filtering algorithm.