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

• Published in: Automatica (Oxford) Vol. 158; p. 111268
• Main Authors: Wang, Shaoying, Wang, Zidong, Dong, Hongli, Shen, Bo, Chen, Yun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2023
• Subjects: Binary encoding schemes; Boundedness; Matrix difference equations; Non-Gaussian noises; Quadratic filtering; Non-Gaussian noises; Matrix difference equations; Binary encoding schemes; Quadratic filtering; Boundedness
• ISSN: 0005-1098; 1873-2836; 1873-2836
• DOI: 10.1016/j.automatica.2023.111268

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.