Recursive Quadratic Filter Design for Non-Gaussian Systems Under Random Access Protocol: A Zero-Order Hold Strategy

This article deals with the recursive quadratic filtering problem for a class of linear discrete-time systems with the random access protocol (RAP) and non-Gaussian noises (NGNs). In order to mitigate undesirable data collisions, the RAP scheduling, used in conjunction with the zero-order hold strategy (ZOHS), is exploited in the sensor-to-filter channel. This coordination of the transmission order of sensors is characterized by a set of independent and identically distributed random variables. The objective of this article is to design a RAP-based quadratic filtering algorithm within the minimum-variance framework. The addressed system is first transformed into an enhanced system, which offers more information about the RAP and NGNs, by assembling the augmented states (including the original state and the latest measurement) and their second-order Kronecker power. With the assistance of two difference equations, an upper bound on the filtering error covariance (FEC) is, then, established, and the gain parameter is subsequently designed by minimizing this upper bound. To address challenges from the RAP scheduling with ZOHS, a matrix decomposition technique is employed. The effectiveness of the proposed RAP-based quadratic filtering algorithm is ultimately confirmed by various simulation results.