Quantized recursive filtering for networked systems with stochastic transmission delays

This paper investigates the recursive filtering problem for a class of networked systems subject to the uniform quantization effects and stochastic transmission delays. The system output is quantized according to a uniform quantization mechanism, and then sent to the remote filter via a communication network undergoing stochastic transmission delays (which are modeled by a sequence of independent and identically distributed variables). To deal with the stochastic transmission delays, an indicator function is delicately designed to ensure that the filtering process is implemented based on the quantized measurement with the newest timestamp available for the filter. With the aid of the indicator function, a free-delay system is obtained by using the augmented system method. The aim of this paper is to design a Kalman-type filter for the augmented system such that an upper bound of the filtering error covariance is guaranteed and minimized. With the aid of the stochastic analysis method, the desired upper bound of the filtering error covariance is derived by recursively solving two Riccati-like difference equations. Then, the upper bound is minimized by properly selecting the filter parameters. Finally, a numerical example is provided to illustrate the validity of the developed filtering scheme.