Recursive Quadratic Filtering for Linear Discrete Non-Gaussian Systems Over Time-Correlated Fading Channels

In this paper, the recursive quadratic filtering issue is addressed for a class of linear discrete-time systems with non-Gaussian noises over time-correlated fading channels. The time-correlated fading channel, whose fading coefficient is modeled by a dynamic process subject to non-Gaussian random disturbance, is adopted to better characterize the time-correlation nature of the communication channel. By resorting to the state/measurement augmentation approach, the underlying system is converted into an augmented one with respect to the aggregation of the original vectors and the second-order Kronecker powers. Accordingly, the focus of this paper is on the design of a recursive quadratic filtering algorithm in the minimum-variance framework. To be more specific, an upper bound is first ensured on the filtering error covariance by solving certain matrix difference equations, and such an upper bound is then minimized by choosing the proper gain parameters. Moreover, sufficient conditions are obtained to guarantee the mean-square boundedness of the filtering error. Finally, some numerical simulations are provided to illustrate the correctness and validity of our developed quadratic filtering algorithm.