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.

中文翻译：

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时间相关衰落信道上线性离散非高斯系统的递归二次滤波


在本文中，针对时间相关衰落信道上具有非高斯噪声的一类线性离散时间系统，解决了递归二次滤波问题。采用时间相关衰落信道，其衰落系数是通过受非高斯随机扰动的动态过程建模的，可以更好地表征通信信道的时间相关性。通过采用状态/测量增强方法，底层系统被转换为关于原始向量和二阶克罗内克幂的聚合的增强系统。因此，本文的重点是在最小方差框架下设计递归二次滤波算法。更具体地说，首先通过求解某些矩阵差分方程来确保滤波误差协方差的上限，然后通过选择适当的增益参数来最小化该上限。此外，还获得了保证滤波误差均方有界性的充分条件。最后，提供了一些数值模拟来说明我们开发的二次滤波算法的正确性和有效性。