ABSTRACT This paper is concerned with the recursive filtering problem for a class of uncertain systems with amplify-and-forward (AF) relays. The parameter uncertainties are described by a set of norm-bounded matrices. An AF relay is located between the sensor and the remote filter to forward the signal received from the sensor to the filter. A set of random variables with certain probability distribution is introduced to characterise the transmission power of the sensor and relay transmitting the measurement. By utilising the average transmission power, a robust filter is first constructed for the stochastic uncertain system. Then, an upper bound is recursively obtained for the filtering error covariance in the presence of random transmission power and parameter uncertainties. The desired gain matrix is further parameterised by minimising the obtained upper bound. Moreover, the boundness is also analysed for the filtering error. Finally, the effectiveness of the proposed filtering algorithm is demonstrated by a numerical example.

中文翻译：

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具有放大转发继电器的不确定随机系统的鲁棒递归滤波

摘要 本文涉及一类具有放大转发 (AF) 中继的不确定系统的递归滤波问题。参数不确定性由一组范数有界矩阵描述。AF 继电器位于传感器和远程滤波器之间，用于将从传感器接收到的信号转发到滤波器。引入一组具有一定概率分布的随机变量来表征传感器和中继传输测量的传输功率。利用平均传输功率，首先为随机不确定系统构造了一个鲁棒滤波器。然后，在存在随机传输功率和参数不确定性的情况下递归地获得滤波误差协方差的上限。通过最小化获得的上限进一步参数化所需的增益矩阵。此外，还分析了过滤误差的边界。最后，通过数值例子证明了所提出的滤波算法的有效性。