Robust recursive filtering for uncertain stochastic systems with amplify-and-forward relays

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.