Recursive Filtering for Stochastic Systems with Filter-and-Forward Successive Relays

In this paper, the recursive filtering problem is considered for stochastic systems over filter-and-forward successive relay (FFSR) networks. An FFSR is located between the sensor and the remote filter to forward the measurement. In the successive relay, two cooperative relay nodes are adopted to forward the signals alternatively, thereby existing switching characteristics and inter-relay interferences (IRI). Since the filter-and-forward scheme is employed, the signal received by the relay is retransmitted after it passes through a linear filter, The objective of the paper is to concurrently design optimal recursive filters for FFSR and stochastic systems against switching characteristics and IRI of relays. First, a uniform measurement model is proposed by analyzing the transmission mechanism of FFSR. Then, novel filter structures with switching parameters are constructed for both FFSR and stochastic systems. With the help of the inductive method, filtering error covariances are presented in the form of coupled difference equations. Next, the desired filter gain matrices are further obtained by minimizing the trace of filtering error covariances. Moreover, the stability performance of the filtering algorithm is analyzed where the uniform bound is guaranteed on the filtering error covariance. Finally, the effectiveness of the proposed filtering method over FFSR is verified by a three-order resistance-inductance-capacitance circuit system.