Joint Actual-Auxiliary Filter Design for Linear Repetitive Processes Over AF Relay Networks With Autocorrelated Rayleigh Fading

This paper addresses the robust filter design problem for a class of Linear Repetitive Processes (LRPs) operating over amplify-and-forward (AF) relay networks subject to autocorrelated Rayleigh fading. To improve communication quality in long-distance transmissions and mitigate the inherent limitations of wireless sensor nodes, a three-terminal AF relay framework with autocorrelated Rayleigh fading under a two-dimensional (2-D) system setting is introduced. Unlike conventional approaches that decouple the fading parameters from the system state, this work defines a globally coupled correlation term that integrates both components, allowing direct incorporation into the filter design. A joint estimation framework is proposed, involving both the actual and an auxiliary filter. By employing mathematical induction, stochastic analysis, and a set of tunable parameters, tight upper bounds for the estimation error covariance are established and minimized through appropriate filter gain selection. Furthermore, the boundedness of the actual filter’s estimation error covariance is rigorously analyzed under mild parameter conditions. The effectiveness and applicability of the proposed filtering scheme are validated through its application to metal rolling process.