Recursive filtering for two-dimensional systems with amplify-and-forward relays: Handling degraded measurements and dynamic biases

This paper is concerned with the recursive filtering issue for a type of two-dimensional shift-varying systems communicated via imperfect networks. The communication network undergoes degraded measurements, stochastic biases, and channel noises, all reflecting real-world constraints. The degraded measurements are governed by three random variable sets with known statistical details, while the stochastic biases follow specific dynamic equations. An amplify-and-forward (AF) relay is implemented to bolster the reliability of transmission from the sensor to the distant filter. The main goal of this study is to formulate an AF relay-based recursive filtering algorithm that can predict system states with the desired performance specification. By employing the inductive technique and meticulous stochastic analysis, an upper bound for the filtering error variance is initially set based on the solutions to recursive difference equations, following which the filter gain is intricately designed to minimize this upper bound at each point in time. Furthermore, a theoretical analysis is conducted on the effect of degradation coefficients on the filtering performance. Finally, the effectiveness of the proposed recursive filtering approach is demonstrated using a numerical example.