An Encoding-Decoding-Based State Estimation Scheme Considering Time Delay in Time-Correlated Fading Channels

This paper investigates the recursive state estimation for time-varying systems under time-correlated fading channels and multiple description coding scheme in the presence of observation delays. The original system with observation delay is firstly transformed into a delay free system by using the reorganized observation method. The measurements are transmitted through a wireless channel, where the channel coefficient exhibits time-dependent fading. For this reason, auxiliary variables are introduced, and an augmented system is constructed to represent both the system state and the channel fading coefficients. Furthermore, a dual-description coding scheme is utilized to encode the time-correlated fading measurements into two equally significant descriptions. A recursive state estimator is first developed to ensure an upper bound on the estimation error covariance. This estimator innovatively integrates both time-correlated channel fading and multiple description coding methods, making it suitable for online computation. Then, the upper bound is minimized by selecting appropriate estimator gain parameters.