Optimal Sequential Fusion Estimation for the Multi-rate 2-D Systems with Fading Channels

This paper investigates the optimal state fusion estimation problem for a class of multi-rate two-dimensional stochastic linear systems with packet dropouts. The systems are formulated by the famous F-M local state-space model, and the phenomenon of fading channels is characterized by a diagonal matrix, in which each component of the diagonal matrix is an independent random variable subject to a certain probability distribution. The purpose of the paper is to develop a two-step recursive filter. Under the two-dimensional circumstance, first and foremost, the multi-rate multi-sensor system is transmitted as a single-rate multi-sensor system by using the lifting technology. Subsequently, determine a local recursive optimal filter so that the estimated error for each moment is minimal, where the filter gains are obtained by the completing squares method. Then a distributed filter is designed by applying the sequential fusion algorithm, which has higher accuracy and reliability. Finally, the rationality of the distributed filter is illustrated by a numerical example.