Recursive state estimation for two-dimensional systems over decode-and-forward relay channels: A local minimum-variance approach

The paper is concerned with the recursive state estimation problem for a class of two-dimensional systems over decode-and-forward relay channels subject to packet dropouts. Taking into account the sensor's limited transmission ability, a decode-and-forward relay is deployed between the sensor and the remote estimator to enlarge the propagation distance and improve the communication quality. The packet dropout phenomenon is described by two sequences of mutually uncorrelated random variables that obey Bernoulli distributions. The main objective of this paper is to design a recursive state estimator for the underlying system with guaranteed estimation performance. An upper bound on the estimation error variance is firstly derived by resorting to some coupled difference equations, and then such an upper bound is locally optimized at each iteration through proper design of the estimator gain. Furthermore, the impacts of the packet dropouts and the decode-and-forward relay on the estimation performance are evaluated with rigorously theoretical analysis. Finally, an illustrative example is presented to validate the effectiveness of the proposed estimation scheme.