A detection-estimation approach with refinement to filtering for Gaussian systems with intermittent observations

In this paper we consider the problem of state estimation for linear discrete-time Gaussian systems with intermittent observations resulting from packet dropouts. We assume that the receiver does not know the sequence of packet dropouts. This is a typical situation, e.g., in wireless sensor networks. Under this hypothesis, the problem of state estimation has been previously solved by the authors using a detection-estimation approach consisting of two stages: the first is a nonlinear optimal detector, which decides if a packet dropout has occurred, and the second is a time-varying Kalman filter, which is fed with both the observations and the decisions from the first stage. This work extends that solution, introducing a refinement stage whose purpose is to significantly improve the decision on packet dropouts and, in turn, on state estimation. The overall estimator has finite memory and the tradeoff between performance and computational complexity can be easily controlled. Numerical results highlight the effectiveness of the approach based on detection-estimation with refinement, which outperforms both the estimator without refinement and the optimal linear filter of Nahi.