Optimal fusion for non-zero process noise

Centralized fusion provides, by definition, the best (optimal) estimation performance by directly using measurements of all sensors. When bandwidth is limited, sensors can only communicate their local processing results or “state estimates” instead of measurements to the fusion node. The goal of optimal fusion is to reconstruct the optimal centralized estimate from the local estimates. When the dynamic system for the state has non-zero process noise, the optimal estimate cannot be obtained by fusing the optimal local estimates unless the communication and fusion rates are the same as the sensor observation rate. For arbitrary communication rates, recent research under the name of distributed Kalman filter (DKF) has developed optimal fusion algorithms that combine local estimates that are not locally optimal. This paper presents a very simple derivation of the DKF that highlights the nature of the DKF. It also generalizes the DKF to handle fusion with memory when the fusion node utilizes the optimal estimate computed at the last fusion time. Since the DKF uses global estimation error covariances for local processing, we discuss communication requirements for its implementation.