Generalized solution to smoothing and out-of-sequence processing

The increasing trend toward multisensor systems is driving an interest for distributed tracking algorithms. In such systems, data transmissions with imperfect communication links often lead to varying time delays. The challenge of online processing of delayed data is generally known as the out-of-sequence (OoS) problem. An exact solution to this problem is given by the accumulated state density (ASD) filter. However, the Rauch-Tung-Striebel (RTS) retrodiction1 is inherently integrated to the ASD approach, so a certain number of states must be updated at each filtering step. In this paper, a generalized form of the ASD filter is presented. In particular, the exact update formula for states that refer to time instants that are older and newer than a given measurement is calculated. As a consequence, OoS data can be processed without applying retrodiction. A novel smoothing scheme is presented that uses the exact cross-covariances of a measurement and a past state without recursion. A numerical evaluation shows that this smoothing scheme is about 25% faster than the RTS equations yet is still exact.