Optimal Update with Multiple Out-of-Sequence Measurements with Arbitrary Arriving Order

In multisensor target tracking systems receiving out-of-sequence measurements (OOSMs) from local sensors is a common situation. In the last decade many algorithms have been proposed to update with an OOSM optimally or suboptimally. However, what one faces in the real world is the multiple OOSMs, which arrive at the fusion center in, generally, arbitrary orders, e.g., in succession or interleaved with in-sequence measurements. A straightforward approach to deal with this multi-OOSM problem is by sequentially applying a given OOSM algorithm; however, this simple solution does not guarantee the optimal update under the multi-OOSM scenario. The work presented here discusses the differences between the single-OOSM processing and the multi-OOSM processing, and presents the general solution to the multi-OOSM problem, which is called the complete in-sequence information (CISI) approach. Given an OOSM, in addition to updating the state at the most recent time, the CISI approach also updates the states between the OOSM time and the most recent time, including the state at the OOSM time. Three novel CISI methods are developed in this paper: the information filter-equivalent measurement (IF-EqM) method, the CISI fixed-point smoothing (CISI-FPS) method and the CISI fixed-interval smoothing (CISI-FIS) method. Numerical examples are given to illustrate the optimality of these CISI methods under various multi-OOSM scenarios.