Optimal algorithm for "Out-of-sequence" estimates with arbitrary communication delays

Sensor data, which are transmitted from local sensors to the central processor, often appear various communication delays because of the uncertain communication channel and various disturbances. Thereby, optimal "Out-of-sequence" Measurements (OOSM) fusion has been presented and attracts plenty of attentions. The OOSM scenario can deal with the delayed fusion problem, but it inevitably comes forth many problems which have influenced its application ability, for example, high computational complexity, the complex algorithm structure, low computational efficiency, and bad real-time performance and so forth. In order to overcome above problems, the concept for the "Out-of-sequence" Estimates (OOSE) fusion has been also presented and it has shown excellent performance to solve the delayed fusion. In this paper, the optimal fusion for single sensor OOSE is researched and the corresponding algorithm is also proposed including its integrated and recursive forms, which are optimal in minimum mean square error (MMSE). Performance analysis and simulation example show that the proposed OOSE method is valid and has many advantages compared with the current OOSM methods and just the estimate accuracy is reduced after a sort.