For addressing multi-target tracking problem with out-of-sequence measurement（ OOSM）

a filtering algorithm is proposed with multiple single-step-lag OOSM for linear system

which denotes as OOSM-Gaussian mixture probability hypothesis density（ GMPHD）. Within the forward prediction framework

taking GMPHD as basis filtering algorithm

predicting and updating each Gaussian component

and then can obtained the target number and state estimation after pruning and merging. etc. Simulation results show that the algorithm can effectively filter out influence of OOSM and can accurately estimate the multi-target number and state.