Improved Gaussian mixture probability hypothesis density smoother

The Gaussian mixture probability hypothesis density (GM-PHD) smoother proposed recently is a closed-form solution to the forward-backward PHD smoother for the linear Gaussian model, it can yield better state estimates than the GM-PHD filter. However, for the standard GM-PHD smoother, when one or more targets disappear during forward filtering, the smoothed PHD will be adjusted improperly in the backward smoothing, thus leading to a target number misestimation problem. In this paper, an improved GM-PHD smoother is proposed to solve such a problem, in which a modified backward corrector is used to adjust the smoothed PHD. Simulated results show that the improved GM-PHD smoother is superior to the standard GM-PHD smoother in both the aspects of target state estimate and target number estimate so that this improved GM-PHD smoother will have an applicable potential in related fields.