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Aiming at improving the tracking performance of the delta-generalized labeled multi-Bernoulli (&#x03B4;-GLMB) filter, we present a one time step lagged &#x03B4;-GLMB smoother in this work, which also inherently outputs targets trajectories and differs from the Probability hypothesis density (PHD), Multi-Bernoulli (MB), and Cardinalized probability hypothesis density (CPHD) smoothers that are incapable of generating target trajectories directly. Under the standard multitarget measurement likelihood and state transition kernel, we show that a &#x03B4;-GLMB distributed multitarget filtering density would result in a same distributed one time step lagged multitarget smoothing density. An efficient implementation of the proposed smoothing algorithm using the standard ranked assignment technique is also given. Numerical results show that the proposed smoother is capable of tracking a time-varying number of targets, in the presence of measurement origin uncertainty, target detection uncertainty, and clutter, and show that the proposed smoother outperforms the &#x03B4;-GLMB filter, and the PHD, MB, and CPHD smoothers of the same time lag on both the estimates of target number and state and it also outperforms the LMB and the approximated &#x03B4;-GLMB smoothers of the same time lag on target number estimate.

Multitarget Tracking Using One Time Step Lagged Delta-Generalized Labeled Multi-Bernoulli Smoothing