It is understood that the forward-backward probability hypothesis density （PHD） smoothing algorithms proposed recently can significantly improve state estimation of targets. However, our analyses in this paper show that they cannot give a good cardinality （i.e., the number of targets） estimate. This is because backward smoothing ignores the effect of temporary track drop- ping caused by forward filtering and/or anomalous smoothing resulted from deaths of targets. To cope with such a problem, a novel PHD smoothing algorithm, called the variable-lag PHD smoother, in which a detection process used to identify whether the filtered cardinality varies within the smooth lag is added before backward smoothing, is developed here. The analytical results show that the proposed smoother can almost eliminate the influences of temporary track dropping and anomalous smoothing, while both the cardinality and the state estimations can significantly be improved. Simulation results on two multi-target tracking scenarios verify the effectiveness of the proposed smoother.
It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.
