Gaussian-Sum-Based Probability Hypothesis Density Filtering with Delayed and Out-of-Sequence Measurements

The problem of multiple-sensor-based multiple-object tracking is studied for adverse environments involving clutter (false positives), missing measurements (false negatives) and random target births and deaths (a priori unknown target numbers). Various (potentially spatially separated) sensors are assumed to generate signals which are sent to the estimator via parallel channels which incur independent delays. These signals may arrive out of order, be corrupted or even lost. In addition, there may be periods when the estimator receives no information. A closed-form, recursive solution to the considered problem is detailed that generalizes the Gaussian-mixture probability hypothesis density (GM-PHD) filter previously detailed in the literature. This generalization allows the GM-PHD framework to be applied in more realistic network scenarios involving not only transmission delays but rather more general irregular measurement sequences where particular measurements from some sensors can arrive out of order with respect to the generating sensor and also with respect to the signals generated by the other sensors in the network.