Wasserstein distance for the fusion of multisensor multitarget particle filter clouds

In a multisensor multitarget tracking application, the evaluation of the cost of assigning particle filter clouds of different sensors as being estimates of the same target is an essential part in the particle cloud association. This paper treats the problem of evaluating the cost of particle filter clouds association based on the Wasserstein distance of different orders, analyzing the implications of clouds cardinality (for weighted particles), and of various resampling methods (for unweighted particles). As the Wasserstein distance at cloud level needs to have defined internally a metric at the particle level, the implications of using therein the Euclidean (for position components only) or Mahalanobis (including higher order components) distances are investigated. The crosscovariance of particle filter clouds is also estimated using the same Wasserstein distance and its introduction in the metric therein is explored. As a conclusion of various simulations, the design of the Wasserstein distance that is found to fit best the purpose of cloud-to-cloud association is presented.