On mixture reduction for multiple target tracking

In multiple hypothesis or probability hypothesis based multiple target tracking the resulting mixtures with ever growing components should be approximated by a reduced mixture. Although there are cost based and more rigorous mixture reduction algorithms, which are computationally expensive to apply in practical situations especially in high dimensional state spaces, the mixture reduction is generally done based on ad hoc criteria and procedures. In this paper we propose a sequentially pairwise mixture reduction criterion and algorithm based on statistical decision theory. For this purpose, we choose the merging criterion for the mixture components based on a likelihood ratio test. The advantages and disadvantages of some of the previous reduction schemes and the newly proposed algorithm are discussed in detail. The results are evaluated on a Gaussian mixture implementation of the PHD filter where two different pruning and merging schemes are designed: one for computational feasibility, the other for the state extraction.