  Many physical systems evolve on matrix Lie groups and mixture filtering
designed for such manifolds represent an inevitable tool for challenging
estimation problems. However, mixture filtering faces the issue of a constantly
growing number of components, hence require appropriate mixture reduction
techniques. In this letter we propose a mixture reduction approach for
distributions on matrix Lie groups, called the concentrated Gaussian
distributions (CGDs). This entails appropriate reparametrization of CGD
parameters to compute the KL divergence, pick and merge the mixture components.
Furthermore, we also introduce a multitarget tracking filter on Lie groups as a
mixture filtering study example for the proposed reduction method. In
particular, we implemented the probability hypothesis density filter on matrix
Lie groups. We validate the filter performance using the optimal subpattern
assignment metric on a synthetic dataset consisting of 100 randomly generated
multitarget scenarios.
