A look at Gaussian mixture reduction algorithms

We review the literature and look at two of the best algorithms for Gaussian mixture reduction, the GMRC (Gaussian Mixture Reduction via Clustering) and the COWA (Constraint Optimized Weight Adaptation) which has never been compared to the GMRC. We note situations that could yield invalid results (i.e., reduced mixtures having negative weight components) and offer corrections to this problem. We also generalize the GMRC to work with vector distributions. We then derive a brute-force approach to mixture reduction that can be used as a basis for comparison against other algorithms on small problems. The algorithms described in this paper can be used in a number of different domains. We compare the performance of the aforementioned algorithms along with a simpler algorithm by Runnalls' for reducing random mixtures, as well as when used in a Gaussian mixture reduction-based tracking algorithm.