Constraint optimized weight adaptation for Gaussian mixture reduction
Huadong Chen, Keh‐Chin Chang, Chris Llewellyn Smith · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2010
Gaussian mixture model (GMM) has been used in many applications for dynamic state estimation such as target tracking or distributed fusion. However, the number of components in the mixture distribution tends to grow rapidly when multiple GMMs are combined. In order to keep the computational complexity bounded, it is necessary to approximate a Gaussian mixture by one with reduced number of components. Gaussian mixture reduction is traditionally conducted by recursively selecting two components that appear to be most similar to each other and merging them. Different definitions on similarity measure have been used in literature. For the case of one-dimensional Gaussian mixtures, Kmeans algorithms and some variations are recently proposed to cluster Gaussian mixture components in groups, use a center component to represent all in each group, readjust parameters in the center components, and finally perform weight optimization. In this paper, we focus on multi-dimensional Gaussian mixture models. With a variety of reduction algorithms and possible combinations, we developed a hybrid algorithm with constraint optimized weight adaptation to minimize the integrated squared error (ISE). In additions, with extensive simulations, we showed that the proposed algorithm provides an efficient and effective Gaussian mixture reduction performance in various random scenarios.