Scalable fusion with mixture distributions in sensor networks

Mixture distributions such as Gaussian mixture model (GMM) have been used in many applications for dynamic state estimation. These applications include robotics, image and acoustic processing, distributed tracking, and multisensor data fusion. However, the recursive processing of the mixture distributions incurs rapidly growing computational requirements. In particular, the number of components in the mixture distribution grows exponentially when multiple of them are combined. In order to keep the computational complexity tractable, it is necessary to approximate a mixture distribution by a reduced one with fewer components. Mixture reduction is traditionally done by iteratively removing insignificantly components or merging similar ones. However, a systematic procedure is needed in order to ensure scalability while trading-off performance. In this paper, we propose a recursive mixture reduction algorithm for Gaussian mixture distribution with a given error bound. To meet the error bound, we applied a constraint optimized weight adaptation to minimize the integrated squared error (ISE) between the reduced distribution and the original one. With extensive simulations, we showed that the proposed algorithm provides an efficient and effective mixture reduction performance in distributed fusion applications.