What´s one mixture divided by another?: A unified approach to high-fidelity distributed data fusion with mixture models

This work examines the problem of using finite Gaussian mixtures (GMs) in Bayesian message passing algorithms for decentralized data fusion (DDF). It is shown that both exact and conservative GM DDF lead to the same problem of finding a suitable GM approximation to a posterior fusion pdf that results from the division of a `naive Bayes´ fusion GM (representing direct combination of possibly dependent information sources) by another non-Gaussian pdf (representing either the actual or estimated `common information´ of the information sources). It is shown that the resulting quotient pdf for general GM fusion is in fact naturally a mixture model pdf, although the fused mixands are non-Gaussian. Parallelizable importance sampling algorithms are proposed to find tractable Gaussian approximations to these non-Gaussian mixtures, leading to GM fusion approximations that are shown to be more robust and accurate than previously proposed techniques.