This work examines the problem of using finite Gaussian mixtures (GM) probability density functions in recursive Bayesian peer-to-peer decentralized data fusion (DDF). It is shown that algorithms for both exact and approximate GM DDF lead to the same problem of finding a suitable GM approximation to a posterior fusion pdf resulting from the division of a `naive Bayes fusion GM (representing direct combination of possibly dependent information sources) by another non-Gaussian pdf (representing removal of either the actual or estimated `common information between the information sources). The resulting quotient pdf for general GM fusion is naturally a mixture pdf, although the fused mixands are non-Gaussian and are not analytically tractable for recursive Bayesian updates. Parallelizable importance sampling algorithms for both direct local approximation and indirect global approximation of the quotient mixture are developed to find tractable GM approximations to the non-Gaussian `sum of quotients mixtures. Practical application examples for multi-platform static target search and maneuverable range-based target tracking demonstrate the higher fidelity of the resulting approximations compared to existing GM DDF techniques, as well as their favorable computational features.
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