  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.
