  In Bayesian peer-to-peer decentralized data fusion, the underlying
distributions held locally by autonomous agents are frequently assumed to be
over the same set of variables (homogeneous). This requires each agent to
process and communicate the full global joint distribution, and thus leads to
high computation and communication costs irrespective of relevancy to specific
local objectives. This work formulates and studies heterogeneous decentralized
fusion problems, defined as the set of problems in which either the
communicated or the processed distributions describe different, but
overlapping, random states of interest that are subsets of a larger full global
joint state. We exploit the conditional independence structure of such problems
and provide a rigorous derivation of novel exact and approximate conditionally
factorized heterogeneous fusion rules. We further develop a new version of the
homogeneous Channel Filter algorithm to enable conservative heterogeneous
fusion for smoothing and filtering scenarios in dynamic problems. Numerical
examples show more than $99.5\%$ potential communication reduction for
heterogeneous channel filter fusion, and a multi-target tracking simulation
shows that these methods provide consistent estimates while remaining
computationally scalable.
