  We propose a novel consensus notion, called "partial consensus", for
distributed GM-PHD (Gaussian mixture probability hypothesis density) fusion
based on a peer-to-peer (P2P) sensor network, in which only highly-weighted
posterior Gaussian components (GCs) are disseminated in the P2P communication
for fusion while the insignificant GCs are not involved. The partial consensus
does not only enjoy high efficiency in both network communication and local
fusion computation, but also significantly reduces the affect of potential
false data (clutter) to the filter, leading to increased signal-to-noise ratio
at local sensors. Two "conservative" mixture reduction schemes are advocated
for fusing the shared GCs in a fully distributed manner. One is given by
pairwise averaging GCs between sensors based on Hungarian assignment and the
other is merging close GCs based a new GM merging scheme. The proposed
approaches have a close connection to the conservative fusion approaches known
as covariance union and arithmetic mean density. In parallel, average consensus
is sought on the cardinality distribution (namely the GM weight sum) among
sensors. Simulations for tracking either a single target or multiple targets
that simultaneously appear are presented based on a sensor network where each
sensor operates a GM-PHD filter, in order to compare our approaches with the
benchmark generalized covariance intersection approach. The results demonstrate
that the partial, arithmetic average, consensus outperforms the complete,
geometric average, consensus.
