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Distributed estimation fusion is concerned with the combination of local estimates from multiple distributed sensors to produce a fused result. In this paper, we characterize local estimates as posterior probability densities, and assume that they all belong to a parametric family. Our starting point is to consider this family as a Riemannian manifold by introducing the Fisher information metric. From the perspective of information geometry, the fused density is formulated as an informative barycenter in the space of probability densities and sought by minimizing the sum of its squared geodesic distances from the local posterior densities. Under Gaussian assumptions, a geodesic projection (GP) method and a Siegel distance (SD) method in the information-geometric framework are proposed to tackle the problem. The GP method gives a fusion result in accord with the covariance intersection estimate but under an information-geometric criterion, while the SD method appears to achieve a better approximation of the informative barycenter. Numerical examples are provided to demonstrate the performance of the proposed estimation fusion algorithms.
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