Information-Geometric Methods for Distributed Multi-Sensor Estimation Fusion

This paper mainly deals with the distributed estimation fusion problem when the correlations are unknown. The local estimates are represented as a set of probability density functions, on which a Riemannian structure endowed with the Fisher metric is built. From the perspective of information geometry, the fused density is formulated as the Fisher barycenter in the space of probability densities and sought by minimizing the sum of squared geodesic distances between itself and the local densities. Under Gaussian assumptions, the orthogonal geodesic method and the Siegel distance method based on the information geometry are proposed to tackle the distributed estimation fusion problem. A vital contribution of this work is that the fusion results derived in this paper are invariant under the affine transformations of state estimates due to the use of the Riemannian manifold and Fisher metric.