Information Fusion via Importance Sampling

Information fusion is a procedure that merges information locally contained at the nodes of a network. Of high interest in the field of distributed estimation is the fusion of local probability distributions via a weighted geometrical average criterion. In numerous practical settings, the local distributions are only known through particle approximations, i.e., sets of samples with associated weights, such as obtained via importance sampling (IS) methods. Thus, prohibiting any closed-form solution to the aforementioned fusion problem. This article proposes a family of IS methods - called particle geometric-average fusion (PGAF) - that lead to consistent estimators for the geometrically-averaged density. The advantages of the proposed methods are threefold. First, the methods are agnostic of the mechanisms used to generate the local particle sets and, therefore, allow for the fusion of heterogeneous nodes. Second, consistency of estimators is guaranteed under generic conditions when the agents use IS-generated particles. Third, a low-communication overhead and agent privacy are achieved since local observations are not shared with the fusion center. Even more remarkably, for a sub-family of the proposed PGAF methods, the fusion center does not require the knowledge of the local priors used by the nodes. Implementation guidelines for the proposed methods are provided and theoretical results are numerically verified.