Multi-sensor Distributed Estimation Fusion Based on Minimizing the Bhattacharyya Distance Sum

In multi-sensor distributed estimation fusion, local estimation errors are generally correlated among local estimates. Usually, correlation is known to exist but unavailable or unclear to be how large it is, and needed to be considered. For this situation, a sensible way is to set up an optimality criterion and optimize it over all possible such correlations. Based on the framework of minimizing the statistical distance sum between the fused density and local posterior densities, a new method is proposed by utilizing Bhattacharyya distance, which is commonly used in measuring the closeness or similarity between two densities. First, the objective function is introduced. Then, we investigate the convexity form of the objective function, and separate the solving procedure into two steps during settling the original optimization problem, which benefit us to acquire the solution of that problem. At last, the acquired solution (fused estimate) is given in an implicit form, however, it can be obtained through iterative algorithm. And, it is pessimistic definite in mean square error (MSE). Numerical examples illustrate this and show the effectiveness of the proposed distributed method by comparing with several other fusion methods under the same framework but using other kinds of statistical distance.

I. Introduction

Estimate fusion is concerned with how to optimally utilize the whole useful information contained among the data sets, and merged into a consistent and coherent representation, in estimating the unknown quantity. According to the architecture of fusion, it is divided into two basic categories: centralized fusion and distributed fusion. In centralized fusion, all raw measurements observed by the sensors are transmitted to the fusion center, while in distributed fusion, each sensor only sends in processed data. They have pros and cons as to performance, communication requirements, reliability, survivability, information sharing, etc. Theoretically speaking, centralized fusion is nothing but traditional estimation with distributed observations, which can be simply disposed by treating as augmented measurements after stacking the data. The latter distributes the burden of processing data over the network but is relatively more challenging, and has received more attention in fusion related research.