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.