An Optimal Hierarchical Arithmetic Average Fusion of GM-PHD Filters

We achieve the optimal Arithmetic Average (AA) fusion algorithm of Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters in a hierarchical structure. First, the optimal single-target estimate fusion is derived, during which the prior estimate is indispensable. Then, the derived optimal estimate fusion is employed as the merging method of the AA fusion. A master filter dedicated to computing prior density is introduced, so our fusion algorithm features a hierarchical structure. Experiment results evidence our algorithm's optimality and superiority over the standard AA fusion.