A belief function distance metric for orderable sets

• A new belief function conflict metric is proposed for orderable sets or for use on discretized, continuous spaces.
• The conflict metric uses the Hausdorff distance as a measure of the “distance” between two belief distributions.
• Results show that performance of the proposed metric is superior to cardinality-based metrics in many realistic cases.

This paper describes a new metric for characterizing conflict between belief assignments. The new metric, specifically designed to quantify conflict on orderable sets, uses a Hausdorff-based measure to account for the distance between focal elements. This results in a distance metric that can accurately measure conflict between belief assignments without saturating simply because two assignments do not have common focal elements. The proposed metric is particularly attractive in sensor fusion applications in which belief is distributed on a continuous measurement space. Several example cases demonstrate the proposed metric’s performance, and comparisons with other common measures of conflict show the significant benefit of using the proposed metric in cases where a sensor’s error and noise characteristics are not known precisely a priori.