Proposal of a probabilistic believes fusion framework. Application to range data fusion

In order to perform occupancy grid building of in-door environmental for autonomous mobile robot, this paper presents a methodology allowing the merging of beliefs associated to hypotheses represented by binary proposition H like "this particular element belongs to this particular set". In this paper, elements processed are vectors representing points which belong to obstacles. Belief notion is introduced in the combined framework of logic and probability theory and the problem is posed as follows: if different sensors give their own belief in an hypotheses H, how is it possible to merge these believes? Two cases necessary to solve formally occupancy grid building are developed: either sensors characterize different points or sensors characterize the same point. Obtained results are applied to ultrasonic range data fusion.