More and more fields of applied computer science involve fusion of multiple data sources, such as sensor readings or model decision. However incompleteness of the models prevent the programmer from having an absolute precision over their variables. Therefore Bayesian framework can be adequate for such a process as it allows handling of uncertainty. We will be interested in the ability to express any fusion process as a product, for it can lead to reduction of complexity in time and space. We study in this paper various fusion schemes and propose to add a consistency variable to justify the use of a product to compute distribution over the fused variable. We will then show application of this new fusion process to localization of a mobile robot and obstacle avoidance.