Measurement models for ambiguous evidence using conditional random sets

In several recent papers we have shown how random set theory provides a theoretically rigorous foundation for much of data fusion. An important missing piece in our approach has been the problem of how to incorporate observations which are ambiguous (e.g. imprecise, fuzzy/vague, contingent, etc.) into conventional Bayesian estimation and filtering theory. If one can do this, the fusion of imprecise observations with ambiguous observations, generated by dynamic (i.e., moving) targets, becomes possible using a familiar Bayes-Markov nonlinear filtering approach. This paper sketches the basis for fusion if one assumes that both observation space and state space are finite.