A Possible Way to Perform Recursive Bayesian Estimate in the Possibility Domain

This paper defines a generalization of the recursive Bayesian estimate (RBE), within the mathematical possibility theory. This generalization is motivated by the fact that the classical RBE, by design, deals only with random variables and can only provide closed-form solution for a few cases. The possibilistic generalization is based on the random-fuzzy variables, thus allowing one to take into account, in a very natural way, both random and systematic contributions to the uncertainty and to implement the RBE for any distribution of system state variables in a simple way. This paper illustrates the advantages of the proposed generalization, by presenting both the theoretical development, and a detailed application example.