Can the Bayesian and Dempster-Shafer approaches be reconciled? Yes

This paper describes a unified approach to the problem of estimating the states of one or more targets, based on fusion of accumulating multisource information which can take one of two forms: ambiguous measurements or ambiguous state-estimates. We show that, as most commonly employed, Dempster-Shafer (DS) fusion methods can be subsumed within the Bayesian theory. Specifically, we show that the following are equivalent to fusion using Bayes' rule: (I) fusion of ambiguous measurements using Dempster's combination rule; and (2) fusion of ambiguous state-estimates using the Fixsen-Mahler "modified" combination. We show that the Voorbraak and pignistic transforms can be understood as posterior probability densities conditioned on, respectively, ambiguous measurements and ambiguous state-estimates. Our approach is based on natural extensions of the recursive Bayes filter. We also derive closed-form formulas for one type of single-target "evidential filter" and briefly show how it can be incorporated into multi-hypothesis multitarget tracker techniques.