Dempster's combination is a special case of Bayes' rule

Abstract

Bayes' rule and Dempster's combination are typically presumed to be radically different procedures for fusing evidence. This paper demonstrates that measurement-update using Dempster's combination is a special case of measurement-update using Bayes' rule. The demonstration is based on an analogy with the Kalman filter. Suppose that the data consists of linear-Gaussian point measurements. Then ask, What additional assumptions must be made so that the Bayes filter can be solved in algebraically closed form? The Kalman filter is the result. In similar fashion, suppose that the data consists of measurements that are "uncertain" in a Dempster-Shafer sense. Then ask, What additional assumptions must be made so that the Bayes filter can be solved in algebraically closed form? Dempster's combination turns out to be the result. Stated differently: Both the Kalman measurement-update equations and Dempster's combination are corrector steps of the recursive Bayes filter, given that it has been restricted to two different types of measurements. © 2011 SPIE.