Bayesian and Dempster-Shafer fusion

The Kalman Filter is traditionally viewed as a prediction-correction filtering algorithm. In this work we show that it can be viewed as a Bayesian fusion algorithm and derive it using Bayesian arguments. We begin with an outline of Bayes theory, using it to discuss well-known quantities such as priors, likelihood and posteriors, and we provide the basic Bayesian fusion equation. We derive the Kalman Filter from this equation using a novel method to evaluate the Chapman-Kolmogorov prediction integral. We then use the theory to fuse data from multiple sensors. Vying with this approach is the Dempster-Shafer theory, which deals with measures of “belief”, and is based on the nonclassical idea of “mass” as opposed to probability. Although these two measures look very similar, there are some differences. We point them out through outlining the ideas of the Dempster-Shafer theory and presenting the basic Dempster-Shafer fusion equation. Finally we compare the two methods, and discuss the relative merits and demerits using an illustrative example.