In this work we focus on the relationship between the Dempster-Shafer (DS) and Bayesian evidence accumulation.
While it is accepted that the DS theory is, in a certain sense, a generalization of the probability theory, the approaches
vary in several important respects, including the treatment of uncertain information and the way the evidence is
combined, making direct comparison of results of the two analyses difficult. In this work we ameliorate these
difficulties by proposing a mathematical framework within which the relationship between the two methods can be made
precise. The findings of the investigation elucidate the role uncertainty plays in the DS theory and enable evaluation of
relative fitness of the two techniques for practical data fusion scenarios.
Among the various ways in which ground targets differ from air-targets, a most important one is that in order to travel substantial distances, ground targets generally need to move on roads. Alpha-beta type filters or Kalman filters, i.e., tracking filters designed for air-targets, have not dealt with constrained target motion. The use of road-constraints changes both the prediction and update steps in the tracing problem. In this paper a Bayesian framework is developed, in which the road information, in standard vector-product form, is incorporated with the predicted target location into the Bayesian prior. Both the maximum a posterior and Bayes least-squares solutions are then computed. An examination of the results shows that the MAP solutions is potentially unstable when two conditions coincide: the target is located near a road bend and the sensors return is located inside the bend. Because of this potential instability, the preferred update solution turns out to be the along-road average of the updated location probability density. Formulas for calculating or effectively approximately the solution and its along-road variance are given, as well as an association measure for multi-target tracking, track initiation, and clutter rejection by gating.