Bayesian tracking with Dempster-Shafer measurements
Ronald Mahler · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
The theory and practice of single-sensor, single-target tracking is well understood when measurement uncertainties are due entirely to randomness. In this case the Bayes filter and its special cases and approximations, such as the Kalman filter, constitute the foundations of tracking. However, the measurement uncertainties in many observation-types (features, natural-language reports, etc.) can arise from ignorance as well as randomness. Approaches such as the Dempster-Shafer (DS) theory claim to address such information but continue to be controversial, especially in tracking. In other papers this year we have shown that this can be attributed to a lack of formal physical modeling techniques. If familiar measurement models are extended in a natural way, measurement fusion using DS combination can be subsumed within the Bayesian theory. In this paper we apply these results to introduce the "evidential filter," a special case of the Bayes filter applicable whenever measurement uncertainty can be modeled in DS form. We derive closed-form formulas for the evidential filter; and show that data-update using Dempster's combination is a special case of Bayes' rule. We also briefly show how to incorporate the evidential filter into multitarget tracking techniques.