Fundamentals of on-road tracking

Among the various ways in which ground targets differ fi om 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 tracking problem. In this paper a Bayesian framework is developed, in which the road information, in standard vector-product (road-segment) form, is incorporated with the predicted target location into the Bayesian prior. Both the maximum a posteriori (MAP) and Bayes least-squares solutions are then computed (These solutions are identical for the unconstrained case.) An examination of the results shows that the MAP solution is potentially unstable when two conditions coincide: the target is located near a road bend and the sensor return is located inside the bend. Because of this potential instability, the preferred update solution turns out to be the along-road average (the appropriate form of the Bayes least-squares solution) of the updated location probability density. Formulas for calculating or effectively approximating 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.