Tracking with measurements of uncertain origin and random arrival times

The problem of estimating the state of a target in the presence of measurements of uncertain origin has received a great deal of attention recently. When this origin question cannot be resolved with certainty, one can only make probabilistic inferences as to which detection (and thus measurement) originated from the target of interest. The investigation reported here deals with a new class of problems characterized by the following: the correct measurement arrival (detection) times for a target of interest occur according to a stochastic process. Another stochastic process governs the arrival times of the false alarms. Thus, detections occur one at a time, and while some of them can be discarded as not having originated from the target, the remaining ones cannot be associated with certainty with the target. This problem is motivated by the fact that in some tracking problems, detections from the target of interest occur on an irregular basis. A procedure that associates probabilistically these measurements to the target is developed together with a corresponding estimator. The optimal estimator, as well as a number of suboptimal algorithms that are real-time implementable, are presented together with simulation results. The simulations also indicate that the probabilistic data association filter with time-of-arrival information is significantly superior to the filter which uses only measurement location information for probabilistic data association.