Ground vehicles can be effectively tracked using a moving target indicator (MTI) radar. However, vehicles whose velocity along the line-of-sight to the radar falls below the minimum detectable velocity (MDV) are not detected. One way targets avoid detection, therefore, is to execute a series of move-stop-move motion cycles. While a target can be acquired after beginning to move again, it may not be recognized as a target previously in track. Particularly for the case of high-value targets, it is imperative that a vehicle be continuously tracked. We present an algorithm for determining the probability that a target has stopped and an estimate of its stopped state (which could be passed to a tasker to schedule a spot synthetic aperature radar (SAR) measurement. We treat a non-detection event as evidence that can be used to update the target state probability density function (PDF). Updating the target state PDF using a non-detection event pushes the probability mass into regions of the state space in which the vehicle is either stopped or traveling at a speed such that the range-rate fails the MDV. The target state PDF updated with the non-detection events is then used to derive an estimate of the stopped target’s location. Updating the target state PDF using a non-detection event is, in general, non-trivial and approximations are required to evaluate the updated PDF. When implemented with a particle filter, however, the updating formula is simple to evaluate and still captures the subtleties of the problem.