A cross-traffic detection system suitable for use on an automated vehicle includes an object-detector and a controller. The object-detector is used to determine locations of a moving-object relative to a host-vehicle. Each of the locations is indicated by a lateral-distance and a longitudinal-distance of the moving-object from the host-vehicle. The controller is in communication with the object-detector. The controller is configured to accumulate a plurality of first-longitudinal-distances of a first-vehicle at a plurality of predetermined-lateral-distances, and determine a path-history of the first-vehicle based on linear-interpolation between successive instances of the plurality of first-longitudinal-distances at corresponding instances of the plurality of predetermined-lateral-distances. The controller is also configured to determine that a second-vehicle is following the path-history of the first-vehicle when the second-vehicle passes within an offset-distance to the path-history that is less than an offset-threshold, and estimate a crossing-distance from the host-vehicle based on the path-history and the offset-distance.