A collision detection system includes at least one sensor. The data from the sensor is input to a recursive filter which selectively uses the input to predict the motion of a target object relative to a host vehicle. The recursive filter continues to use the data from the sensor until the target object is within a threshold distance of the host vehicle. Within the threshold distance, the sensor does not reliably provide accurate data. Accordingly, the recursive filter omits the sensor input from motion estimates when the target object is within the threshold distance, which leads to significant improvement in target motion prediction.