On the accuracy of trajectory tracking and prediction

A simple method to estimate the standard deviation of both the tracking accuracy and the prediction accuracy of ballistic space objects is discussed. The method is based on the application of the Taylor series expansion to the closed-form solution of the motion equation of the trajectories and the utilization of the least square technique. The result obtained is an intrinsic property of the trajectory itself and is independent of measurement method or measurement algorithm. For a trajectory of range angle 90°, the accuracy of impact point prediction improves 790 times for the first 45 measurements; however, the accuracy improves only three times for the last 100 measurements right before impact