Launch Point Estimation with a Single Passive Sensor Without Trajectory State Estimation

The goal of this article is to provide a real-time implementable algorithm to estimate the launch point (LP) of a thrusting object using angle-only measurements. The measurements are obtained in the object's thrusting stage and from a single passive sensor (fixed or moving with constant velocity). It is assumed that one has a delayed acquisition, which means that the measurements are available only at some point after the launch time and the target's mass decreases (i.e., its acceleration increases) due to fuel burn/ejection. Previous works on this problem mainly estimate the target's state, which, for a passive sensor, requires a long batch of measurements, is sensitive to noise, and is ill-conditioned. In the present article, we only use a set of measurements (azimuth and elevation angles) to estimate the LP without motion state estimation. A polynomial fitting with the least-squares method is used to estimate the LP-based zero angular rate (which determines the launch time) and known LP altitude. Statistical analysis is provided to choose the optimal polynomial order, including overfitting and underfitting evaluation. Then, the estimated launch time is obtained by the 'weighted average'. Compared with a more complicated state-of-the-art technique that relies on state estimation, the proposed approach provides a much simpler and effective way to implement in a real-time system.