Launch point estimation with a single fixed passive sensor without trajectory state estimation

This paper considers the problem of estimating the launch point (LP) of a thrusting object from a single fixed sensor's 2-D angle-only measurements (azimuth and elevation). It is assumed that the target follows a mass ejection model and the measurements obtained are available starting a few seconds after the launch time due to limited visibility. Previous works on this problem estimate the target's state, which, for a passive sensor, requires a long batch of measurements, is sensitive to noise and ill-conditioned. In this paper, a polynomial fitting with the least squares approach is presented to estimate the LP without motion state estimation. We provide a statistical analysis to choose the optimal polynomial order, including overfitting and underfitting evaluation. Next, we present Monte Carlo simulations to show the performance of the proposed approach and compare it to the much more complicated state of the art technique that relies on state estimation. It is shown that the proposed method provides a much simpler and effective way than the state estimation methods to implement in a real-time system.