Estimation for a Thrusting/Ballistic Object With Mass Ejection From a Single Fixed Passive Sensor With Delayed Acquisition

The trajectory estimation problem of a thrusting/ballistic object in three-dimensional (3-D) space has been previously solved with 2-D measurements (azimuth and elevation angles from a fixed passive sensor, either starting from the launch time or with a delayed acquisition) under the assumption of constant mass. However, since the mass decreases as the fuel burns, this should be accounted for. This paper investigates several approaches with different parameter vectors to solve the trajectory estimation and impact point prediction (IPP) with measurements starting after the launch time, i.e., delayed acquisition for both constant mass motion model and mass ejection motion model. For the mass ejection motion model, the mass ejection rate is an extra component of the parameter vector to be estimated. The invertibility of the Fisher information matrix (FIM) of the parameter vectors is also used to confirm the observability (estimability) of the system. The Cramer–Rao lower bound (CRLB) is the inverse of the FIM if it is invertible. The CRLB of the IPP is also derived. We develop the maximum likelihood estimator of the considered motion parameter vectors. Performance comparison between the models considered is given and the statistical efficiency of the best model is confirmed via simulation results.