Optimal Reentry Time Estimation of an Upper Stage from Geostationary Transfer Orbit

The reentry time of the cryogenic stage of the Indian Geostationary Satellite Launch Vehicle GSLV-F01/CS is carried out as an optimal estimation problem. The response surface methodology (RSM) with genetic algorithm (GA) is applied to determine the optimal estimates of B (ballistic coefficient) and initial osculating eccentricity (e). The investigation employs two-line elements (TLEs), determined 165 days before the reentry epoch. An accurate reentry time prediction of the cryogenic stage is made seven days before its reentry. The state vector and osculating orbital elements are obtained from the TLEs with the help of the SGP4/SDP4 theories. The RMS error in the mean apogee altitude of the least-squares estimation is found to be 194.6397 km with the reentry time of 24 November 2007 22:58 UTC, whereas the RMS error of the RSM with GA is found to be 151.9323 km. It was observed that toward the end of the orbital life, the RSM with GA provides better estimates of the reentry times with lesser percentage errors than the least-squares method.