TLE orbit determination using simplex method

Two-Line Element (TLE) datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications. The datasets have uneven qualities that may affect the reliability of the propagated positions of space objects using a single TLE. The least squares approach to use multiple TLEs also suffers from the poor quality of some TLEs, and reliable error information cannot be available. This paper proposes a simplex algorithm to estimate an optimal TLE from multiple TLEs and obtain the uncertainty of each element. It is a derivative-free technique that can deal with various orbit types. Experiments have demonstrated that using the TLE estimated from the simplex method is more reliable, stable, and effective than those from the batch least squares method. As an application example, the optimal TLE and its uncertainty are used for predicting the fallen area, keeping the actual fallen site in the prediction areas.