Positioning Error Estimation Method for Short-Arc Angles-Only Initial Orbit Determination

The development of space surveillance capabilities has received increased emphasis with time. Suitable evaluation parameters are investigated to analyze the effects of multiple factors on short-arc angles-only initial orbit determination. This investigation is crucial for designing surveillance system parameters. In this paper, the orbit determination equations where the target state is linear were derived by assuming that Lagrangian coefficients are constant and taking the minimum residual sum as the optimization objective. From this paper's analysis, it was demonstrated that because the position uncertainty distribution primarily lies in the line-of-sight vector, the upper limit of relative positioning error (RPE) can be used as the evaluation parameter of the determination accuracy in scenarios where a high-orbit target is observed by a low-orbit sensor observes. An empirical relationship was also found, indicating that the upper limit of RPE is proportional to the observation error, -2.5 power of the observation arc length, and the 0.5 power of the observation interval.