Adaptive entropy and covariance-based simplified Gaussian mixture algorithm for nonlinear uncertainty propagation in orbital elements

Orbit uncertainty propagation (OUP) holds a crucial role in space situational awareness analysis. Achieving a balance between accuracy and computational burden stands out as two essential aspects of OUP. In this paper, an adaptive entropy and covariance-based simplified Gaussian mixture (AECSG) uncertainty propagation method using modified equinoctial orbital elements is developed for OUP, which can reduce the computational burden while ensuring accuracy. The AECSG is developed based on the framework of adaptive entropy-based Gaussian mixture information synthesis (AEGIS). It incorporates a novel non-linearity detection method aimed at optimizing the splitting process. To circumvent the issues arising from frequent splits and ill-conditioned covariance matrices resulting from numerical calculation errors, the AECSG employs a simplex sigma-point selection strategy coupled with an optimized data transfer structure. Comparative evaluation against the AEGIS demonstrates that AECSG achieves a favorable balance between accuracy and computational burden in OUP, as evidenced by numerical simulations.