Modeling the Doppler Shift in Cislunar Environment with Gaussian Mixture Models

This study investigates the RF-based Doppler shift distribution characterization of the Lunar South Pole (LSP) based inter-satellite link (ISL) in varying inclination. Doppler shift in parts per million (ppm) is determined and analyzed, as it provides an independence from the carrier frequency. Due to unknown relative velocity states duration, the Gaussian Mixture Model (GMM) is found to be the best fitting distribution for ISLs with 1^∘ inclination interval Doppler shift with respect to a predetermined satellite. Goodness-of-fit is investigated and quantified with Kullback-Leibler (KL) divergence and weighted mean relative difference (WMRD) error metrics. Simulation results show that ISL Doppler shifts reach up to ±1.89 ppm as the inclination of the other orbit deviates higher from the reference orbit, inclining 80^∘. Regarding the error measurements of GMM fitting, the WMRD and KL divergence metrics for ISL take values up to 0.6575 and 2.2963, respectively.