Low Earth orbit (LEO) satellites are leveraged to support new position, navigation, and timing (PNT) service alternatives to GNSS. These alternatives require accurate propagation of satellite position and velocity with a realistic quantification of uncertainty. It is commonly assumed that the propagated uncertainty distribution is Gaussian; however, the validity of this assumption can be quickly compromised by the mismodeling of atmospheric drag. We develop a machine learning approach that corrects error growth in the argument of latitude for a diverse set of LEO satellites. The improved orbit propagation accuracy extends the applicability of the Gaussian assumption and modeling of the errors with a corrected mean and covariance. We compare the performance of a time-conditioned neural network and a Gaussian Process on datasets computed with an open source orbit propagator and publicly available Vector Covariance Message (VCM) ephemerides. The learned models predict the argument of latitude error as a Gaussian distribution given parameters from a single VCM epoch and reverse propagation errors. We show that this one-dimensional model captures the effect of mismodeled drag, which can be mapped to the Cartesian state space. The correction method only updates information along the dimensions of dominant error growth, while maintaining the physics-based propagation of VCM covariance in the remaining dimensions. We therefore extend the utility of VCM ephemerides to longer time horizons without modifying the functionality of the existing propagator.

翻译：低地球轨道（LEO）卫星被用于支持全球导航卫星系统（GNSS）以外的新型定位、导航与授时（PNT）服务。这类替代方案要求精确传播卫星位置与速度，并对其不确定性进行真实量化。通常假设传播的不确定性分布服从高斯分布，然而该假设的有效性会因大气阻力建模误差而迅速失效。本文提出一种机器学习方法，用于修正多种低地球轨道卫星纬度幅角的误差增长。改进的轨道传播精度扩展了高斯假设的适用性，并通过修正后的均值与协方差对误差进行建模。我们在基于开源轨道传播器与公开的矢量协方差消息（VCM）星历计算的数据集上，对比了时间条件神经网络与高斯过程的性能。学习得到的模型能够根据单个VCM历元参数及反向传播误差，将纬度幅角误差预测为高斯分布。研究表明，这一维模型能够捕获阻力建模误差的影响，并可映射至笛卡尔状态空间。该修正方法仅沿主导误差增长维度更新信息，同时保持其余维度中基于物理的VCM协方差传播特性。因此，我们在不改变现有传播器功能的前提下，将VCM星历的有效性扩展至更长时间范围。