Gauss's method of orbit determination (OD) is one of the most popular, minimal assumption target tracking techniques in astrodynamics, especially for generating an initial state estimate. However, due to Gauss's method's assumption of Keplerian motion (part of the larger two-body problem), this method cannot be applied in a cislunar environment, where three body, non-planar effects dominate. In this work, we showcase a hybrid Particle Gaussian Mixture (H-PGM) filtering method, a purely recursive probabilistic OD framework that relies upon a sequential combination of the Markov Chain Monte Carlo (MCMC) based Particle Gaussian Mixture-II (PGM-II) and Kalman update based Particle Gaussian Mixture-I (PGM-I) filters. This method allows us to fuse probabilistic information with angles-only observations from terrestrial telescopes for short- and long-term cislunar target tracking. This method also allows us to fuse other target \textit{a priori} information in an effort to reduce target uncertainty in the short term. This hybrid filtering technique is demonstrated for several popular and important cislunar orbit regimes and compared with several homogeneous and hybrid filtering frameworks.

翻译：高斯轨道确定方法是天体动力学中最流行的、假设最少的目标跟踪技术之一，尤其适用于生成初始状态估计。然而，由于高斯方法假设开普勒运动（隶属于更广泛的两体问题），该方法无法应用于受三体、非平面效应主导的地月空间环境。本研究展示了一种混合粒子高斯混合(H-PGM)滤波方法，这是一种纯递归概率轨道确定框架，依赖于基于马尔可夫链蒙特卡洛(MCMC)的粒子高斯混合-II(PGM-II)与基于卡尔曼更新的粒子高斯混合-I(PGM-I)滤波器的序贯组合。该方法使我们能够将来自地面望远镜的角度观测信息与概率信息相融合，用于地月空间目标的短期与长期跟踪。该方法还允许融合其他目标先验信息，以在短期内降低目标不确定性。该混合滤波技术已在几种典型且重要的地月轨道区域中得到验证，并与多种同质及混合滤波框架进行了性能比较。