GNSS Precise Point Positioning in Cislunar Space: A Study on Regularized Least Squares and Availability

The ongoing Lunar GNSS Receiver Experiment (LuGRE) mission is demonstrating that Global Navigation Satellite System (GNSS) can be a major enabler for radionavigation in cislunar space and on the Moon, offering a complementary solution to ground-based tracking infrastructures. However, cislunar Orbit Determination (OD) and timing with GNSS signals remains challenging due to severe pathloss effects, frequent side lobe receptions, and degraded satellite geometry. This study evaluates a single-frequency precise point positioning (SF-PPP) approach for kinematic OD, leveraging the group and phase ionospheric calibration (GRAPHIC) model to process undifferenced code and phase observations. The method incorporates Tikhonov regularization within a batch nonlinear least square (LS) estimator to tackle the ill-conditioning caused by the inherent rank deficiency of the positioning model. The algorithm is assessed through post-processing of raw GNSS observables collected during a hardware-in-the-loop (HIL) test, simulating representative LuGRE payload operations. Results show that the proposed regularized estimator ensures more than 89 % solution availability in most of the scenarios and achieves sub-kilometer positioning accuracy, even in scenarios with insufficient measurement redundancy.