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

Oliviero Vouch, Luca Morichi, Simone Zocca, Alex Minetto, Fabio Dovis

Peer Reviewed

Abstract:	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 postprocessing 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. Index Terms—Global navigation satellite systems, Radio navigation, Space exploration, Kinematic orbit determination, Least squares approximations, Tikhonov method.
Published in:	2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) April 28 - 1, 2025 Salt Lake Marriott Downtown at City Creek Salt Lake City, UT
Pages:	1014 - 1025
Cite this article:	Vouch, Oliviero, Morichi, Luca, Zocca, Simone, Minetto, Alex, Dovis, Fabio, "GNSS Precise Point Positioning in Cislunar Space: A Study on Regularized Least Squares and Availability," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 1014-1025.
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