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The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10−7. Although this is still below the required precision of better than 10−8 for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations. [ABSTRACT FROM AUTHOR]

Tiangong-2 is the first Chinese real space laboratory, launched into earth orbit with an altitude of approximately 393 km on September 15, 2016. Precise orbit determination (POD) is one of the essential conditions for conducting onboard scientific research. The precise orbit of Tiangong-2 is mainly determined by the reduced-dynamic method using space-borne global navigation satellite system (GNSS) data, which are collected by an onboard dual-frequency GNSS receiver. The in-flight performance of the receiver is first assessed in terms of tracking ability, code multipath errors and noise levels of code and carrier phase observations. Then, the effects of refined non-gravitational force models and GNSS antenna phase center variations (PCVs) on the POD are analyzed. The estimated empirical accelerations are substantially reduced by 45% in the along-track direction using a macro-model compared to that using a cannonball model for drag computation. The application of antenna PCVs correction leads to better consistency between reduced-dynamic and kinematic orbit solutions. Satellite laser ranging validation shows that the accuracy of Tiangong-2 precise orbits is 1.7 cm after using the improved reduced-dynamic method. Based on the orbit determination results, the quality of Tiangong-2 orbit predictions is assessed for periods without and with the refined non-gravitational force models. The use of the macro-model and high-quality density models for drag computation is shown to help improve orbit prediction quality. [ABSTRACT FROM AUTHOR]