The GRACE-FO satellite's laser ranging interferometer (LRI) measurements suffer from a significant number of phase anomalies, which can directly affect the gravity field recovery. To address this issue, we proposed an improved difference method (ImDFM) for phase anomaly processing, which enhances the traditional difference method (DFM) through two improvements: (1) combine the phase smoothing technique to handle cycle slips, single event upsets, and Mega phase jumps (PJs) which DFM hard to process; and (2) propose a novel time-tag synchronization offsets estimation method based on PJs to rectify the accuracy degradation caused by time-tag synchronization anomalies. Compared to the mainstream template method (TPM), ImDFM offers a significant advantage in conciseness. We evaluated the accuracy of ImDFM and residual spike characteristics by comparing the ImDFM product (S11) with the template-based product (S10) and the official JPL RL04 product in phase anomaly, LRI1B and gravity field results. The results show that (1) ImDFM can process phase anomalies with an accuracy better than 600 \boldmath $ \mathrm{pm/\sqrt{Hz}@1Hz}$ and the residual spikes mainly affect frequency band above 2 Hz; (2) the accuracy of estimated time-tag synchronization offset is better than 4 $\mu$ s, which can effectively correct the loss of accuracy; (3) the residual spikes in S11 are below 7nm/s, which does not affect the accuracy of gravity field recovery. The RL04 is still affected by phase anomalies, resulting in relatively higher noise above degree 30. In summary, the ImDFM proposed in this paper provides a high precision and concise approach for processing phase anomalies.

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.