A Concise Phase Anomaly Correction Method for GRACE Follow-On Laser Ranging Interferometer Measurements

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathrm{pm/\sqrt{Hz}@1Hz}$</tex-math></inline-formula> and the residual spikes mainly affect frequency band above 2 Hz; (2) the accuracy of estimated time-tag synchronization offset is better than 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> 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.