The GRACE Follow-On satellite mission measures distance variations between its two satellites in order to derive monthly gravity field maps, indicating mass variability on Earth on a scale of a few 100 km originating from hydrology, seismology, climatology and other sources. This mission hosts two ranging instruments, a conventional microwave system based on K(a)-band ranging (KBR) and a novel laser ranging instrument (LRI), both relying on interferometric phase readout. In this paper, we show how the phase measurements can be converted into range data using a time-dependent carrier frequency (or wavelength) that takes into account potential intraday variability in the microwave or laser frequency. Moreover, we analyze the KBR-LRI residuals and discuss which error and noise contributors limit the residuals at high and low Fourier frequencies. It turns out that the agreement between KBR and LRI biased range observations can be slightly improved by considering intraday carrier frequency variations in the processing. Although the effect is probably small enough to have little relevance for gravity field determination at the current precision level, this analysis is of relevance for detailed instrument characterization and potentially for future more precise missions.

The gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites’ center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the nonzero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has a significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.

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.

When using the dynamic approach to recover the time-variable gravity field, the reference orbit generated by the perturbation model and the non-conservative force observed from the accelerometer should be introduced at first, and then the observation equations of the residual orbit and the residual range rate are established. This introduces a perturbation model error and instrument noise. Thus, there are low-frequency errors in the residual orbit and the residual range rate. Currently, most studies only focus on the low-frequency error of the residual range rate, neglecting the influence of the low-frequency error in the residual orbit. Therefore, under the condition of the perturbation model error and instrument noise including the constant term and 1CPR term, the low-frequency error formulas of the residual orbit and residual range rate are derived according to the characteristics of the solution of the Hill equation. Then, the influence of the low-frequency error on the residuals is analyzed by using the simulation and the real data processing respectively. In the simulation and real data processing, the accuracy of the recovered gravity field can maintain a good consistency for different arc lengths by removing the low-frequency error in the residual orbit. Finally, the time-variable gravity field model UCAS-IGG (University of Chinese Academy of Sciences-Institute of Geodesy and Geophysics) was solved from January 2005 to February 2010 by removing the low-frequency error of the residual orbit and residual range rate. Compared with the official institutions, the UCAS-IGG presents a good consistency in the estimating time-variable gravity field signal. This study demonstrates how the effect of the low-frequency error of the residual orbit should be taken into consideration when the longer arc length is used to recover a time-variable gravity field. Using a long arc length can reduce the variables of the initial state and recover the influence of the small force.

The inter-satellite distance changes of the GRACE Follow-On spacecraft are measured by the main science instrument, the K-Band Ranging (KBR) system, and by the new Laser Ranging Interferometer (LRI), which exhibits a higher precision. The official ranging data is provided by the Science Data System (SDS) in the so-called KBR1B and LRI1B data products, which are available in the latest version v04. However, the Albert Einstein Institute (AEI) in Hannover is deriving alternative LRI1B data products (v50+v52). These data sets allow us to investigate different processing strategies that might improve the quality of the ranging data.We will present the most important processing steps for the AEI-derived data products and compare them to the official SDS v04 data. The main differences in the processing regardthe deglitching algorithm, which is essential to remove disturbances induced by thruster activations or by single event upsets transformation of LRI time-tags to GPS time using a smooth and at day-bounds continuous correction formed by CLK1B, TIM1B, datation reports and empirical offsets obtained by daily cross-correlating KBR and LRI (only v50) conversion of phase-to-range using a novel formula that was published recently and that can utilize a time-depend laser frequency (scale factor) light-time-correction using alternative formulas that are expected to be more precise tilt-to-length (TTL) coupling correction, which is similar to the antenna offset correction (AOC) in KBR1B but missing in LRI1B v04 so far. Furthermore, we have implemented a quality flag to indicate special events such as sun-blinding periods or momentum transfer events that might reduce the quality of the ranging data. This allows to down-weight affected segments during gravity field recovery. By comparing LRI1B v04 and AEI-derived LRI1B data, a verification and validation of the official dataset is possible. We will conclude with some examples where the LRI1B data quality can be improved compared to the v04 results.Our LRI1B datasets are available at:  https://www.aei.mpg.de/grace-fo-ranging-datasets