Scale Factor Determination for the GRACE-Follow On Laser Ranging Interferometer including Thermal Coupling

TL;DR

This paper develops precise formulas for converting LRI phase measurements into range, analyzes errors and thermal effects, and proposes models to reduce dependency on MWI, enhancing the accuracy of the GRACE-FO laser ranging data.

Contribution

It introduces new formulas for range conversion considering varying carrier frequency and thermal effects, and presents models that reduce reliance on MWI calibration.

Findings

Derived formulas for phase-to-range conversion with variable carrier frequency.

Identified dominant errors due to carrier frequency uncertainty and time biases.

Developed a thermal coupling model that minimizes LRI-MWI residuals.

Abstract

The GRACE Follow-On satellites carry the very first inter-spacecraft Laser Ranging Interferometer (LRI). After more than four years in orbit, the LRI outperforms the sensitivity of the conventional Microwave Instrument (MWI). However, in the current data processing scheme, the LRI product still needs the MWI data to determine the unknown absolute laser frequency, representing the ruler for converting the raw phase measurements into a physical displacement in meters. In this paper, we derive formulas for precisely performing that conversion from the phase measurement into a range, accounting for a varying carrier frequency. Furthermore, the dominant errors due to knowledge uncertainty of the carrier frequency as well as uncorrected time biases are derived. In the second part, we address the dependency of the LRI on the MWI in the currently employed cross-calibration scheme and present three different models for the LRI laser frequency, two of which are largely independent of the MWI. Furthermore, we analyze the contribution of thermal variations on the scale factor estimates and the LRI-MWI residuals. A linear model called Thermal Coupling (TC) is derived that significantly reduces the differences between LRI and MWI to a level where the MWI observations limit the comparison.