Scale Factor Determination for the GRACE-Follow On Laser Ranging Interferometer including Thermal Coupling. (arXiv:2207.11470v2 [astro-ph.IM] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Misfeldt_M/0/1/0/all/0/1">Malte Misfeldt</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Muller_V/0/1/0/all/0/1">Vitali M&#xfc;ller</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Muller_L/0/1/0/all/0/1">Laura M&#xfc;ller</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wegener_H/0/1/0/all/0/1">Henry Wegener</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Heinzel_G/0/1/0/all/0/1">Gerhard Heinzel</a> (Max-Planck-Institut f&#xfc;r Gravitationsphysik (Albert-Einstein-Institut) and Institut f&#xfc;r Gravitationsphysik, Leibniz Universit&#xe4;t Hannover, Callinstra&#xdf;e 38, D-30167 Hannover, Germany)

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.

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.

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