Improving LIGO calibration accuracy by using time-dependent filters to compensate for temporal variations

The response of the Advanced LIGO interferometers is known to vary with time [arXiv:1608.05134]. Accurate calibration of the interferometers must therefore track and compensate for temporal variations in calibration model parameters. These variations were tracked during the first three Advanced LIGO observing runs, and compensation for some of them has been implemented in the calibration procedure. During the second observing run, multiplicative corrections to the interferometer response were applied while producing calibrated strain data both in real-time and in high-latency. In a high-latency calibration produced after the second observing run and during the entirety of the third observing run, a correction involving updating filters was applied to the calibration -- the time dependence of the coupled cavity pole frequency $f_{\rm cc}$. This paper describes the methods developed to compensate for variations in the interferometer response requiring time-dependent filters, including variable zeros, poles, gains, and time delays. The described methods were used to provide compensation for well-modeled time dependence of the interferometer response, which has helped to reduce systematic errors in the calibration to $<2$% in magnitude and $<2^{\circ}$ in phase across LIGO's most sensitive frequency band of 20 - 2000 Hz [arXiv:2005.02531, arXiv:2107.00129]. Additionally, this paper shows how such compensation is relevant for astrophysical inference studies by reducing uncertainty and bias in the sky localization for a simulated binary neutron star merger.