Postprocessing of tilt-to-length noise with coefficient drifts in TianQin using a null time-delay interferometry channel

Tilt-to-length (TTL) coupling is expected to be one of the major noise sources in the interferometric phase readouts in the TianQin mission. Arising from the angular motion of spacecraft (SC) and the onboard movable optical subassemblies (MOSAs), TTL noise needs to be removed in postprocessing after suppressing the laser phase noise with the time-delay interferometry (TDI) technique. In this article, we show that we can estimate the TTL coupling coefficients using the null TDI channel $\ensuremath{\zeta}$ and remove the TTL noise in the commonly used Michelson variables with the estimated coefficients. We introduce the theoretical model of TTL noise in TDI and consider linear drifts in the linear TTL coefficients for noise estimation and subtraction. The TTL coefficients with drifts are estimated successfully with an accuracy of $10\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}/\mathrm{rad}$ in our numerical simulation. We discuss the impact of point-ahead angle compensation error and wavefront error, and find it necessary to estimate linear drift coefficients and quadratic TTL coefficients to keep TTL noise residuals below the 0.3 pm noise reference curve. However, the estimation accuracy suffers greatly from the correlation between yaw jitter measurements that contain the same SC jitter. Assuming all angular jitters induced by MOSAs are independent, choosing a frequency range with relatively higher MOSA yaw jitter noise levels is beneficial to the TTL coefficient estimation.