Clock noise reduction in geometric time delay interferometry combinations

Time-delay interferometry (TDI) is a critical data post-processing technique in space-borne laser interferometer gravitational wave detection, which is developed to suppress the overwhelming laser phase noise below the instrumental noise floor by time-shifting and synthesizing the interferometric data streams. There are virous kinds of TDI combinations, and geometric TDI, as a special means to search TDI combination, has been widely used because of its clear physical significance, i.e. constructing virtual equal-arm interferometer to realize an excellent differential performance of the laser phase noise. To achieve the desired noise level, it is necessary to further suppress the phase fluctuations of the onboard ultra-stable oscillators (USO) used as reference clocks. In this paper, we analyze the characteristics of geometric TDI clock noise residual, and formulate it into a general expression. We find the intrinsic equal-arm length constraint of geometric TDI is a sufficient condition for clock noise reduction, which makes the clock noise terms only appear in differential form. Based on this, we propose a clock noise reduction scheme. Compared with the existing algorithms, our method benefits from the sufficient condition to avoid the problem that the clock noise terms without any time-shift operators cannot be properly handled.