Time-Delay Interferometry: The Key Technique in Data Pre-Processing Analysis of Space-Based Gravitational Waves

Space gravitational wave detection primarily focuses on the rich wave sources corresponding to the millihertz frequency band, which provide key information for studying the fundamental physics of cosmology and astrophysics. However, gravitational wave signals are extremely weak, and any noise during the detection process could potentially overwhelm the gravitational wave signals. Therefore, data pre-processing is necessary to suppress the main noise sources. Among the various noise sources, laser phase noise is dominant, approximately seven orders of magnitude larger in strength than typical gravitational wave signals, and requires suppression using time-delay interferometry (TDI) techniques, which involve combining raw data with time delays. This paper will be based on the basic principles of TDI to present methods for obtaining multi-type TDI combinations, including algebraic methods for solving indeterminate equations and geometric methods for symbolic search. Furthermore, the applicability of TDI under actual operating conditions will be considered, such as the arm locking in conjunction with the TDI algorithm. Finally, the sensitivity functions for different types of TDI combinations will be provided, which can be used to evaluate the signal-to-noise ratio (SNRs) of different TDI combinations.