Space gravitational wave detection primarily focuses on the rich wave sources corresponding to the millihertz frequency band, which provide key information for studying the fundamentalphysics 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. Amongthe various noise sources, laser phase noise is dominant, approximately seven orders of magnitudelarger in strength than typical gravitational wave signals, and requires suppression using time-delayinterferometry (TDI) techniques, which involve combining raw data with time delays. This paperwill 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 methodsfor symbolic search. Furthermore, the applicability of TDI under actual operating conditions will beconsidered, such as the arm locking in conjunction with the TDI algorithm. Finally, the sensitivityfunctions for different types of TDI combinations will be provided, which can be used to evaluate thesignal-to-noise ratio (SNRs) of different TDI combinations.