Enhancing noise characterization with robust time delay interferometry combination

Time delay interferometry (TDI) is essential for suppressing laser frequency noise and achieving the targeted sensitivity for space-borne gravitational wave (GW) missions. In Paper I, we examined the performance of the fiducial second-generation TDI Michelson configuration versus an alternative, the hybrid Relay, in noise suppression and data analysis. The results showed that both TDI schemes have comparable performances in mitigating laser and clock noises. However, when analyzing chirp signal from the coalescence of massive binary black holes, the Michelson configuration becomes inferior due to its vulnerable T channel and numerous null frequencies. In contrast, the hybrid Relay is more robust in dynamic unequal-arm scenarios. In this work, we further investigate the noise characterization capabilities of these two TDI configurations. Our investigations demonstrate that hybrid Relay achieves more robust noise parameter inference than the Michelson configuration. Moreover, the performance can be enhanced by replacing the T channel of hybrid Relay with a second-generation TDI null stream $C^{12}_3$. The combined three data streams, including two science observables from the hybrid Relay and $C^{12}_3$, could reduce the instabilities of noise spectra in the targeting frequency band and form an optimal dataset for characterizing noises.