Instrumental noise estimation algorithm based on time-delay interferometry combinations

Spaceborne gravitational wave (GW) detectors employ heterodyne interferometry to measure the minute spacetime deformation between two free-falling test masses (TMs) in the frequency range of ${10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{Hz}$ to 1 Hz. Time-delay interferometry (TDI) is a key data processing technique that suppresses the primary laser phase noise by combining time-shifted interferometer measurements. The noises due to TM acceleration and optical metrology system (OMS) displacement are secondary but inevitable, governing the upper limit of the detector's sensitivity. The optimal scenario is that all remaining technical noises should be suppressed below these inevitable ones. In this regard, a precise assessment of secondary noise is crucial for the success of ongoing spaceborne GW detection missions. The present study proposes a novel scheme for estimating such noises via noise transfer functions, which is independent of specific noise models. In particular, it is pointed out that the noise transfer functions specific to distinct TDI combinations furnish a matrix. When the matrix is not singular, the frequency profiles of the underlying inevitable noise can be extracted by inverting it. As an example, we estimate the TM acceleration and OMS noises from signals generated by numerical simulations where the presence of an unknown plasma noise is also assumed. It is argued that our algorithm facilitates in-flight instrument performance monitoring without requiring additional measurement, potentially enhancing the reliability and accuracy of GW detection.