Time delay interferometry and principal component analysis for noise cancellation of TianQin

TianQin is a proposed space-borne laser interferometer which aims to detect gravitational waves in the low frequency band (10⁻⁴ Hz–10⁰ Hz). However, for space-borne interferometry detectors the laser phase noise is expected to be 7–8 orders of magnitude higher than the gravitational wave signals, due to unequal and time-varying arm lengths. Time delay interferometry (TDI) is an effective method to cancel laser phase noise by synthesizing virtual equal arm interferometric measurements with time delayed Doppler data combinations. In previous work it has been shown that TDI variables can also be understood within the context of principal component analysis (PCA), as combinations of eigenvectors of the total noise covariance matrix. It is therefore possible to generate the same TDI variables using a PCA approach – by computing the eigenvectors of the noise covariance matrix at a specific time. In this paper we extend significantly the previous work on a PCA approach to generating TDI variables by presenting TDI sensitivity curves for TianQin approximated as both a static and moving constellation of satellites. We compare the covariance matrix for the static and moving case, from the point of view of performing statistical inference using PCA. We also demonstrate the equivalency between the ‘conventional’ second generation TDI variables and those obtained using PCA.