Adaptive Modeling of Correlated Noise in Space-Based Gravitational Wave Detectors

Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often assume uncorrelated noise and ignore the off-diagonal elements in the noise covariance matrix. This could lead to some bias in the parameter estimation of gravitational wave signals. In this paper, we present a framework for reconstructing the full noise covariance matrix, including frequency-dependent auto- and cross-correlated power spectral densities, without assuming the parametric analytic expressions of the noise model. Our approach combines spline interpolation with trigonometric basis functions to construct a semi-analytical representation of the noise. We then employ trans-dimensional Bayesian inference to fit the correlated noise structure.The resulting software package, $\texttt{NOISAR}$, successfully recovers both auto- and cross-correlated power spectral features with a relative error of about $10\%$.