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

Accurately estimating the statistical properties of noise is important in space-based gravitational wave data analysis. Traditional methods often assume uncorrelated noise or impose restrictive parametric forms on cross-channel correlations, which could lead to biased estimation in complex instrumental noise. This paper introduces a spline-based framework with trans-dimensional Bayesian inference to reconstruct the full noise covariance matrix, including frequency-dependent auto- and cross-power spectral densities, without prior assumptions on noise shapes. The developed software $\mathtt{NOISAR}$ can recover the features of the noise power spectrum curves with a relative error $\leq 10\%$ for both auto- and cross-one.