Modeling non-stationary noise: applications in gravitational wave astronomy

Abstract

In an ideal world, the measurement noise in gravitational wave data would be stationary and Gaussian. In reality, neither of these conditions holds. Here a general framework is introduced that can be used to model non-stationary noise in an easily interpretable way, using a dynamic power spectrum $S(f,t)$. The construction is a Gram-factor model for the noise covariance matrix that is positive semi-definite by construction. This construction generalizes the familiar stationary power spectrum $S(f)$. The dynamic spectrum encodes the properties of the noise covariance matrix in any basis, including the frequency domain, time domain, and time-frequency wavelet domain. Closed form expressions are given for discrete Fourier representations of the data, and for discrete Wilson-Daubechies wavelet representations of the data. Both take the form of Gramian matrices. Examples are provided, including the non-stationarity caused by window functions, the modulated response to galactic binary signals for space-based detectors, and other, more general types of non-stationarity.