AI Insight
This study presents a Bayesian statistical method for accurately estimating spectral properties in time series data at very low frequencies, where traditional methods fail due to limited data averaging. The approach provides exact mathematical solutions for analyzing noise characteristics and correlations in multivariate datasets, with particular application to gravitational wave experiments. When applied to LISA Pathfinder mission data, the method successfully identified and removed temperature-related noise and quantified its coupling to the measurement system.
Why it matters
This technique is critical for precision gravitational wave detection missions like LISA, which operate at sub-Hz frequencies where even small noise sources can obscure signals. The method enables more reliable separation of genuine gravitational wave signatures from instrumental and environmental noise, potentially improving the sensitivity of future space-based gravitational wave observatories.
⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: We consider the problem of estimating cross-spectral quantities in the low-frequency regime, where long observation times limit averaging over large ensembles of periodograms, thereby preventing the use of approximate Gaussian statistics. This case is relevant for precision low-frequency gravitational experiments such as LISA and LISA Pathfinder. We present a Bayesian method for estimating spectral quantities in multivariate Gaussian time series. The approach, based on periodograms and Wishart statistics, yields closed-form expressions at any given frequency for the marginal posterior distributions of the individual power spectral densities, the pairwise coherence, and the multiple coherence, as well as for the joint posterior distribution of the full cross-spectral density matrix. In the context of noise projection — where one series is modeled as a linear combination of filtered versions of the others, plus a background component — the method also provides closed-form posteriors for both the susceptibilities, i.e., the filter transfer functions, and the power spectral density of the background. We apply the method to data from the LISA Pathfinder mission, showing effective decorrelation of temperature-induced acceleration noise and reliable estimation of its coupling coefficient.