Quantitative analysis of LISA pathfinder test-mass noise

LISA Pathfinder (LPF) is a mission aiming to test the critical technology for the forthcoming space-based gravitational-wave detectors. The main scientific objective of the LPF mission is to demonstrate test masses free falling with residual accelerations below 3 x 10(-14) m s(-2) / root Hz at 1 mHz. Reaching such an ambitious target will require a significant amount of system optimization and characterization, which will in turn require accurate and quantitative noise analysis procedures. In this paper, we discuss two main problems associated with the analysis of the data from LPF: i) excess noise detection and ii) noise parameter identification. The mission is focused on the low-frequency region ([0.1, 10] mHz) of the available signal spectrum. In such a region, the signal is dominated by the force noise acting on test masses. At the same time, the mission duration is limited to 90 days and typical data segments will be 24 hours in length. Considering those constraints, noise analysis is expected to deal with a limited amount of non-Gaussian data, since the spectrum statistics will be far from Gaussian and the lowest available frequency is limited by the data length. In this paper, we analyze the details of the expected statistics for spectral data and develop two suitable excess noise estimators. One is based on the statistical properties of the integrated spectrum, the other is based on the Kolmogorov-Smirnov test. The sensitivity of the estimators is discussed theoretically for independent data, then the algorithms are tested on LPF synthetic data. The test on realistic LPF data allows the effect of spectral data correlations on the efficiency of the different noise excess estimators to be highlighted. It also reveals the versatility of the Kolmogorov-Smirnov approach, which can be adapted to provide reasonable results on correlated data from a modified version of the standard equations for the inversion of the test statistic. Closely related to excess noise detection, the problem of noise parameter identification in non-Gaussian data is approached in two ways. One procedure is based on the maximum-likelihood estimator and another is based on the Kolmogorov-Smirnov goodness-of-fit estimator. Both approaches provide unbiased and accurate results for noise parameter estimation and demonstrate superior performance with respect to standard weighted least squares and Huber's norm. We also discuss the advantages of the Kolmogorov-Smirnov formalism for the estimation of confidence intervals of parameter values in correlated data.