Quantitative analysis of LISA pathfinder test-mass noise

Abstract

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 × 10 −14 m s −2 / √ Hz at 1 mHz. Reaching such an ambitious target will require a significant amount of system optimisation and characterisation, 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 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 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.

Optimal design of calibration signals in space-borne gravitational wave detectors

“…It is worth noticing here that the allowed range of discrepancy in the parameters is orders of magnitude higher than the expected uncertainty in the parameters. Indeed, previous studies [8,12,20,24,30] have shown that the order of magnitude of expected error on the parameters considered in our analysis is σ G df σ G lfs 10 −5 for the control gains, σ ω 2 1 σ ω 2 2 10 −10 s −2 for the stiffnesses and σ S21 10 −8 for the sensing cross-coupling.…”

“…We are now prepared to compare the results obtained analytically with the prediction of the numerical algorithm based on the dispersion function -Eq. (12). To do so we inject a white noise data stream to the input channel under consideration, which for the analysis of the F 2121 term is the drag-free channel.…”

“…(27), the noise enters in the numerical analysis through the evaluation of the Fisher matrix in Eq. (12). In the later, the noise spectrum of the instrument is computed by generating time series with the LPF state-space model configured with no signal injections and then computing the power spectrum.…”

Kolmogorov-Smirnov like test for time-frequency Fourier spectrogram analysis in LISA Pathfinder

“…Moreover, the analysis of noise is typically performed in the frequency or time-frequency domain therefore we aim to develop a noise analysis tool that is suited for such data. The problem of the statistical analysis of noise in the frequency domain was already formulated in [7] where a number of data analysis strategies were developed and compared. In this paper we present a further refinement of the Kolmogorov-Smirnov test presented in [7] and we extend its range of application to the time-frequency domain.…”

“…The problem of the statistical analysis of noise in the frequency domain was already formulated in [7] where a number of data analysis strategies were developed and compared. In this paper we present a further refinement of the Kolmogorov-Smirnov test presented in [7] and we extend its range of application to the time-frequency domain. The analysis of time-frequency data is particularly interesting since it allows to identify and characterize non-stationary noise.…”