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Free keywords:
General Relativity and Quantum Cosmology, gr-qc, Physics, Data Analysis, Statistics and Probability, physics.data-an
Abstract:
In this paper we discuss two main problems associated with the analysis of
the data from LISA Pathfinder (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. 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.
