Details
| Original language | English |
|---|---|
| Article number | 042003 |
| Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |
| Volume | 90 |
| Issue number | 4 |
| Publication status | Published - 15 Aug 2014 |
Abstract
LISA Pathfinder (LPF), the precursor mission to a gravitational wave observatory of the European Space Agency, will measure the degree to which two test masses can be put into free fall, aiming to demonstrate a suppression of disturbance forces corresponding to a residual relative acceleration with a power spectral density (PSD) below (30fm/s2/Hz)2 around 1 mHz. In LPF data analysis, the disturbance forces are obtained as the difference between the acceleration data and a linear combination of other measured data series. In many circumstances, the coefficients for this linear combination are obtained by fitting these data series to the acceleration, and the disturbance forces appear then as the data series of the residuals of the fit. Thus the background noise or, more precisely, its PSD, whose knowledge is needed to build up the likelihood function in ordinary maximum likelihood fitting, is here unknown, and its estimate constitutes instead one of the goals of the fit. In this paper we present a fitting method that does not require the knowledge of the PSD of the background noise. The method is based on the analytical marginalization of the posterior parameter probability density with respect to the background noise PSD, and returns an estimate both for the fitting parameters and for the PSD. We show that both these estimates are unbiased, and that, when using averaged Welch's periodograms for the residuals, the estimate of the PSD is consistent, as its error tends to zero with the inverse square root of the number of averaged periodograms. Additionally, we find that the method is equivalent to some implementations of iteratively reweighted least-squares fitting. We have tested the method both on simulated data of known PSD and on data from several experiments performed with the LISA Pathfinder end-to-end mission simulator.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 90, No. 4, 042003, 15.08.2014.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Data series subtraction with unknown and unmodeled background noise
AU - Vitale, Stefano
AU - Congedo, Giuseppe
AU - Dolesi, Rita
AU - Ferroni, Valerio
AU - Hueller, Mauro
AU - Vetrugno, Daniele
AU - Weber, William Joseph
AU - Audley, Heather
AU - Danzmann, Karsten
AU - Diepholz, Ingo
AU - Hewitson, Martin
AU - Korsakova, Natalia
AU - Ferraioli, Luigi
AU - Gibert, Ferran
AU - Karnesis, Nikolaos
AU - Nofrarias, Miquel
AU - Inchauspe, Henri
AU - Plagnol, Eric
AU - Jennrich, Oliver
AU - McNamara, Paul W.
AU - Armano, Michele
AU - Thorpe, James Ira
AU - Wass, Peter
PY - 2014/8/15
Y1 - 2014/8/15
N2 - LISA Pathfinder (LPF), the precursor mission to a gravitational wave observatory of the European Space Agency, will measure the degree to which two test masses can be put into free fall, aiming to demonstrate a suppression of disturbance forces corresponding to a residual relative acceleration with a power spectral density (PSD) below (30fm/s2/Hz)2 around 1 mHz. In LPF data analysis, the disturbance forces are obtained as the difference between the acceleration data and a linear combination of other measured data series. In many circumstances, the coefficients for this linear combination are obtained by fitting these data series to the acceleration, and the disturbance forces appear then as the data series of the residuals of the fit. Thus the background noise or, more precisely, its PSD, whose knowledge is needed to build up the likelihood function in ordinary maximum likelihood fitting, is here unknown, and its estimate constitutes instead one of the goals of the fit. In this paper we present a fitting method that does not require the knowledge of the PSD of the background noise. The method is based on the analytical marginalization of the posterior parameter probability density with respect to the background noise PSD, and returns an estimate both for the fitting parameters and for the PSD. We show that both these estimates are unbiased, and that, when using averaged Welch's periodograms for the residuals, the estimate of the PSD is consistent, as its error tends to zero with the inverse square root of the number of averaged periodograms. Additionally, we find that the method is equivalent to some implementations of iteratively reweighted least-squares fitting. We have tested the method both on simulated data of known PSD and on data from several experiments performed with the LISA Pathfinder end-to-end mission simulator.
AB - LISA Pathfinder (LPF), the precursor mission to a gravitational wave observatory of the European Space Agency, will measure the degree to which two test masses can be put into free fall, aiming to demonstrate a suppression of disturbance forces corresponding to a residual relative acceleration with a power spectral density (PSD) below (30fm/s2/Hz)2 around 1 mHz. In LPF data analysis, the disturbance forces are obtained as the difference between the acceleration data and a linear combination of other measured data series. In many circumstances, the coefficients for this linear combination are obtained by fitting these data series to the acceleration, and the disturbance forces appear then as the data series of the residuals of the fit. Thus the background noise or, more precisely, its PSD, whose knowledge is needed to build up the likelihood function in ordinary maximum likelihood fitting, is here unknown, and its estimate constitutes instead one of the goals of the fit. In this paper we present a fitting method that does not require the knowledge of the PSD of the background noise. The method is based on the analytical marginalization of the posterior parameter probability density with respect to the background noise PSD, and returns an estimate both for the fitting parameters and for the PSD. We show that both these estimates are unbiased, and that, when using averaged Welch's periodograms for the residuals, the estimate of the PSD is consistent, as its error tends to zero with the inverse square root of the number of averaged periodograms. Additionally, we find that the method is equivalent to some implementations of iteratively reweighted least-squares fitting. We have tested the method both on simulated data of known PSD and on data from several experiments performed with the LISA Pathfinder end-to-end mission simulator.
UR - http://www.scopus.com/inward/record.url?scp=84927615797&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.90.042003
DO - 10.1103/PhysRevD.90.042003
M3 - Article
AN - SCOPUS:84927615797
VL - 90
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
SN - 1550-7998
IS - 4
M1 - 042003
ER -