Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission
Résumé
It is usual in the data analysis of physical measurements to deal with highly correlated noise. In addition, outliers, saturation events or data transmission losses can arise, leading to interruptions in the measured time series. We investigate the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and enables us to estimate the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to numerous processing of similar data, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of 10 −15 . The challenge of the data processing is to find a WEP violation signal around a well defined frequency in data samples disrupted by deterministic perturbations, colored noise and data gaps. We test our method with different gaps patterns and noise of known PSD and find that the results agree with the mission requirements. We show that it also provides a test of significance to assess the uncertainty of the measurement.
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