  After performing highly sensitive acceleration measurements during two years
of drag-free flight around the Earth, MICROSCOPE provided the best constraint
on the Weak Equivalence Principle (WEP) to date. Beside being a technological
challenge, this experiment required a specialised data analysis pipeline to
look for a potential small signal buried in the noise, possibly plagued by
instrumental defects, missing data and glitches. This paper describes the
frequency-domain iterative least-square technique that we developed for
MICROSCOPE. In particular, using numerical simulations, we prove that our
estimator is unbiased and provides correct error bars. This paper therefore
justifies the robustness of the WEP measurements given by MICROSCOPE.
