Reconstruction of the free-falling body trajectory in a rise-and-fall absolute ballistic gravimeter

Absolute ballistic gravimeters can measure the free-fall acceleration with an uncertainty of few parts in 10(9). Typically, the vertical trajectory of a test body subjected to the gravity field is tracked using interferometric methods, and a mathematical model of the motion is fitted to the time-position coordinates in a least-squares adjustment. In this paper, we describe a non-linear regression analysis applied to the IMGC-02 transportable gravimeter, developed at the Istituto Nazionale di Ricerca Metrologica (INRIM). We show how the method yields an accurate estimate of the free-fall acceleration avoiding measurement of the vertical gradient.