Accuracy assessment of analysis of a free-fall gravimeter data

The measurement of the local acceleration due to gravity is based on the orbit reconstruction of the free fall in vacuo of a test mass [1]. In the set-up of the Istituto di Metrologia “G. Colonnetti” the test mass, which embeds a retroreflector, is tossed up and its ascent and descent are tracked and timed by a laser interferometer and a rubidium clock. The data actually supplied by the instrument is time versus fixed fringe number and the gravity value is obtained by fitting time-height pairs to a parabolic motion model. In order to overcome the limits of this procedure, to assess data processing, and to achieve full information about the test mass orbit, traveling interference fringes have been digitized by means of a fast Analog to Digital (AD) converter with 8-bit resolution and the entire interferometer signal is recorded for subsequent analysis [2]. The present article deals with the reconstruction of the test mass orbit and error propagation through gravity calculation. Owing to timing errors and noise correlation, the uncertainty resulting from conventional error propagation through least squares calculation is smaller than the actual one. To avoid underestimation, noise characterization and modeling was carried out and asymptotic formulae expressing the measurement uncertainty were obtained and verified against experimental data.