Comparison of three digital fringe signal processing methods in a ballistic free-fall absolute gravimeter

Abstract

This paper reports results of comparison of three digital fringe signal processing methods implemented in the same free-fall absolute gravimeter. A two-sample zero-crossing method, a windowed second-difference method and a method of non-linear least-squares adjustment on the undersampled fringe signal are compared in numerical simulations, hardware tests and actual measurements with the MPG-2 absolute gravimeter, developed at the Max Planck Institute for the Science of Light, Germany. The two-sample zero-crossing method realizes data location schemes that are both equally spaced in distance and equally spaced in time (EST) along the free-fall trajectory. The windowed second-difference method and the method of non-linear least-squares adjustment with complex heterodyne demodulation operate with the EST data. Results of the comparison verify an agreement of the three methods within one part in 10 9 of the measured gravity value, provided a common data location scheme is considered.

Relativity, Doppler shifts and retarded times in deriving the correction for the finite speed of light: a comment on ‘Second-order Doppler-shift corrections in free-fall absolute gravimeters’

“…The gravity value is calculated by the least squares fit of the model As the corrections can not be obtained without the data models, so the results and approaches of different authors can not be compared without specifying the models they used. In some cases, special steps have to be taken to achieve the model agreement and enable the comparison [9]. In [1], however, both the corrections are derived , and the results are compared with no model involvement.…”

Simple digital phase-measuring algorithm for low-noise heterodyne interferometry

“…However, owing to the limited computation power, none of them permit real-time processing of signals above several megahertz. In addition, no results can be obtained for constant time intervals, in contrast to homodyne interferometers [22,23], because the zero-crossing time of the modulated signal is not always in a constant period. Thus, these three conventional methods must be improved for making real-time measurements of dynamic motion with digital phase meters.…”

Optimal zero-crossing group selection method of the absolute gravimeter based on improved auto-regressive moving average model

“…In the same time window, the zero-crossing point is calculated by the windowed second-difference method [5] . The peak-valley value of the signal is 2A, and the threshold value is set as K so that the sampling points in [−KA, KA] approach a straight line.…”

“…Svilov compared the differences of these three methods with the same absolute gravimeter. [5] The two-sample zero-crossing detection method has high requirements on computer performance and relatively poor accuracy, but it is widely used due to its simple calculation rules. The windowed second-difference method is slower in the process of finding the zero-crossing points of fitted line.…”