Accuracy assessment of the two-sample zero-crossing detection in a sinusoidal signal

Abstract

The accuracy of a two-sample zero-crossing detection method is assessed by analytical uncertainty propagation and is verified in numerical simulations. Approximated expressions are given to evaluate uncertainty components due to linear interpolation, quantization, white noise and time jitter. The combined standard uncertainty of a detected zero phase is expressed as a function of the signal frequency, power of external noise and parameters of the digitizer used. The evaluation of the uncertainty of the measurand, derived from several detected zero-crossings, is illustrated with applications in frequency, displacement and free-fall acceleration measurements. The reported results can be used for uncertainty analysis and parameter optimization of a measurement system or a procedure, involving processing of sinusoidal signals.

Frequency-domain analysis of absolute gravimeters

“…The floor recoil appears at the start of free-fall in the corner-cube absolute gravimeters. It is widely discussed in the literature [10,11,[13][14][15][16][17][18][19]. Such a perturbation produces a systematic measurement error.…”

“…Depending on the particular set-up on the measurement site and on the drop duration T used, the recoil effect contributes differently to the uncertainty budget of the MPG-2 absolute gravimeter 6 (just to compare, at T = 0.2 s instead of T = 0.12 s it could be less than 0.5 µGal). Since the information on the least-squares residuals is available without the usage of additional hardware [10,11,[13][14][15][16][17][18][19], the uncertainty budgets of other absolute gravimeters could also be upgraded with the relevant estimate of the recoil effect. However, one should be aware that it still might be an incomplete estimate, since the possible unrecognized low-frequency vibration components might give a non-negligible contribution to the combined measurement uncertainty (see figure 7).…”

“…One of the dominant sources of measurement error in absolute gravimetry is ground vibrations, which affect the reference reflector, alter the measured distance intervals and distort the computed g value. Starting from the earliest measurements of g based on optical interferometry [4][5][6][7][8], vibration perturbations have always been considered [9][10][11][12][13][14][15][16][17][18][19]. The problem is also unavoidable in atom absolute gravimeters, which use an atom interferometer to measure the free-fall acceleration of the atom cloud [20][21][22][23][24].…”

“…In[15][16][17][18] the simplified expression (4.10) from[29] was used, assuming a very large initial velocity (or the EST scheme) and ignoring the high-frequency limit of this approximation (it is irrelevant for the MPG-2 absolute gravimeter because of very large N).…”

A Method of m-Point Sinusoidal Signal Amplitude Estimation

“…Next, in order to determine the estimator general form, three and m subsequent initial sinusoidal signal samples occurring in the signal period are used. In the literature, point estimators of sinusoidal signal parameters are amply represented and find many practical applications [3]- [5].…”