Frequency Estimation Method for Increasing Accuracy of PM by Combining Multipoint Software Zero-Crossing Recognition and Least Square Regression

To increase the measurement accuracy of a proton magnetometer (PM), a frequency estimation method based on multipoint software zero-crossing recognition and least squares (LS) regression is proposed in this article. First, the amplified free induction decay (FID) signal is sampled by a high-resolution analog-to-digital converter (ADC) with a higher sampling rate. Then, all voltage zero-crossing times (VZT) of the sampled FID signal are estimated by the LS regression. To improve the accuracy of estimation, a method used to obtain the minimum sampling rate is deduced, and a data-selection strategy used to select the data near the VZT is given. Finally, the frequency to be measured is calculated by the LS regression method with the date of the VZT, and the total error is deduced. Simulation and experimental results show that, compared with the hardware zero-crossing recognition method, the nonlinear errors caused by hysteresis comparators are completely eliminated, and the errors caused by random noise of the sensor and circuit are largely reduced; what’s more, the noise power spectral density (NPSD) of the PM is approximately 10 pT/Hz
$^{1/2}$
in the range of 0.1–1 Hz.