A Linearized Model of FID Signal for Increasing Proton Magnetometer Precision

A linearized model of frequency measurement for the Free Induction Decay (FID) signal is proposed to increase the Proton Magnetometer (PM) precision. First, the nonlinear model of frequency measurement is set up according to the characteristic of the FID signal. Then, according to the error analysis of the MCFM method, the model is linearized on the condition of precision requirement. Furthermore, to reduce the nonlinear error caused by approximate treatment and the trigger time error caused by the random noise, the Least Squares (LS) method is adopted to estimate the slope of the linearized model, and the frequency to be measured is the inverse of the slope. Finally, a PM Prototype is made to verify the effectiveness of the proposed method. Experimental results show that the precision of frequency measurement is obviously increased if the proposed method is adopted for the noised sine signal. Moreover, the RMSD and the NPSD of magnetic-field measurement are about 0.13 nT and 80 pT/Hz^1/2, respectively if the proposed method is adopted by PM, which is better than the comparison method.