## 2 Related Work
### The Compensation Influence of the Fluxgate Magnetometer Noise
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Compensation** & **No White Noise** & **1\% White Noise** & **5\% White Noise** & **10\% White Noise** \\ \hline c1 & 2.7063 & 2.7693 & 2.6785 & 2.6026 \\ c2 & 1.6073 & 2.0583 & 1.8476 & 1.6074 \\ c3 & \(-\)0.2453 & \(-\)0.2356 & \(-\)0.3369 & \(-\)0.4062 \\ c4 & \(2.1681\times 10^{-5}\) & \(-\)5.4560 \(\times 10^{-5}\) & \(-\)3.6020 \(\times 10^{-5}\) & \(-\)1.9696 \(\times 10^{-5}\) \\ c5 & \(-\)4.6649 \(\times 10^{-6}\) & \(-\)4.5530 \(\times 10^{-6}\) & \(-\)4.7164 \(\times 10^{-6}\) & \(-\)9.0702 \(\times 10^{-6}\) \\ c6 & \(-\)1.0169 \(\times 10^{-5}\) & \(-\)1.0227 \(\times 10^{-5}\) & \(-\)7.7326 \(\times 10^{-6}\) & \(-\)7.7468 \(\times 10^{-6}\) \\ c7 & \(1.6431\times 10^{-5}\) & \(-\)4.5945 \(\times 10^{-5}\) & \(-\)3.3852 \(\times 10^{-5}\) & \(-\)1.7170 \(\times 10^{-5}\) \\ c8 & \(-\)4.7042 \(\times 10^{-6}\) & \(-\)3.6484 \(\times 10^{-6}\) & \(-\)6.4742 \(\times 10^{-6}\) & 1.0502 \(\times 10^{-5}\) \\ c9 & \(1.469\times 10^{-4}\) & \(6.4670\times 10^{-5}\) & \(2.5494\times 10^{-5}\) & 1.1084 \(\times 10^{-5}\) \\ c10 & \(-\)9.5252 \(\times 10^{-4}\) & \(-\)8.3109 \(\times 10^{-4}\) & \(-\)0.0011 & \(-\)0.0013 \\ c11 & \(-\)2.5920 \(\times 10^{-6}\) & \(-\)2.4164 \(\times 10^{-6}\) & \(-\)9.0160 \(\times 10^{-7}\) & \(-\)1.1915 \(\times 10^{-6}\) \\ c12 & \(1.9710\times 10^{-6}\) & \(2.6852\times 10^{-6}\) & \(3.6735\times 10^{-6}\) & \(9.0144\times 10^{-6}\) \\ c13 & \(-\)2.5627 \(\times 10^{-6}\) & \(-\)2.8103 \(\times 10^{-6}\) & \(-\)1.8221 \(\times 10^{-6}\) & \(-\)1.4755 \(\times 10^{-6}\) \\ c14 & \(-\)9.5580 \(\times 10^{-4}\) & \(-\)8.3262 \(\times 10^{-4}\) & \(-\)0.0011 & \(-\)0.0013 \\ c15 & \(2.3457\times 10^{-5}\) & \(2.3677\times 10^{-5}\) & \(1.9844\times 10^{-5}\) & \(7.3923\times 10^{-6}\) \\ c16 & \(1.9224\times 10^{-6}\) & \(1.8049\times 10^{-6}\) & \(2.6602\times 10^{-6}\) & \(3.2138\times 10^{-6}\) \\ c17 & \(-\)2.3222 \(\times 10^{-6}\) & \(-\)3.9508 \(\times 10^{-6}\) & \(-\)1.7717 \(\times 10^{-5}\) & \(-\)2.3474 \(\times 10^{-5}\) \\ c18 & \(-\)0.0010 & \(-\)8.8769 \(\times 10^{-4}\) & \(-\)0.0011 & \(-\)0.0014 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The compensation coefficients solved by the fluxgate magnetometer data after adding different amplitudes noise. Figure 1 shows the results before and after compensated by different compensation coefficients. Additionally, (a), (b), (c), and (d) represent the time-domain waveforms of the interfered magnetic field before and after compensation when Gaussian white noise with an amplitude of 0% (noise is not added), 1%, 5%, and 10% of the stability amplitude of the fluxgate magnetic field is added, respectively. In order to evaluate the performance of the four compensation coefficients, the compensation results in Figure 1 are quantitatively analyzed to calculate the standard deviation of the residual interference before and after compensation and the IR, as shown in Table 2.  
As can be seen from the compensation results shown in Figure 1, the compensation effect gradually decreases as the amplitude of the added white noise increases. Taking STD as the evaluation index, the larger the amplitude of white noise added, the larger the residual magnetic interference after compensation. It proves that the fluxgate magnetometer noise has a very significant influence on the compensation effect. To summarize, the larger the noise of the fluxgate magnetometer, the worse the compensation results. The equipment noise is also often unpredictable due to the complex \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Compensation** & **Before Compensation** & **After Compensation** & **IR** \\
**Coefficients** & **(rms, pT)** & **(rms, pT)** & \\ \hline No white noise & 150.4878 & 11.0523 & 13.6160 \\
1\% white noise & 150.4878 & 12.9478 & 11.6227 \\
5\% white noise & 150.4878 & 24.1168 & 6.2399 \\
10\% white noise & 150.4878 & 35.4036 & 4.2506 \\ \hline \hline \end{tabular}
\end{table}