# Dynamic Compensation of a Fluxgate Magnetometer Based on a Hybrid Optimizing Algorithm
## 5 Conclusions  
In this paper, the principle of dynamic error compensation of the fluxgate magnetometer was introduced first. The dynamic error compensation of the magnetometer was realized by the series dynamic compensator behind the magnetometer. A parameter-calculating method of the dynamic compensator based on the hybrid optimization strategy of the GA-SA algorithm was proposed. Finally, simulation and experimental verification were carried out.  
First, the compensation effect of different compensator orders under the input of a step signal was analyzed by simulation, and it was confirmed that the compensation effect is best when the compensator order is second order. The comparison of the three algorithms shows that the GA-SA compensation is the closest to the simulation input signal; the overshot after compensation was 50% of the GA and 17% of the SA, and the response time was 18.22% of that before compensation and 46.43% and 92.86% of the GA and SA.  
Second, the signal test results of the step signal input show that the step response time was reduced to 5.5% of that before dynamic compensation.  
Further, sinusoidal signal input and tests with different frequencies were carried out. The amplitude-frequency and phase-frequency characteristic curves show that the attenuation of the maximum value of the magnetic sensor decreased from 0.24% to 0.10% in the 0.01-10 Hz frequency band after dynamic compensation, and the phase difference was less than \(-0.5^{\circ}\).  
At last, the geomagnetic measurement results show that the dynamic measurement results, after being compensated by the proposed method, reduced the standard deviation error from 95.30/277.35/108.51 nT to 3.41/2.36/2.75 nT in three geomagnetic vector components. Moreover, the dynamic compensated results are mostly close to the real calibrated geomagnetic field values, which verifies the effectiveness and accuracy of the proposed dynamic compensation method.  
Figure 20: Dynamic measurement and static/dynamic compensation results: (**a**) results of raw data; (**b**) results of data subtracting the calibration value.  
To sum up, the accuracy and convergence of the proposed algorithm were proved by a simulation and an experiment. Moreover, dynamic compensation had certain compensation effects on the magnetometer in this paper, which improved the dynamic magnetic measurement performance and its application capabilities.  
Conceptualization, Z.C. and Q.Z.; methodology, Z.C.; software, Z.W.; validation, M.P.; formal analysis, Z.L.; investigation, D.C.; resources, Y.X.; data curation, Z.C. and Z.W.; writing--original draft preparation, Z.C.; writing--review and editing, D.C. and Q.Z.; visualization, Z.C. and Z.W.; supervision, Q.Z.; project administration, M.P.; funding acquisition, M.P. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of Hunan Province under Project 2021 JJ40687.  
Not applicable.  
Data Availability StatementData supporting this study's findings are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.