## 4 Field Data Test  
The experiment was conducted at a site in Changchun City, Jilin Province, China, with the test area covering 12 \(\times\) 11 m. This experiment simulated a realistic measurement scenario of unexploded ordnance (UXO) targets using an unmanned aerial vehicle (UAV) magnetic survey system. The magnetic measurement platform utilized was a multi-rotor airborne magnetic survey system, and the flight platform was a DJI M300 RTK multi-rotor  
Figure 10: Comparison of azimuth estimation error under different SNRs. Figure 9: Comparison of inclination estimation error under different SNRs. UAV designed for autonomous flight along a pre-planned flight path with enhanced flight stability. The measurement instrument was a compact, high-precision rubidium optically pumped scalar magnetometer with a maximum sampling rate of 10 Hz. The UXO target consisted of a safely deactivated 122 mm caliber artillery shell casing buried at a depth of approximately 0.7 m to simulate an actual measurement site. The UAV magnetic survey system maintained a flight height of 1 m, a flight speed of 1 m/s, and a line spacing of 1 m, and the sampling rate of the magnetometer was set at 10 Hz to ensure high data quality. Figure 11 illustrates a schematic of the UXO target and the raw magnetic anomalies measured without processing (the actual coordinates have been replaced by distances). Figure 12 depicts the schematic diagram of the UAV aerial magnetic system and the simulated UXO target. The measured magnetic anomalies were processed to isolate the magnetic anomalies attributable only to the target. Utilizing the International Geomagnetic Reference Field (IGRF), the local normal geomagnetic field was calculated at 55,148 nT. The team subtracted this normal field value from the measurement data to eliminate the geomagnetic background field. In addition, they subtracted the mean value of the data to ensure that the average baseline of the anomaly data was zero. The processed data are displayed in Figure 13.  
Table 7 provides the known parameter information of the artillery shell target, while Table 8 compares the parameter estimation results of the LM-OBF method to two other ones. The parameter estimation results demonstrate that the LM-OBF algorithm showed superior performance in the presence of specific noise levels and aligns well with the known information. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Target** & \(x_{0}\) & \(y_{0}\) & \(z_{0}\) & \(m\) & \(I_{0}\) & \(A_{0}\) \\ \hline
122 mm projectile & 6.5 & 7 & 0.7 & / & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Known parameters of the artillery shell target. Figure 11: (a) Schematic diagram of a 122 mm caliber artillery shell. (b) Raw anomalies of the measured data. Figure 12: (**a**) UXO target and UAV magnetic survey system. (**b**) Conducting survey line flight and data acquisition. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & \(\mathbf{x_{0}}\) & \(\mathbf{y_{0}}\) & \(\mathbf{z_{0}}\) & \(\mathbf{m}\) & \(\mathbf{I_{0}}\) & \(\mathbf{A_{0}}\) \\ \hline LM & 6.75 & 6.54 & 1.52 & 5.725 & 1.25 & \(-\)50.26 \\ NMLM & 6.85 & 7.12 & 1.08 & 5.650 & 0.26 & \(-\)60.32 \\ LM-OBF & 6.53 & 7.06 & 0.83 & 4.835 & \(-\)10.96 & 99.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameter estimation results of different methods. Figure 14 further validates the parameter estimation effectiveness of the LM-OBF method on actual measured data. Figure 14a displays the processed raw anomalies, Figure 14b shows the original anomaly energy \(E\) after two-dimensional OBF processing, Figure 14c presents the restored energy \(E\) from the parameter estimation results, and Figure 14d illustrates the residuals of the parameter estimation. The application of field data underscores that the LM-OBF method exhibits robust adaptability to actual noisy data and provides superior parameter estimation results compared to traditional methods. Figure 14: (**a**) Raw anomaly. (**b**) The energy \(E\) of the raw anomaly.