## Data processing Flow Chart
NRMSE was compared separately for the horizontal and vertical components for each of the three correction equations: (2), (3), and (4) and only vessel attitude was corrected. The NRMSE values for the horizontal components show 0.0608, 0.0251, 0.037, and 0.0365, and for the vertical component, the values exhibit 0.0322, 0.0134, 0.0244, and 0.0224, respectively. This indicates that the correction using Equation (3) converges well to the ambient magnetic field (IGRF model) in both horizontal and vertical components. The corresponding correction results and their residual histograms are presented in Figures 5 and 6, respectively. These results can be explained by the structural advantages of Equation (3) when applying the least squares method. In Equation (3), the right-hand side consists entirely of the stable and well-defined background magnetic field values, typically derived from the IGRF or a stably obtained background magnetic field. This enables the independent optimization for the unknown variables (\(B\), H\({}_{\text{pb}}\)) on the left-hand side, enhancing numerical stability during the least squares fitting process. Comparing the method presented in [26] with that of [25], the equations used for correction are identical in all aspects except for the non-orthogonality correction matrix (P), which is excluded in [25]. However, the method in [26] performs the correction using only the principal components (xx, yy, zz) of the susceptibility tensor, whereas [25] employs all nine components of the tensor as variables. This suggests that utilizing not only the major but also the minor components of the susceptibility tensor may have the capability to eliminate not only the generally known magnetic characteristics of the platform but also other unknown linear features exhibiting low-frequency electromagnetic noise. Therefore, we found that the correction approach based on Equation (3) achieved more accurate and reliable results compared to Equations (2) and (4). Consequently, we applied the correction coefficients obtained from Equation (3) to the entire dataset for comprehensive magnetic data correction (see Figure S5). \begin{table}
\begin{tabular}{l c c} \hline \hline Correction coefficients from Equation (2) & \(A=\begin{bmatrix}0.9679&-0.0188&-0.6011\\ -0.0099&0.9549&-0.4577\\ -0.0053&0.0059&0.1001\end{bmatrix}\) H\({}_{\text{p}}=\begin{bmatrix}22187.7\\ 17958.7\\ 35814.7\end{bmatrix}\) \\ \hline \hline Correction coefficients from Equation (3) & \(B=\begin{bmatrix}1.0079&0.0465&-0.3216\\ -0.0051&1.0342&-0.1424\\ -0.0228&0.0013&1.0947\end{bmatrix}\) H\({}_{\text{pb}}=\begin{bmatrix}14143.3\\ 5436.44\\ -4308.16\end{bmatrix}\) \\ \hline \hline \end{tabular}
\begin{tabular}{l c c} \hline \hline Correction coefficients from Equation (4) & \(A=\begin{bmatrix}0.9959&0&0\\ 0&0.9968&0\\ 0&0&0.9993\end{bmatrix}\) P = \(\begin{bmatrix}1&0&0\\ -0.0012&1&0\\ 0.0007&0.0015&1\end{bmatrix}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Twelve constants of the ship’s magnetization determined from the figure-of-rotation tracks using Equation (2) (up), Equation (3) (middle) and Equation (4) (down). Figure 5: Comparison of correction results for correction maneuver track 1 (Figure 1b). (**a**) Ship’s attitude corrected. (**b**) Correction results from Equation (2) [24]. (**c**) Correction results from Equation (3) [25]. (**d**) Correction results from Equation (4) [26]. All equations are based on the same model formulation; they yield different results due to their different approaches to parameter optimization in the least squares method. Black: raw data; blue: ambient magnetic field (IGRF-13); red: corrected data. Figure 6: Histograms of the misfit between the ambient magnetic field (IGRF-13) and the corrected USV magnetic field for the horizontal and vertical components measured along rotation track 1.