## 3 The Procedure of TC Center Estimation
### Stage 1: Coarse Estimation  
1. Determining SSWD points and candidate points: Given that the TC center might fall outside the SAR image's coverage, a candidate area larger than the SAR image coverage is defined. Initially, the SAR image's width and height are denoted as \(\Delta Lon\) and \(\Delta Lat\), respectively. A grid of SSWD points is then created using an interval of \(m_{1}\), resulting in a grid size of \(\frac{\Delta Lon}{m! }\times\frac{\Delta Lat}{m!}\). Subsequently, a candidate area centered on the SAR image's center is defined with a width of \(2\Delta Lon\) and a height of \(2\Delta Lat\). A grid of candidate points is generated within this expanded area using an interval of \(M_{1}\), leading to a total grid size of \(\frac{2\Delta Lon}{M! }\times\frac{2\Delta Lat}{M!}\). In this study, both \(m_{1}\) and \(M_{1}\) are set to \(0.01^{\circ}\). It is important to note that the SSWDs are retrieved from the image slices centered on SSWD points, and the TC center position is determined from these candidate points;
2. SSWD retrieval and quality control: SSWD retrieval from SAR images is typically based on wind streak information. The scale of these wind streaks usually ranges from several kilometers to over ten kilometers. Consequently, centered on these points, image slices with dimensions of 1000 \(\times\) 1000 pixels are extracted from the original SAR image. The SSWDs are then retrieved from these image slices by the improved  
Figure 1: Flowchart of the TC-center estimation algorithm. \(\beta\) represents the compensation angle. The coarsely estimated center position is derived from Stage 1, the precisely estimated center position is derived from Stage 2, and NRCS-adjusted center position is derived from the optional stage. local gradient (ILG) method [30]. Subsequently, slide a \((2A+1)\times(2A+1)\) window over the SSWD points and for the SSWD point \((i,j)\), calculate  
\[ \begin{split} S=(\sin 2\theta_{i,j}-\frac{\sum_{i^{\prime}=-A,i^{ \prime}\
eq i}^{A}\sum_{j^{\prime}=-A,i^{\prime}\
eq j}^{A}\sin 2\theta_{i^{ \prime},j^{\prime}}}{\left(2A+1\right)^{2}-1})\\ +(\cos 2\theta_{i,j}-\frac{\sum_{i^{\prime}=-A,i^{\prime}\
eq i}^{ A}\sum_{j^{\prime}=-A,i^{\prime}\
eq j}^{A}\cos 2\theta_{i^{\prime},j^{\prime}}}{ \left(2A+1\right)^{2}-1})\end{split}  \tag{1}\]  
where \(\theta_{i,j}\) represents the retrieved SSWD. In this stage, \(A\) is set to 5, and the SSWD is removed if \(S>0.5\) or \(S<0.001\). The variable \(S\) represents the dispersion of the SSWD. A higher \(S\) value indicates greater variability in the SSWDs within the window, whereas a lower \(S\) value suggests more consistency. Therefore, we set maximum and minimum thresholds of 0.5 and 0.001, respectively, for \(S\) to remove outliers;
3. Estimating the TC center position: A total of 121 compensation angles within \([-50^{\circ},10^{\circ}]\) were set at an interval of 0.5\({}^{\circ}\). For each compensation angle, the retrieved SSWD is adjusted by adding the compensation angle. Subsequently, the perpendicular lines of these compensated SSWDs are calculated, and the number of these perpendicular lines passing through each candidate point is counted. As illustrated in Figure 2, if the distance from a candidate point to a line is less than \(M_{1}/2\), the line is considered to pass through the candidate point. It should be noted that the rule for determining whether a line passes through a point is different from that in [23]. This procedure described above is repeated for each of the 121 compensation angles, generating a corresponding set of heatmaps. The values on each heatmap correspond to the number of perpendicular lines passing through each candidate point. As shown in Figure 3, the local maximum values on these heatmaps vary with the compensation angles, where the curve's peak value denotes the global maximum value across all heatmaps. The position associated with this peak value on the corresponding heatmap is the location of the coarsely estimated TC center.