# An Efficient GNSS Coordinate Recognition Algorithm for Epidemic Management
## 6 Simulation Result  
In this section, we compare the performance of O_PtInPy, L_Rect, c_, and our algorithm. Since a targeted area will be partitioned into a set of square areas in our algorithm, \"sqr\" is used to refer to our algorithm. Moreover, c_ uses a set of circles to cover a targeted area. This placement of circles starts from a seed point. The position of the seed point is selected as follows. First, a large rectangle that can cover a targeted area is defined. Then, this large rectangle is divided into 3 \(\times\) 4 smaller rectangles of the same size. If the center points of the smaller rectangles are in the targeted area, these center points are used as seed points. Various seed points generate various numbers of small areas. Briefly, c_max, c_min, and c_avg are used to represent the maximum, minimum, and average numbers of small areas, respectively. The points retrieved from the database are simply called candidate points. Candidate points are divided into inner points and outer points. For a candidate point, it may or may not be necessary to execute PtInPy to confirm if this point is an inner point. The points that need to be confirmed through PtInPy are termed confirmed points.  
Figure 10: The distribution of targets. (**a**) The distribution of targets in City 2; (**b**) The distribution of targets in City 3.  
Figure 9: The polygons of targeted cities. The red areas are the corresponding polygons of City 1, City 2, and City 3.  
For convenience, \(n_{\text{cand}}\), \(n_{\text{inner}}\), \(n_{\text{outer}}\), \(n_{\text{conf}}\), and \(n_{\text{area}}\) are used to refer to the numbers of candidate points, inner points, outer points, confirmed points, and subareas, respectively.  
Table 3 compares \(n_{cand}\), \(n_{\text{conf}}\), and \(n_{cand}/n_{inner}\) for O_PtInPy and L_Rect in City 1, City 2, and City 3. For O_PtInPy, in City 1, City 2, and City 3, the values of \(n_{\text{cand}}\) were all 1,112,188. Since each candidate point needed to be confirmed by using PtInPy, the value of \(n_{\text{conf}}\) was also 1,112,188. In City 1, 89,209 target points were finally obtained, but a total (\(n_{\text{cand}}\)) of 1,112,188 candidate points were retrieved from the database. The ratio of \(n_{cand}\) to \(n_{inner}\) was about 12.47. The ratios for City 2 and City 3 were about 7.09 and 7.60. For L_Rect, in City 1, City 2, and City 3, the values of \(n_{cand}\) were, 13,869, 19,057, and 256,725, respectively. Since each candidate point also needed to be confirmed by using PtInPy, \(n_{\text{conf}}\) was equal to \(n_{cand}\). Accordingly, the rates were about 1.55, 1.21, and 1.76, respectively.  
Next, the performance of sqr, c_max, c_min, and c_avg in City 1 was compared. Moreover, for c_, the radiuses of the small areas were 1/16, 1/32, 1/64, 1/128, and 1/256 based on one degree of latitude and longitude. We let both methods configure circles and squares with the same area. If the radius of a circle is \(r\), the side length of the corresponding square is \(sl\), as shown in (4), where \(\pi\) is the ratio of the circumference of a circle to its diameter.  
\[sl\text{:=}\sqrt{\pi\times r^{2}} \tag{4}\]