# Bidirectional Sliding Window for Boundary Recognition of Pavement Construction Area Using GPS-RTK
## 3 Experiments
### Recognition of Pavement Construction Area Boundary
#### 3.3.2 Recognition of Curved Polygon Pavement Construction Area Boundary  
The three types of curved polygons PCA boundary shown in Figure 1d-f are all composed of straight line segments and curved line segments, and the method of identifying straight line segments was explained in Section 3.3.1. Identifying a curved line segment in the PCA boundary enables the recognition of that boundary. We designed two curves along the road with curvature radii of 70 to 300 m as mentioned in Section 1 and then added the GPS-RTK measurement errors as mentioned in Section 3.2. Then, we sampled the two curves to simulate the data acquired by GPS-RTK, as shown in Figure 11.  
Figure 11: Curved polygon PCA boundary to be recognized.  
Figure 10: (**a**) Recognition of the straight polygon PCA boundary; (**b**) Bias between the acquired data and corresponding point data on the fitted function.  
Figure 12 shows the PIP detected by the BSW algorithm and the fitting error across 10 experiments with window widths of 10, 13 and 15 respectively. Figure 12a,d,g show PIP detection and curve fitting. Specifically, blue dots indicate the obtained data, black stars and blue circles represent PIP detected by SWC and SWA respectively, and the red curve is the fitted curve. Figure 12b,e,h and Figure 12c,f,i indicate the deviation between the data points on the two curves to be fitted and the actual deviation under different window sizes. From Figure 12, it can be seen that the larger the window size, the more PIP, and the larger the error of the fitted curve on both sides. Therefore, the size of the sliding window should be set as narrow as is possible whilst allowing the algorithm to effectively detect the PIP.  
However, when the window was too small, the algorithm could recognize some of the PIP, as is shown in Figure 13a. Figure 13b shows the determination coefficient of the sliding window at each point and we can see that the small amplitude fluctuation of the determination coefficients greatly affected PIP identification; that is, PIP was extremely sensitive to fluctuations in the determination coefficients, which must be avoided. Therefore, it is extremely important to set the SW at an appropriate width.  
Figure 12: Curved quadrilaterals PCA boundaries under different window sizes. PIP detection with window widths of 10 (**a**), 13 (**d**), 15 (**g**), respectively; deviation of boundary_1 under 10 experiments with window widths of 10 (**b**), 13 (**e**), 15 (**h**), respectively; and deviation of boundary_2 under 10 experiments with window widths of 10 (**c**), 13 (**f**), 15 (**i**), respectively.  
We used Algorithm 1, mentioned above, for experimental verification, as shown in Figure 14a,b. Although there were some misdetected PIP, PIP detection was no longer sensitive to fluctuations of determination coefficients. Due to the randomness of the measurement error, we conducted 50 experiments and plotted the bias between the acquired data and the fitted data. As shown in Figure 14c,d, the RP fitting effect over the middle section of the curve was good, almost reaching GPS-RTK single-point positioning accuracy; the PIP fitting effect of the two sides of the curve was slightly worse, but accuracy was at worst to the 0.1 m level.  
Figure 14: PIP detection (**a**); determination coefficient of the sliding window at each point and the set threshold 0.85 (red), 0.9 (black), 0.95 (green) (**b**); and bias between the acquired data and corresponding point data on the curve (**c**,**d**).  
Figure 13: PIP detection with window width of 3; (**a**) Effects on PIP detection; (**b**) Determination coefficient of the sliding window at each point and the set threshold 0.85 (red), 0.9 (black), 0.95 (green).