## 3 Results and Discussion
### Impact of Network Dimension on Positioning Performance  
For the \"3+1+1\" configuration, the dimensions relate to the distance between the seafloor base stations and the height of the subsurface buoy. The EPGs of different dimensions can be scattered or concentrated in the underwater space. We need to analyze the impact of the seafloor base station distance and subsurface buoy height on the user positioning range, available station number, and positioning accuracy. Figure 3a shows the EPG values with various available stations in the \"3+1+1\" network configuration. We defined EPGs with 3, 4, and 5 available station numbers as EPG\({}_{\text{ASN}=3}\), EPG\({}_{\text{ASN}=4}\), and EPG\({}_{\text{ASN}=5}\), respectively. For the convenience of comparison, we also expressed EPGs with 0, 1, and 2 available station numbers as EPG\({}_{\text{ASN}=0}\), EPG\({}_{\text{ASN}=1}\), and EPG\({}_{\text{ASN}=2}\), respectively. From Figure 3a, in general, the seafloor base station distance has a much greater impact on the EPG with different available station numbers than the subsurface buoy height. When the height was constant, EPG\({}_{\text{ASN}=0}\) decreased with the increase in distance; when the distance was 13-19 km, EPG\({}_{\text{ASN}=0}\) tended to be stable. However, EPG\({}_{\text{ASN}=0}\) gradually increased when the distance was greater than 19 km. Due to the limited acoustic positioning range (10 km), there were always grid points with unavailable base stations. EPG\({}_{\text{ASN}=1}\) increased with the distance at first; when the distance was close to 11 km, EPG\({}_{\text{ASN}=1}\) was stable; when the distance was greater than 19 km, EPG\({}_{\text{ASN}=1}\) showed a decreasing trend. EPG\({}_{\text{ASN}=2}\) was significantly lower than the others, and EPG\({}_{\text{ASN}=2}\) began to increase when the distance was greater than 19 km. EPG\({}_{\text{ASN}=3}\) increased with the distance at first; when the distance approached 19 km, EPG\({}_{\text{ASN}=4}\) reached the maximum value and then decreased. EPG\({}_{\text{ASN}=4}\) was similar to EPG\({}_{\text{ASN}=3}\), while the maximum value of EPG\({}_{\text{ASN}=4}\) occurred when the distance was close to 11 km, and EPG\({}_{\text{ASN}=4}\) disappeared with distances greater than 19 km. EPG\({}_{\text{ASN}=5}\) showed a downward trend with the distance. When the distance was greater than 17 km, the distance between the seafloor base stations exceeded the maximum acoustic range (10 km), and user positioning with five stations was no longer possible. Figure 3b shows the average, standard deviation, and maximum values of PDOP. PDOP was inversely proportional to the geometric structure formed by the user and stations, and the user positioning accuracy based on the network configuration was affected by the seafloor base station distance and the subsurface buoy height. After the removal of outliers with the IQR criterion, most PDOP values were less than 30, except for when the height was above 2.5 km. We found that PDOP outliers appeared when users were located near the seafloor base stations. Moreover, when the height was lower than 1.5 km, the PDOP value changed slowly with the seafloor base station distance. When the distance increased from 7 km to 9 km, the variation of PDOP was obvious. Since the subsurface buoy height had little impact on EPG, we investigated the spatial distribution of the EPG with the fixed subsurface buoy height and various seafloor base station distances (Figure 3c,d). The height was fixed at 2.9 km, and the distances were 7 km and 9 km, respectively. In both scenarios, grids with five available stations covered the station array, and grids with three and four available stations were outside the station array. It is obvious that they were all within a circle in the plane, and the radius was approximately 10 km. Because the subsurface buoy and surface buoy were above the horizontal center of the seafloor base station array, grids with at least three available base stations were widely distributed.