## 5 Validation Results and Analysis
### Air-Ground NLOS Identification Based on Ray Intersection Detection
As shown in the figure, the number of visible cooperative members of the traditional angle-only method is less than that of the proposed method, which suggests that the traditional angle-only method may misidentify the visible signals of nearby cooperative members as nonvisible and separate them. To further verify and analyze the visibility of unmanned vehicle 1, radar maps of the surrounding 3D environment and visibility range of unmanned vehicle 1 at simulation times of 450 were generated, as shown in Figure 20.  
Figure 16: Azimuth of each member relative to unmanned vehicle 1. Figure 17: Distance of each air–ground member relative to unmanned vehicle 1. Figure 18: Number of satellites visible to unmanned vehicle 1. Figures 18 and 20 show that at 450 s of simulation, UGV1 has one visible member, UGV3, which is judged correctly by the visibility analysis method in this paper, but UGV3 is within the terrain cover range, which leads to its mistaken separation by the traditional pure angle visibility analysis method. The visible distance, true distance, and visible judgment moments of UGV2 and UGV3 relative to UGV1 during the simulation are shown in Figures 21 and 22. The localization errors of unmanned vehicle 1 in a complex terrain environment under different cooperative methods are shown in Figure 23.  
First, we study the case of a small number of reference members, where only one reference member unmanned vehicle 2 supports unmanned vehicle 1. Figure 23 shows the position error of UGV1 among different methods. The root-mean-square error of localization is 13.15 m before cooperation, 9.96 m for the method without identifying NLOS signals, 13.41 m for the angle-based method, and 8.12 m for the range/angle-based method. The cooperative localization method without NLOS identification improves the localization accuracy by 24.2%, the traditional angle-based NLOS identification method by \(-\)2.0%, and the range/angle-based method by 38.3%. Unmanned vehicle 1's localization error diverges at 400-480 s and 700-780 s of simulation with less than four satellites (satellite navigation limited) before co-navigation. This is because small robots are usually equipped with low-cost MEMS, whose errors will diverge without reference information. If UGV2 performs cooperative navigation for UGV 1 without NLOS identification, UGV 1 suffers NLOS errors during 20-80, 150-280 and 370-500 s. When the traditional angle-only NLOS identification method is used to co-navigate unmanned vehicle 1, unmanned vehicle 1 is not affected by NLOS error; however, because the traditional angle-only method mistakenly separates the LOS signals of UGV2, the localization error of unmanned vehicle 1 still diverges during 500-530 and 700-800 s, causing no improvement under cooperative navigation. If the proposed NLOS identification method is used for the cooperative navigation of unmanned vehicle 1, the NLOS error of unmanned vehicle 1 is suppressed, the LOS signal of the visible member is preserved, and the localization accuracy of the unmanned vehicle 1 is higher during 500-530 and 700-800 s.  
Then, we study the case of five reference members supporting UGV1. Figure 24 shows that the root-mean-square error of localization varies among the different methods, which is 13.15 m before cooperation, 9.60 m for the method without identifying NLOS signals,  
Figure 23: Localization error under one reference member. Figure 10:0 UGV3 visibility, true distance to UGV1. 3.69 m for the angle-based method, and 0.96 m for the range/angle-based method. The cooperative localization method without NLOS identification improves the localization accuracy by 27.0%, the angle-based method by 71.9%, and the range/angle-based method by 92.7%. Combining Figures 19 and 23, unmanned vehicle 1's inertial navigation system localization error diverges at 400-480 s and 700-780 s of simulation with less than four satellites (satellite navigation limited) before co-navigation, and the localization error is the largest among the four methods.