# A Method for Managing ADS-B Data Based on a 4D Airspace-Temporal Grid (GeoSOT-AS)
## 6 Experiments and Results
### GeoSOT-AS Shape Change Law Analysis Test  
This section demonstrates the availability and consistency within a certain error of the Chinese domestic airspace and similar airspace regions under this segmentation framework; thus, it serves as one of the criteria for the rationality of the ADS-B data carrying framework. In this section, the 300 m stratification and the planar dimensional profile of the grid at the eighth level (~1 km level) were selected for two aspects of index analysis, and the airspace at typical representative locations in China, including the following six regions: the extreme locations of the north and south latitudes, and the airspace in the north, south, wide and deep areas where the airspace traffic and utilization rates in China are relatively dense, and the deformation law of the grid edge length and grid capacity, or the deformation law of the grid volume is calculated. The shape variation of the regional grid was analyzed. The variation pattern of grid edge length and grid volume for each location is shown below. Figure 10a shows the variation pattern of grid edge length with height layer, and Figure 10b shows the variation pattern of grid volume with height layer. Figure 9: Geographical distribution of data: (**a**) the distribution of planar latitude and longitude; (**b**) height range distribution; (**c**) time range distribution. From Figure 10, it was observed that the grid deformation in the same area varies less with altitude (i.e., in the spatial range of airspace \(<\)50,000 m, the local airport and urban airspace grid can be approximated to a uniform scale size, which is suitable for unified airspace planning and zonal block management of ADS-B data with a local deformation rate of 0.8%). Alternatively, for longitudinal observation, the grid deformation ratio equation was set for different regions of China. The grid scale of the airspace at marker \(i\) was set to \(\mu_{i}\), the standard ratio parameter calculation selects the grid scale of GeoSOT-AS standard level 7, set to \(\mu_{norm}\); whereas the maximum deformation rate equation is expressed by Equation (10):  
\[S_{deflection}=\bigg{|}\frac{\mu_{i}-\mu_{norm}}{\mu_{i}+\mu_{norm}}\bigg{|}. \tag{10}\]  
Similarly, the deformation rate of the grid volume was expressed by Equation (11), the grid scale of the airspace at mark \(j\) is set to \(\sigma_{j}\), and the standard volume under the 300 m height layer is set to \(\sigma_{norm}\), which is the standard block volume calculated by the grid scale of the seventh level of GeoSOT-AS standard, and the deformation rate of the grid volume is expressed by Equation (11):  
\[V_{offset}=\bigg{|}\frac{\sigma_{j}-\sigma_{norm}}{\sigma_{j}+\sigma_{norm}} \bigg{|}. \tag{11}\]  
From the above formula, the base deformation rate analysis table was drawn (Table 6). As can be seen from the above table, in the airspace of important locations in China, and at the same latitudes, the maximum GeoSOT-AS grid edge length scale is at around 16% deformation, whereas the maximum grid volume offset rate is 31.9%, within a certain management error range. There is no obvious conflict between this degree of deformation \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Grid Scale (km)**} & **Max Deflection** & \multirow{2}{*}{**Volume ( \(\times 10^{7}\) m\({}^{3}\))**} & **Volume Change** \\  & & **Rate** & & **Rate** \\ \hline Harbin & 0.667 & 0.164 & 13.347 & 0.319 \\ Beijing & 0.727 & 0.121 & 15.856 & 0.239 \\ Shanghai & 0.802 & 0.073 & 19.296 & 0.145 \\ Guangzhou & 0.861 & 0.037 & 22.239 & 0.075 \\ Shenzhen & 0.865 & 0.035 & 22.447 & 0.070 \\ Haikou & 0.879 & 0.027 & 23.180 & 0.054 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Maximum deformation rate analysis. Figure 10: Analysis of shape change law with height: (**a**) grid scale variation; (**b**) capacity variation. rate and volume offset rate, and the actual use under the framework of the four-dimensional spatiotemporal grid of this airspace for the actual ADS-B data.