# A Method for Managing ADS-B Data Based on a 4D Airspace-Temporal Grid (GeoSOT-AS)
## 6 Experiments and Results
### Fixed-Time Temporal Range Indexing  
A randomly selected time period of interest \"2020-04-26 00:00:00\"-\"2020-04-26 24:00:00\" was selected for the whole day, and Table 9 displays the specific information regarding the spatial extent of interest. Each set of data in the table forms a cube that encloses a box. The objective is to test the average efficiency of spatiotemporal filtering queries.  
According to different data volume--20%, 40%, 60%, 80%, and 100%--the efficiency of spatiotemporal indexes constructed in three ways was tested. First, MongoDB's own spatial index based on latitude and longitude was used, plus time dimension and data id to construct a composite spatiotemporal index. Second was MongoDB's 2 dsphere spatial index, plus time dimension and data id to build composite spatiotemporal index. The third way was the use of a spatiotemporal index based on space-time grid encoding as index primary key. The three methods are named as LLHT index, 2 dsHT index, and GeoSOT-AS code index, accordingly. Take the first row of data as an example to introduce the three different forms of indexing, which is detailed in Appendix A. Experimental results are shown in Table 10.  
From the efficiency test results in Figure 11, it was found that the response time of spatiotemporal query increased when the data volume of each index increased. The first type of composite spatiotemporal index was constructed by LLHT index, which is a spatial latitude and longitude index with height and time dimensions. The spatiotemporal query efficiency is good when the data volume is <20%, and the query time is limited to 100 ms; however, as the data volume increases, the index gradually shows its disadvantage, and the query is abnormally slow, reaching 1000 ms at its slowest. The second 2 dsHT index, a composite spatiotemporal index constructed by using 2 dsphere spatial index plus height dimension and time dimension, was found to be more efficient under different data volumes, but the efficiency of this index decreases slightly as the data volume increases; however, it is more efficient than the first way of construction, improving the average index speed by 77%. The third type of GeoSOT-AS code index, based on spatiotemporal grid coding, has comparable efficiency to the first two methods when the data volume is small because it takes a relatively fixed period of time to match the spatial blocks; however, as  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Data** & \multirow{2}{*}{**LLHT Index (ms)**} & \multirow{2}{*}{**2 dsHT Index (ms)**} & \multicolumn{3}{c}{**GeSOT-AS Code**} \\
**Amount** & & & & & **Index (ms)** & \\ \hline  & Fetch time & Index time & Fetch time & Index time & Fetch time & Index time \\
20\% & 21.8 & 127.6 & 8.4 & 45.4 & 1.2 & 8.2 \\
40\% & 42.0 & 353.0 & 12.6 & 82.4 & 1.8 & 19.8 \\
60\% & 77.6 & 501.6 & 16.8 & 110.0 & 2.2 & 24.4 \\
80\% & 124.6 & 754.4 & 23.0 & 167.6 & 2.4 & 27.4 \\
100\% & 138.2 & 927.8 & 34.8 & 192.2 & 3.0 & 30.6 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Comparison table of index query time under different methods.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Lower Left Corner Coordinates** & **Upper Right Corner Coordinates** & **Height Range** \\ \hline (118.193828\({}^{\circ}\) E, 24.49224\({}^{\circ}\) N) & (119.19387\({}^{\circ}\) E, 24.702114\({}^{\circ}\) N) & 0.0–9.6 km \\ \hline (11.849844\({}^{\circ}\) E, 44.002925\({}^{\circ}\) N) & (11.997022\({}^{\circ}\) E, 44.109069\  
the data volume increases, the index constructed by this approach is more efficient than the other two when dealing with spatiotemporal queries above the full data volume, improving the average region information extraction time to 81%.