# Air Traffic Trajectory Operation Mode Mining Based on Clustering
## 4 Simulation  
### Experimental Design  
After modifying and reconstructing the sample set in a single track, AE was used to reconstruct it as a whole. The track correction method described in Sections 2.1 and 2.2 was used to correct the track sample set of Baiyun Airport, and after removing the seriously damaged invalid tracks, there were 1263 remaining tracks in the sample set. When establishing the clustering model, due to the relatively fixed operation mode in the terminal area and strong overall regularity, a large number of samples was not required. At the same time, to verify the feasibility of the algorithm, it was necessary to horizontally compare the models measured by DTW. To avoid time consumption, 10% of the tracks will be randomly selected for the analysis of typical operation modes.  
Firstly, the sample set used by OFAE was constructed. The input of the autoencoder is required to be a matrix with fixed dimensions, so the track samples cannot be directly used as input and need to be isometric. The previous reconstruction fills in the vacancy value of the timestamp, which is essentially an up-sampling, but in fact, the too-long sequence  
Figure 9: The flow chart of the algorithm.  
is not friendly to the autoencoder, so it was necessary to carry out down-sampling. The length of the sequence was limited to 100, that is, each track contained 100 track points, and the characteristics of the track points are as follows:  
\[P_{t}=(x,y,z,v_{H},v_{V},\sin\theta,\cos\theta) \tag{23}\]  
where \(x,y,z\) are the three-dimensional position coordinates of the aircraft. For the horizontal speed, \(v_{H}\), and vertical speed, \(v_{V}\), of the aircraft, the timestamp information of the original track was lost in the process of up- and down-sampling, so the differential term was introduced to describe the instantaneous state of the aircraft. Using \(\theta\) as the heading, it can describe the instantaneous motion state of the aircraft as the speed. Here, the sine and cosine value was used instead of the angle itself. The sine and cosine value of the heading combined with the speed can directly reflect the position change, but the angle value has no actual physical significance.  
The \(i\)th track in the clustering sample set is expressed as: \(\textit{Trail}_{i}=\left\{P_{1},P_{2},\ldots,P_{100}\right\}\), with 700 dimensions in total, and then the dimension of the sample matrix to be compressed was 126 \(\times\) 700. The numerical normalization was carried out according to the column, the information matrix, \(L\), was obtained after use of the autoencoder and compression, and the reconstructed sample set, \(\hat{X}\), was obtained after decoding the information matrix. The comparison effect of the two is shown in Figure 10, in which the green line on the left is the reconstructed track and the blue line on the right is the original trajectory.  
Observing the general form before and after reconstruction in Figure 10, it can be seen that OFAE has a good anomaly detection ability, which can remove the deviated track that is difficult to classify into a specific mode, and better maintain the overall situation of other normal tracks.  
In Figure 11A, there are many scattered abnormal tracks in the red wireframe area of the original track. Although these tracks may also come from the real operation, they cannot be clustered due to their extremely low frequency. They are noise to the clustering model, so they need to be identified and eliminated during reconstruction.  
Figure 11B shows the horizontal projection of the reconstructed trajectory set. It can be clearly seen that the scattered trajectory of the red dotted box in the original trajectory is eliminated under the constraint of one norm between groups. At the same time, the constraint of two norms within the group also makes the reconstructed trajectory more condensed in clusters with low density.  
Figure 10: Reconstruction of the sample set comparison.