Read the note on the flight trajectory analysis of the terminal area based on spectral clustering

I. Preface

As the related visualization project progresses to the clustering algorithm part of flight trajectory, some related papers are read and some abstracts are made.

Both the source of the paper and the Chinese network will be affirmed.

Two. Source of papers

Analysis of flight trajectory in terminal area based on spectral clustering

Ma Yong, Hu Minghua, Gu Xin, Yuanli Gang
(School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Jiangsu 210016)

Aeronautical computing Technology, Volume 45th, 5th, September 2015

Three. Paper notes

　　

1. Abstract: In order to realize intelligent processing of massive flight data and describe the operation characteristics of terminal area, the flight trajectory analysis method based on spectral clustering is studied. Based on the analysis of flight characteristics in terminal area, a method for calculating the similarity of Euclidean distance trajectory based on heading factor correction is proposed. The Gaussian kernel function is used to smooth the noise reduction of the similarity matrix, and the automatic selection of the scale parameters in the function is realized. An improved spectral clustering algorithm is used to classify the flight trajectory of the terminal area.

2. Core: Flight, trajectory, clustering, spectral clustering algorithm

3. Thought notes

3.1 Trajectory is composed of discrete points, the trajectory of a single flight as the basic unit of the cluster, according to the similarity between different trajectories

3.2 The radar data preprocessing, screening, select the trajectory set, and trajectory of the track set length, each track time normalization [0,1]

3.3 Two trajectories point-to-points to calculate the isometric distance, and the mean value to measure the Euclidean distance similarity between the trajectories.

3.4 to two traces TI,TJ, point pairs as follows, similarity Sij = Sji, calculation formula is

　　　　

　　　　

D (x) is the variance, δ represents the correction of the course to two trace similarity (the paper represents two traces in the distance of 1 n mile, but the angle is greater than 10 ° of the number of points), based on the calculation of the difference matrix S

　　　　

　　　　　

3.5* affinity Matrix, Gaussian noise reduction ( parameter selection )

3.6 K-means clustering based on affinity Matrix, 2 parameters, affinity matrix A, number of clusters K

A) calculates the sum of the rows in a, constructs a diagonal matrix D, i.e.

　　　　　　　　

Then construct the canonical affinity matrix L

　　　　　　　　

b) the characteristic vector structure matrix of the first k large eigenvalues corresponding to VNXK

c) v normalized to the unit matrix Z

　　　　　　　　

d) each row in Z is clustered as a point K-means (the trajectories in the track set T are divided into different classes based on the clustering result. When line I in Z is divided into Class C, the track set T is also divided into Class C accordingly.

3.7 Matrix L Eigenvalue distribution can be determined K (for the 1th step of the algorithm to find the matrix L, if the finite data set exists K ideal separation of each other cluster, then L of the first k large eigenvalues of 1, K + 1 eigenvalues are strictly less than 1)

Four. Presentation of paper results

Taking the flight data of Guangzhou Baiyun Airport terminal area on March 8, 2014 as an example, the above algorithm is used to cluster.

Trajectory data preprocessing time interval 0.01s, each track 101 points constitute a point sequence description.

Considering that the entry and departure fields have 8 and 5 entry and departure programs respectively, choose the number of clusters to enter k = 8, the number of off-field clustering k = 5. According to the above parameters, using the improved K-means algorithm proposed in the previous section to cluster the selected first K eigenvectors, the 455 original entry flight trajectories are divided into 8 classes, 439 of the original flight trajectories are divided into 5 classes, and the clustering Results 1 and Figure 2 are shown. The graph shows that the algorithm realizes the clear division of all the tracks in the terminal area, and each classification result can accurately describe the characteristics of each type of flight trajectory.

　　

　　

　　

　　

　　

　　

　　

Read the note on the flight trajectory analysis of the terminal area based on spectral clustering