# Trajectory Clustering for Air Traffic Categorisation

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. Methodology

- Building flight trajectories (Section 3.1). Trajectories are derived by sourcing the messages of the flights belonging to the geographic area and time period of interest, containing the information on the origin and destination (OD) of flights.
- Introduction of data mining techniques this study relies on (Section 3.2):
- -
- The DBSCAN algorithm to cluster the trajectories between ODs (Section 3.2.1);
- -
- Pearson’s ${\chi}^{2}$ test to analyse the impact of a set of variables on distribution of trajectories into clusters (Section 3.2.2).

- Clustering on all OD pairs (Section 4). The application of the DBSCAN algorithm to all data produces biased results because it appears that some OD pairs are served by only one airline, or one type of aircraft, or one cost profile (and are not the same ODs for the three cases). However, airlines’ behaviour can be analysed only when some alternatives are possible. Therefore, we conclude that each analysis (i.e., trajectory clustering in relation to airlines, aircraft types, cost profiles) needs to be applied on tailored data sub-sets, where ODs that have only one value of the variable under consideration are not included.
- Clustering on specific OD pairs (Section 5). Data sub-sets for each analysis are created and all results are described.

#### 3.1. Trajectory Preparation

#### 3.1.1. Data Filtering

- with the callsign not matching the regular expression$$\u02c6[\mathsf{A}-\mathsf{Z}]\left\{3\right\}[0-9]\{1,4\}[\mathsf{A}-\mathsf{Z}]\{0,2\}\$$$
- where the first three letters of the callsign represent an airline that is not a scheduled carrier (e.g., a 3-letter code AWC belongs to Titan Airways, which is a charter airline, so all their trajectories are excluded) – the list of airlines was obtained from EUROCONTROL’s Demand Data Repository additional data sets,

- low profile: all low-cost carrier flights;
- high profile: all full-service carrier flights into a hub airport, and regional flights into a hub airport;
- base profile: all other flights.

#### 3.1.2. Trajectory Creation

#### 3.2. Applied Techniques

#### 3.2.1. DBSCAN

#### 3.2.2. Pearson’s ${\chi}^{2}$ Test

## 4. Initial Analyses

#### 4.1. Initial Data Inspection

#### 4.2. Clustering Characteristics

## 5. Results of Variables’ Relations Analyses

#### 5.1. Relation between Clusters and Airlines

- the OD pairs served by only one airline;
- the OD pairs with less than 30 flights;
- and, for each OD, flights by an airline that had less than 30 flights in the season between that OD.

#### 5.2. Relation between Clusters and Aircraft Types

- the OD pairs served by only one aircraft type;
- the OD pairs with less than 30 flights;
- and, for each OD, flights by an aircraft type that had less than 30 flights in the season between that OD,

#### 5.3. Relation between Clusters and the Cost Profile

- the OD pairs with one cost type;
- the OD pairs with less than 30 flights.

## 6. Conclusions

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## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ACI | Airports Council International |

ADS-B | Automatic Dependent Surveillance-Broadcast |

DBSCAN | Density-Based Spatial Clustering of Applications with Noise |

ECAC | European Civil Aviation Conference |

GCD | Great-Circle Distance |

MTOW | Maximum Take-off Weight |

OD | Origin-Destination |

TMA | Terminal Manoeuvring Area |

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**Figure 4.**Relation between the GCD between ODs and number of flights, number of clusters and number of airlines. (

**a**) GCD vs. number of flights; (

**b**) GCD vs. number of clusters; (

**c**) GCD vs. number of airlines.

**Figure 5.**Relations between the aircraft type, clusters and GCD. (

**a**) Aircraft type vs. GCD length; (

**b**) Aircraft type vs. trajectory cluster.

**Figure 6.**Relations between the flight cost profile, number of clusters and GCD between the ODs. (

**a**) ODs with one cost profile; (

**b**) ODs with two cost profiles.

**Figure 7.**Depiction of the dependence between the airlines and trajectory clusters, and their distribution across number of flights and GCD between ODs. (

**a**) number of clusters vs. number of airlines; (

**b**) number of flights vs. number of airlines; (

**c**) GCD vs. number of airlines; (

**d**) GCD vs. number of airlines, scatterplot.

**Figure 8.**Distribution of GCD for Not dependent, one cluster ODs, and an example of Not dependent, multiple clusters for an OD. (

**a**) Distribution of GCD for OD pairs with one trajectory cluster; (

**b**) trajectory clusters between Brussels and Barcelona.

**Figure 9.**Trajectories, clusters and distribution of trajectories between airlines serving Milan Malpensa and Bari OD. (

**a**) Cluster 0 (blue) and cluster 1 (red) trajectories; (

**b**) Airline 1 (red) and Airline 2 (blue) trajectories.

**Figure 10.**Depiction of the dependence between the aircraft types and trajectory clusters, and their distribution across number of flights and GCD between ODs. (

**a**) No. of OD pairs vs. number of aircraft types; (

**b**) GCD vs. number of aircraft types; (

**c**) number of clusters vs. number of aircraft types; (

**d**) number of flights vs. number of aircraft types.

**Figure 11.**Depiction of the dependence between the cost types and trajectory clusters, and their distribution across number of flights and GCD between ODs. (

**a**) number of OD pairs with one or two cost types, showing dependence; (

**b**) GCD vs. number of cost types; (

**c**) cost types vs. number of clusters; (

**d**) cost types vs. number of flights.

Cluster | ||||
---|---|---|---|---|

Airline | 0 | 1 | 2 | 3 |

Airline 1 | 0 | 4 | 0 | 169 |

Airline 2 | 198 | 12 | 3 | 0 |

Cluster | ||
---|---|---|

Airline | 0 | 1 |

Airline 1 | 20 | 346 |

Airline 2 | 118 | 2 |

**Table 3.**Contingency table for Madrid–London Gatwick OD pair, showing the distribution of trajectories across airlines, cost type and clusters.

Cluster | |||
---|---|---|---|

Airline | Cost Type | 0 | 1 |

Airline 1 | Low | 105 | 161 |

Airline 2 | High | 154 | 1 |

Airline 3 | High | 176 | 6 |

Airline 4 | High | 176 | 0 |

Aircraft Type | |||
---|---|---|---|

Airline | A | B | C |

Airline 1 | 187 | 64 | 0 |

Airline 2 | 0 | 0 | 144 |

Airline 3 | 0 | 176 | 0 |

Airline 4 | 0 | 0 | 164 |

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**MDPI and ACS Style**

Bolić, T.; Castelli, L.; De Lorenzo, A.; Vascotto, F. Trajectory Clustering for Air Traffic Categorisation. *Aerospace* **2022**, *9*, 227.
https://doi.org/10.3390/aerospace9050227

**AMA Style**

Bolić T, Castelli L, De Lorenzo A, Vascotto F. Trajectory Clustering for Air Traffic Categorisation. *Aerospace*. 2022; 9(5):227.
https://doi.org/10.3390/aerospace9050227

**Chicago/Turabian Style**

Bolić, Tatjana, Lorenzo Castelli, Andrea De Lorenzo, and Fulvio Vascotto. 2022. "Trajectory Clustering for Air Traffic Categorisation" *Aerospace* 9, no. 5: 227.
https://doi.org/10.3390/aerospace9050227