# Extracting aircraft conflict-resolution situations from historical ADS-B data

Kim Gaume, Xavier Olive, David Gianazza, Richard Alligier, Nicolas Durand

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## To cite this version:

Kim Gaume, Xavier Olive, David Gianazza, Richard Alligier, Nicolas Durand. Extracting aircraft conflict-resolution situations from historical ADS-B data. Transportation Research Interdisciplinary Perspectives, 2025, 34, pp.101669. 10.1016/j.trip.2025.101669. hal-05364285

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# Extracting aircraft conflict-resolution situations from historical ADS-B data

Kim Gaume<sup>a,b,*</sup>, Xavier Olive<sup>a,b</sup>, David Gianazza<sup>a</sup>, Richard Alligier<sup>a</sup>, Nicolas Durand<sup>a</sup>

## ARTICLE INFO

### Keywords:

Deconfliction

Information extraction

ADS-B

Regression

## ABSTRACT

Existing conflict resolution models are often based on theoretical frameworks that, while providing optimal solutions under specific criteria, may not fully align with real-world controller decision-making practices. This gap between model predictions and actual behaviour can lead to low acceptance of automated tools. Understanding how controllers resolve conflicts in daily operations could help design assistance tools that generate advisories more likely to be accepted and integrated into their workflow. This study introduces a data-driven methodology for identifying and cataloguing air traffic deconfliction instances using historical ADS-B data. By analysing trajectory deviations and their impact on predicted aircraft separations, we extract instances of deconfliction and encode them into a structured dataset. This dataset captures key elements of each event, including sector information, deviated aircraft details, predicted non-deviated trajectories, and surrounding traffic conditions. Our approach facilitates large-scale analysis of air traffic control decision-making, providing a foundation for developing conflict resolution models that better reflect operational practices. This paper details the methodology and process used to construct this dataset.

## 1. Introduction

The safety of aircraft in the upper airspace is based on the respect of safety distances set at 5 NM (Nautical Miles) laterally and 1000 ft (ft) vertically. A violation of these two constraints results in a loss of separation. One of the key responsibilities of air traffic controllers is to anticipate future risks of loss of separation, known as conflicts, and issue appropriate instructions to adjust flight trajectories and ensure adequate separation. Currently, controllers primarily rely on their training and experience to detect and address these situations. However, increased complexity demands quicker and more precise decision-making, putting additional strain on operators. To mitigate this burden, automated conflict detection and resolution tools aim to identify potential conflicts and suggest optimal resolutions.

However, the implementation of these tools faces an acceptability challenge, as they can only be effective if controllers are willing to use them. To become part of standard air traffic control practice, the tools must earn the users' trust. This largely depends on how well they align with the standard cognitive processes of the human operators, as controllers are more likely to use a tool that integrates seamlessly into their workflow without requiring drastic changes to their established practices. Decision-support tools must assist rather

than disrupt the natural decision-making processes of the controllers. While deconflicting traffic, controllers have to deal with a variety of uncertainties, which can be connected to the wind, aircraft speed, pilot reaction times and other external factors. The way these uncertainties are perceived and dealt with not only depends on the context but also on each individual controller's internal state and personal habits and preferences. Failure to take these factors into consideration will inevitably affect the performance and acceptance of the tools.

Calibrating conflict resolution tools to make their proposed solutions acceptable to human controllers requires examples of deconflictions performed by controllers, from which one could extract uncertainty models and deconfliction practices. Our work aims at providing such a dataset of conflict resolutions.

In this paper, we extract deconfliction instances from recorded trajectory and flight plan data, considering portions of trajectories that deviate significantly from their original flight plan. Not all of these deviations are actually related to deconfliction actions (some of them might be caused by weather events, for example). We propose two heuristics to extract deconfliction situations from trajectory data, one based on a fixed threshold on the predicted separation between deviated aircraft and surrounding traffic, and the other based on a variable

<footnote><sup>a</sup> Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse, 7 avenue Édouard Belin, 31055 Toulouse, France</footnote>

<footnote><sup>b</sup> ONERA – DTIS, Université de Toulouse, 2 avenue Marc Pélegrin, 31055 Toulouse, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: kim.gaume@onera.fr (K. Gaume), xavier.olive@onera.fr (X. Olive), david.gianazza@enac.fr (D. Gianazza), richard.alligier@enac.fr (R. Alligier), nicolas.durand@enac.fr (N. Durand).</footnote>

<footnote n="1">¹ Time to CPA: considering the deviated aircraft and another aircraft in its neighbourhood, the *time to CPA* is the time between the start of deviation and the time when both aircraft reach their closest positions (closest point of approach).</footnote>
separation threshold depending on the time to the Closest Point of Approach.¹ Both heuristics also use the duration of the deviation from planned route and a threshold on the time to CPA to filter out irrelevant traffic instances.

KNN-median regression and quantile regression allow us to deter-
mine the values of the heuristics' thresholds. The rationale is that
lateral deviations not related to deconfliction actions are equally likely
to decrease or increase distance to neighbouring aircraft, resulting
in median values close to zero. Conversely, lateral deviations due to
deconfliction are expected to increase this distance, showing strictly
positive median values.

These ideas have already been explored in our previous works,
to determine a unique approximate threshold (Gaume et al., 2023)
based on the closest neighbour of the deviated aircraft and using KNN-
median regression, or to explore small deviations (Gaume et al., 2024)
and distinguish routine turns from small turns aiming at deconflicting
traffic. We now consider all neighbouring traffic, with potentially sev-
eral conflicting aircraft, and introduce an additional heuristic where
separation thresholds vary with the time to CPA and are automatically
extracted from the data using linear quantile regression.

A catalogue of conflict resolution situations is built using the pro-
posed heuristics and made available to the scientific community. The
current version of the dataset is on a shared folder http://bit.ly/
4jaF45R. This work is performed using a historical database from the
OpenSky Network, covering the twelve AIRAC cycles ranging from Jan-
uary 27 to December 29, 2022 in the Air Control Centre of Bordeaux,
France.

This paper is structured as follows. Section 2 reviews the context of our work and related developments. Section 3 presents the methodology underlying our analysis. Section 4 describes the input dataset and the exploration carried out to identify potential deconfliction manoeuvres. Section 5 summarizes the parameters of the heuristics used for extraction, and provides an overview and first validation of the resulting catalogue. Finally, Section 6 concludes the paper and outlines perspectives for future work.

## 2. Context and literature review

Solving air traffic conflicts requires conflict detection, which itself relies on the availability of accurate trajectory predictions. Prior work on trajectory prediction for conflict detection and resolution introduced a variety of models, including polygonal zones modelling the speed, time, and direction uncertainties of manoeuvred aircraft (Granger et al., 2001), probabilistic models of the predicted trajectory (Paielli and Erzberger, 1997; Prandini et al., 2000), confidence intervals (Chen et al., 2020), and specialized machine learning models for time-series data (Cheng et al., 2022).

Detecting conflicts can be done in different ways, depending on the
underlying trajectory model. In a probabilistic framework (Paielli and
Erzberger, 1997; Prandini et al., 2000), a probability of conflict is com-
puted from the probabilistic trajectory predictions, and conflicts can
be considered as critical beyond a certain probability threshold. When
using polygonal zones around nominal trajectory predictions (Granger
et al., 2001), conflicts are detected when the uncertainty zones come
closer than the standard separation. Some machine learning methods
bypass trajectory prediction entirely. For instance, in Pérez-Castán et al.
(2022), conflicts and critical scenarios are simulated by modifying
historical Automatic Dependent Surveillance-Broadcast (ADS-B) data
from the OpenSky Network, with machine learning employed to predict
conflicts among the extracted trajectories.

Concerning conflict resolution, several methods have been proposed
in the literature. For instance, in Pallottino et al. (2002), Cafieri and
Durand (2014), mixed-integer programming is applied to find opti-
mum conflict resolutions, without considering trajectory prediction
uncertainties. In Lehouillier et al. (2017), the conflict resolution prob-
lem is modelled as a minimum weight maximum clique problem and

solved with a mixed-integer linear programming method, without tak-
ing uncertainties into account. Other approaches, such as evolutionary
algorithms (Durand et al., 1996; Sathyan et al., 2017) or ant colony
optimization (Liu et al., 2018) do not guarantee the optimality of
the solutions, but can compute good solutions within a limited time
budget. They can also easily accommodate more realistic uncertainty
models. In Allignol et al. (2013), A constraint programming approach
is compared with an evolutionary algorithm, taking speed and lat-
eral uncertainties into account, using pre-computed lateral manoeuvre
combinations.

The above methods mostly address the conflict resolution problem as an optimization problem — find the shortest path to destination while avoiding conflicts — and heavily rely on mathematical modelling. Other works address human factors in conflict resolution, studying various aspects of the controllers' behaviour. In Rantanen and Nunes (2005), for example, the authors study the controller decision process and its implications in terms of workload. Other approaches try to capture the controller's internal state using neurophysiological indicators, with the aim to detect abnormalities and risk factors related to human operators (Arico et al., 2017). In addition, heuristic models have been developed to describe how controllers judge risk and detect conflicts, taking into account cognitive strategies and individual differences in decision-making (Stankovic et al., 2008).

Developing decision tools to provide solutions to conflict resolution problems raises acceptability issues. Human controllers are more likely to accept solutions that align with their own thought process (Hilburn et al., 2016; Vela et al., 2021). Consequently, they might be more prone to reject automated tools proposing solutions that do not align with their usual practices and internal representations.

In Gotteland et al. (2021), a genetic algorithm is used to learn the uncertainty parameters of the trajectory prediction, using datasets of examples of conflict resolutions. On artificial data with known uncertainties, this method was able to find the lateral and speed uncertainty parameters that were used to produce the data. It also showed promising results on small datasets of human-made resolutions obtained from real-time experiments. However, it has not yet been experimented on large real-life historical datasets of conflict resolutions, due to the unavailability of such data at present.

Several approaches have explored the possibility to use Machine
Learning to produce more realistic deconfliction suggestions. For ex-
ample, Tran et al. (2020) use a reinforcement learning method based
on deconflictions performed by real controllers on simulated conflicts,
whereas (Kim et al., 2021) uses imitation learning with the objective
to learn from deconfliction manoeuvres in historical data.

Other data-driven approaches focus on the manoeuvres issued by
the controllers, or their actions in general, using large real-life datasets
of past aircraft trajectories. This is the case for (Dang et al., 2021) which
uses unsupervised learning. Olive and Basora (2020) use an autoen-
coder architecture and analyse the distribution of reconstruction errors
to detect significant events and classify them based on their likelihood
of being related to deconfliction actions or other manoeuvres, such as
weather avoidance.

In Gaume et al. (2023), we made a first attempt at extracting
such a dataset of conflict resolution examples from historical ADS-B
and flight plan data. This previous study focused on persistent lateral
deviations from the intended route, and characterized them as resulting
from deconfliction actions when the closest predicted separation with
the neighbouring traffic fell below a certain threshold and when the
deviation resulted in an increased separation. A KNN-Median regres-
sion method allowed us to extract this threshold directly from the
data, which resulted in a value of 8 NM. Although the regulatory
minimum lateral separation in French upper airspace is 5 NM, our
analysis suggests that controllers apply an additional safety buffer to
account for uncertainties. Gaume et al. (2024) focused on small, non-
persistent lateral deviations from the intended route, and extended
our median analysis approach to other variables to identify which of
these deviations are just routine turns between successive segments of the route, and which ones might be more likely related to “direct-to” instructions issued by a controller to avoid a conflict.

This paper is based on open ADS-B historical data and flight plan data. Building on the previously introduced works, we describe a structured approach to building a catalogue of detected deconfliction situations using a successive threshold selection method. The goal of the resulting dataset is to enable the study of deconfliction patterns in air traffic control and provide real-life input data for training automated conflict models.

## 3. Methodology

The steps of our methodology are described here conceptually, and a case study based on these steps is detailed in Section 4. Let us start with an overview of the method, before going into more detail for each step. A summary of the notations introduced in this section can be found at the end of the paper.

### 3.1. Method overview

In order to extract deconfliction actions from recorded trajectory data, we start by collecting traffic situations in which the flight trajectory is not aligned with any waypoint of the planned route. Such non-alignments can have multiple causes: routine turns between successive route segments, persistent deviations due to meteorological events, lateral manoeuvres instructed by an air traffic controller, etc.

Our objective is to determine whether or not such an observed lateral deviation from the planned route is caused by a controller action in order to avoid a loss of separation with another flight. We are interested in extracting two types of deconfliction actions: persistent lateral deviations resulting from “turn left or right” instructions, and shorter deviations resulting from “direct-to” instructions. “Direct-to” instructions aim at avoiding a conflict with the neighbouring traffic by redirecting the flight towards another navaid of its flight plan. These situations can be difficult to distinguish from routine turns.

Extracting deconfliction actions (either “turn left/right” or “direct-to”) is particularly challenging in the absence of any labelled data concerning the controller actions on the traffic. We propose the following heuristic method to identify deconfliction actions:

1. for each deviated flight, compute trajectory prediction $\hat{A}$ assuming flight has not been deviated

2. for each neighbouring flight B, compute the following quantities:

* minimum distance $\hat{d}_{min}$ between predicted trajectory $\hat{A}$ of deviated flight and trajectory of B,

* minimum distance $d_{min}$ between actual trajectory A of deviated flight and trajectory of B.

3. identify the deviation as resulting from a deconfliction action if there is a neighbour for which (a) the proximity of the two aircraft would have represented a danger had the deviation not occurred (b) the observed deviation actually increases the separation (c) the time $t_{CPA}$ between the beginning of deviation and the closest point of approach (CPA) between the two flights is sufficiently long to be consistent with a deconfliction action. This can be formalized by the three following conditions:

(a) $\hat{d}_{min} < D$

(b) $d_{min} > \hat{d}_{min} + \epsilon$

(c) $t_{CPA} > T_{CPA}$

where $\epsilon$ and $T_{CPA}$ are chosen time thresholds, and $D$ is a chosen distance threshold.

The value of $D$ should be greater than the standard separation (5 NM in the upper airspace), to account for uncertainties on the future positions of both aircraft at the time the decision was taken to deviate one of them. We consider the two following conceptual choices for the distance threshold $D$:

* $D$ is a fixed threshold

* or $D = D(t_{CPA})$ is a variable threshold depending on time to CPA (closest point of approach)

The question arises as to what values to choose for $D$, $\epsilon$ and $T_{CPA}$ in the above heuristic method. We introduce a data-driven approach based on median regression to extract the threshold values (either fixed or variable) from large amounts of historical trajectory data. The basic idea of this approach is that a deconfliction action should result in an increased separation between conflicting trajectories, whereas lateral deviations that are not caused by deconfliction actions are as likely to decrease the separation as to increase it.

The quantity of interest in this approach is the separation increase or decrease, represented by the quantity $d_{min} - \hat{d}_{min}$. By considering a large number of observations and putting this quantity in relation with a chosen potential explanatory variable $x$, we can observe the evolution of the median value of $d_{min} - \hat{d}_{min}$ as a function of $x$. A median value of zero occurs when the number of observations for which $d_{min} - \hat{d}_{min} > 0$ (separation increase) equals the number of observations for which $d_{min} - \hat{d}_{min} < 0$ (separation decrease). By observing the median values of $d_{min} - \hat{d}_{min}$, we can identify sub-domains of $x$ where the median is strictly positive, thus indicating separation increases caused by voluntary deconfliction actions, and other sub-domains where this median is zero, characterizing lateral deviations unrelated to deconfliction actions.

Typically, in order to find a distance threshold $D$ allowing us to distinguish a deconfliction action when $\hat{d}_{min} < D$ from a lateral deviation not caused by a deconfliction action when $\hat{d}_{min} \ge D$, we observe the median value of the separation increase/decrease $d_{min} - \hat{d}_{min}$ as a function of the predicted separation $\hat{d}_{min}$ (see Fig. 6 for a case study on Bordeaux airspace). The threshold $D$ is then chosen as the limit between the sub-domain where the median values are strictly positive and the sub-domain where the median is zero. This reasoning can be extended to other variables than the predicted separation $\hat{d}_{min}$, and several variables can be combined (e.g. $\hat{d}_{min}$ and $t_{CPA}$) in order to determine variable thresholds, or to filter out routine turns from “direct-to” instructions.

The proposed approach to infer threshold values from data requires a median regression method. We apply a KNN median-regression method to plot the curve of the median as a function of $\hat{d}_{min}$ and visually determine the most adequate value for $D$, when assuming a fixed threshold. Quantile linear regression is used to automatically infer threshold values $D(t_{CPA})$ from the data for each quantile of $t_{CPA}$, when assuming variable thresholds depending on the conflict anticipation.

The heuristic method and threshold inference approach are detailed in the following sub-sections. The median regression methods are described in Sections 3.6.1 and 3.6.2.

### 3.2. Detection of lateral deviations

The first step is to identify trajectory segments where an aircraft deviates laterally from its planned route. Many deviations are routine and intentional (e.g. bypassing one or more navaids to shorten the route), and should not be confused with conflict-resolution manoeuvres. To detect candidate deconfliction manoeuvres, we therefore focus on deviations where the aircraft temporarily loses alignment with all navaids in its filed flight plan.

To minimize the detection of accidental alignments, we only consider navaids within a 200 NM radius that are aligned with the aircraft's track angle while allowing a maximum tolerance of 2 degrees. Given the paper's focus solely on lateral deviations, we minimize the risk of introducing a potential vertical component in deconfliction by exclusively extracting deviations where the aircraft maintains a stable altitude within a threshold of $\pm 50$ ft.
### 3.3. Counterfactual prediction

Consider a recorded trajectory A exhibiting a lateral deviation beginning at $t_1$ and ending at $t_2$. We analyse the trajectory from $t_1$ up to a maximum time horizon of $t_1 + \tau$, where $\tau = 20$ min. This horizon is adjusted if trajectory A exits the considered airspace before $t_1 + \tau$, or if a significant altitude change occurs.

Though we cannot know for sure what would have happened had the aircraft not been deviated, we approximate a “counterfactual” trajectory $\hat{A}$ that remains aligned with the original flight plan instead of being deviated at time $t_1$. Let $P_0 = (\varphi_0, \lambda_0, h_0)$ be the last recorded position just before $t_1$, with latitude $\varphi_0$, longitude $\lambda_0$, and altitude $h_0$. The ground speed $v_g$ is estimated as the average over a time window<fnref n="2" /> prior to $t_1$, and the vertical speed is set to zero so that the altitude remains constant at $h_0$.

We then build an ordered sequence of waypoints

$$Q = (P_0, N_1, N_2, \dots, N_m),$$

where $N_1$ is the navaid towards which the aircraft is flying just before being deviated at $t_1$, and $\{N_j = (\varphi_j, \lambda_j, h_0), j > 1\}$ are the subsequent navaids of the flight plan.

For each leg from $N_{j-1}$ to $N_j$, we compute the great-circle distance $d_j$ and the corresponding travel time $\frac{d_j}{v_g}$, so that times over waypoints propagate as $t_j = t_{j-1} + \frac{d_j}{v_g}$. Between $t_{j-1}$ and $t_j$, the horizontal position is interpolated at constant speed along the great-circle arc joining $N_{j-1}$ and $N_j$. Denoting by $P(t)$ this interpolated position, we also compute the associated ground track $\theta(t)$ as the forward azimuth of the arc. Turns are considered instantaneous at waypoints: $\theta(t)$ is allowed to jump at times $t_j$, while the speed remains constant.

The predicted trajectory beyond time $t_1$ – assuming the aircraft had not been deviated – is this sequence of points $P(t)$, that we interpolate at 1 Hz for consistency:

$$\hat{A}(Q, v_g) = \{ (P(t), \theta(t), h_0) : t_1 \le t \le \min(t_1 + \tau, t_{exit}) \}, \quad (1)$$

We illustrate this construction in Fig. 1, which shows a recorded trajectory A in solid blue when aligned with a navaid and in orange for the deviated segment, alongside its counterfactual continuation $\hat{A}$ (dashed grey) reconstructed from the flight plan. The last observed position $P_0$ before deviation and the successive navaids $N_1, N_2, \dots$ define the waypoint sequence Q used for interpolation.

This trajectory model is very simple, but we are only trying to approximate the projection made by the controller when considering a potential manoeuvre for a flight cruising at a constant flight level, so there is no need for a point-mass model of the aircraft dynamics.

Once the counterfactual trajectory $\hat{A}$ is reconstructed, the next step is to determine which surrounding trajectories could have posed a conflict risk and are therefore relevant for assessing the deviation.

### 3.4. Neighbour selection

For another aircraft trajectory B to be considered potentially problematic for trajectory A, it must intersect the horizontal plane where A's deviation occurs within the relevant time frame. However, trajectory B may not maintain a consistent altitude during this period; it could intersect A's horizontal plane while ascending or descending to a different flight level (FL). Given this variability in B's altitude between $t_1$ and $t_1 + \tau$, we only consider segments of B's trajectory within a specified altitude range around A's altitude. To be able to ignore irrelevant segments, we ensure that trajectories are not resampled, which means they may not be continuous.

<figure><img src="image_4.png" /><figcaption>Fig. 1. Illustration of counterfactual trajectory reconstruction. The actual recorded trajectory A is shown in blue, with the deviation segment in orange. The counterfactual trajectory $\hat{A}$ (dashed grey) follows the planned waypoints $P_0, N_1, N_2, \dots$, which are indicated by pink crosses.</figcaption></figure>

Following this approach, each deviation dev extracted from our original dataset is associated with a set $\mathcal{N}$ of potentially relevant neighbouring trajectory segments that meet the following criteria for each trajectory point p:

$$t_1 < p Profiling < \min(t_{exit}, t_1 + \tau) \quad (2)$$

$$\text{dev.altmin} - \text{margin}_{\text{alt}} < \text{p.altitude} < \text{dev.altmax} + \text{margin}_{\text{alt}} \quad (3)$$

where $t_{exit}$ is the time at which the aircraft leaves the centre or changes altitude.

Deviations that happen in the absence of any nearby aircraft that might have been avoided are not considered as candidates for deconfliction manoeuvres. As for deviations with one or more identified relevant aircraft in the neighbourhood, we now want to assess whether or not a potential loss of separation could have occurred if the aircraft had not been deviated.

### 3.5. Conflict assessment

We then compare the actual (deviated) trajectory A with the counterfactual $\hat{A}$ in the presence of neighbouring traffic. For each pairwise encounter we compute:

* the actual minimum separation $d_{min}$ between A and the considered adverse flight B,

* the predicted minimum separation $\hat{d}_{min}$ between $\hat{A}$ and B,

* the time to closest point of approach $t_{CPA}$, that is the time between the start of deviation $t_1$ and the time when $\hat{A}$ and B are closest,

* and the duration $\Delta t$ of the lateral deviation observed in the actual trajectory A.

A deviation is classified as a deconfliction manoeuvre when there is at least one neighbouring aircraft for which the following conditions are satisfied: (i) the deviation increases the actual separation with at least one neighbouring aircraft by more than a tolerance $\epsilon$, (ii) the time to closest point of approach $t_{CPA}$ exceeds a minimum threshold $T_{CPA}$, and (iii) the predicted minimum separation on the counterfactual trajectory, $\hat{d}_{min}$, falls below a threshold D.

<footnote n="2">² In the present catalogue, the averaging window is 20 min, which will be reduced in future iterations.</footnote>
### 3.6. Threshold inference

Unlike the regulatory minimum of 5 NM, the threshold $D$ is not fixed in advance but inferred directly from the data using regression methods so as to capture operational controller practices rather than theoretical constraints. Deconfliction manoeuvres are intended to increase the distance between conflicting trajectories. Conversely, manoeuvres unrelated to deconfliction are not expected to follow this pattern. If a manoeuvre occurs in a low-risk context where the predicted closest distance between aircraft is significantly large, it should be equally likely to either increase or decrease this distance. Therefore, among the extracted deviations where the closest proximity is beyond the risk threshold $D$, we expect an approximately equal number of deviations that increase distance as those that decrease it, resulting in a median variation close to zero. When the closest proximity falls below $D$, however, the expected change should be strictly positive, with larger values indicating a higher risk and aiming to maintain the distance above the 5 NM separation, ideally surpassing $D$. In this context, the median comes as a natural quantity of interest: it is robust to outliers and directly reflects whether deviations systematically increase separation or simply fluctuate symmetrically around zero.

#### 3.6.1. KNN median regression

The $k$-nearest neighbours (KNN) approach is a simple non-parametric method that adapts locally to the data distribution, and when combined with median aggregation, it effectively smooths random variations while retaining the underlying operational signal. This makes KNN-median regression particularly well-suited to uncover the empirical thresholds that controllers apply in practice.

Its simplicity and effectiveness have led to its use in diverse applications, from sales prediction (Kohli et al., 2021) or disease risk (Uddin et al., 2022) to human action recognition (Wang et al., 2021) and other classification tasks (Andrian et al., 2019). In KNN regression, the prediction for a given data point is computed as the average of the target variable values of its $k$ nearest neighbours in the feature space. A detailed introduction to this method, alongside kernel-based alternatives, is provided by Altman (1992).

Formally, given a dataset $D = \{(x_i, y_i)\}_{i=1}^n$, where $x_i$ represents the feature vector and $y_i$ the corresponding response, the predicted value for a new data point $x_0$ is given by:

$$ \hat{y}(x_0) = \frac{1}{k} \sum_{i \in \mathcal{N}_k(x_0)} y_i, $$

where $\mathcal{N}_k(x_0)$ is the set of the $k$ nearest neighbours of $x_0$, determined using a chosen distance metric (e.g., Euclidean or Manhattan distance). However, this approach can be sensitive to outliers, as the mean is affected by extreme values. To address this issue, KNN median regression replaces the mean with the median:

$$ \hat{y}_{\text{med}}(x_0) = \text{median}\{y_i : i \in \mathcal{N}_k(x_0)\}. $$

This formulation enhances robustness, as the median is less influenced by extreme values, making it a better choice when dealing with skewed distributions or datasets with outliers. The choice of $k$ is crucial, as a small $k$ leads to high variance, while a larger $k$ smoothens predictions but may introduce bias. Due to its flexibility and non-parametric nature, KNN median regression is particularly useful for capturing non-linear relationships without requiring a complex model.

To estimate our thresholds empirically, we apply a $k$-nearest neighbours (KNN) regression where the target variable is the separation increase or decrease induced by the deviation. For each candidate deviation $i$ we compute $y_i = d_{\min}^{(i)} - \hat{d}_{\min}^{(i)}$, the difference between the observed and counterfactual minimum separations. We also evaluate the corresponding value $x_i$ of the chosen explanatory variable $x$, for this deviation $i$.

Considering this data, and given a query point $x$, the KNN algorithm retrieves the $k$ closest samples $\{(x_j, y_j)\}$ and returns the median of their $y_j$ values:

$$ \hat{f}(x) = \text{median}\{y_j : j \in \mathcal{N}_k(x)\}. $$

In our experiments we set $k = 200$, and apply the regression to different explanatory variables. The explanatory variable $x_i$ can be the predicted proximity $\hat{d}_{\min}^{(i)}$ (see Section 4.4.1), the deviation duration $\Delta_i^{(i)}$ (Section 4.4.2), or the time to CPA $t_{CPA}$ (Section 4.4.3).

The resulting regression curves (see Fig. 6 for example) indicate whether deviations are equally likely to increase or decrease separation (median ≈ 0) or whether they systematically increase it (median > 0), thereby identifying the empirical thresholds that characterize deconfliction manoeuvres.

#### 3.6.2. Quantile regression

The median curves produced by KNN are visually informative, but do not directly provide a closed-form estimate of the threshold. Yet, such an explicit estimate is essential for systematically analysing how the threshold $D$ varies with other parameters. To address this limitation, we complement the previously described KNN approach with linear quantile regression, which provides an easily interpretable estimate of the median and thus allows thresholds to be extracted and compared across different contexts.

Quantile regression is a statistical technique that extends traditional regression methods by estimating conditional quantiles of a response variable, rather than the mean. While ordinary least squares (OLS) regression focuses on minimizing the squared differences between observed and predicted values to model the conditional mean, quantile regression instead models the conditional quantiles, such as the median ($q = 0.5$) or any other quantile of interest.

The median is a measure of location that divides a dataset into two equal parts. In the context of quantile regression, it corresponds to the 0.5 quantile ($q = 0.5$), which minimizes the sum of absolute residuals rather than squared residuals. This property makes the median particularly robust to outliers, as it is less influenced by extreme values compared to the mean. In median regression, the objective is to estimate the relationship between predictors and the response variable so that 50% of observed responses fall below the estimated regression line, while 50% fall above. This makes quantile regression an ideal approach for analysing skewed distributions or datasets exhibiting heteroscedasticity (i.e., non-constant variance).

Originally proposed by Koenker and Bassett (1978), quantile regression has developed into a comprehensive statistical strategy that addresses the limitations of classical regression models focused solely on means. Its applications span a wide variety of fields. In finance, Liu et al. (2023) applied a quantile-on-quantile approach to examine the impact of crude oil price volatility on stock returns, revealing that the effect varies across different quantiles of market performance. Similarly, in survival analysis, Peng (2021) highlighted how quantile regression provides a flexible and interpretable framework for modelling covariate effects on survival outcomes across different time points. It has also been used in environmental economics, as shown by Opoku and Aluko (2021), who analysed the heterogeneous impact of industrialization on environmental degradation across different quantile levels, demonstrating that industrialization worsens environmental degradation at lower quantiles but mitigates it at higher quantiles.

To estimate conditional quantiles, quantile regression solves an optimization problem that minimizes a weighted sum of absolute residuals. Given a dataset with a response variable $Y$ and predictor variables $X$, the quantile regression model estimates the conditional quantile function as:

$$ \min_{\beta} \sum_{i=1}^{n} \rho_{q}(Y_{i} - X_{i}\beta), $$

where:
<table><caption>Fig. 2. AIRAC cycle dates for 2022, along with an illustration of the LFBBBDX air control centre.</caption><thead><tr><td>Cycle</td><td>Start date</td></tr></thead><tbody><tr><td>A2201</td><td>2022-01-27</td></tr><tr><td>A2202</td><td>2022-02-24</td></tr><tr><td>A2203</td><td>2022-03-24</td></tr><tr><td>A2204</td><td>2022-04-21</td></tr><tr><td>A2205</td><td>2022-05-19</td></tr><tr><td>A2206</td><td>2022-06-16</td></tr><tr><td>A2207</td><td>2022-07-14</td></tr><tr><td>A2208</td><td>2022-08-11</td></tr><tr><td>A2209</td><td>2022-09-08</td></tr><tr><td>A2210</td><td>2022-10-06</td></tr><tr><td>A2211</td><td>2022-11-03</td></tr><tr><td>A2212</td><td>2022-12-01</td></tr><tr><td>A2213</td><td>2022-12-29</td></tr></tbody></table>

<figure><img src="image_5.png" /></figure>

* $Y_i$ represents the observed response for the ith data point,

* $X_i$ is the corresponding predictor or set of predictors,

* $\beta$ is the vector of coefficients to be estimated,

* $\rho_q(u)$ is the loss function, which adjusts the weighting of residuals based on the chosen quantile $q$.

The loss function is defined as:

$$ \rho_q(u) = \begin{cases} q \cdot u, & \text{if } u \ge 0, \\ (1-q) \cdot |u|, & \text{if } u < 0. \end{cases} $$

This function ensures that positive residuals ($u \ge 0$) are weighted by $q$, while negative residuals ($u < 0$) are weighted by $1-q$. This asymmetric weighting allows the model to estimate different quantiles of the response variable. For the special case of median regression ($q = 0.5$), the loss function simplifies to the absolute value:

$$ \min_{\beta} \sum_{i=1}^{n} |Y_i - X_i\beta| $$

In this case, quantile regression is equivalent to linear regression by least absolute deviations. When estimating variables threshold values $D(t_{CPA})$ depending on the time to closest point of approach (see Section 4.4.1), we use the minimum distance $\hat{d}_{min}$ as explanatory variable, and determine one threshold value per quantile of $\hat{d}_{min}$ (see Figs. 7 and 8). To do this, we consider the data points for which $\hat{d}_{min} < 5$ NM and compute the linear median of $Y_i = d_{min}^{(i)} - \hat{d}_{min}^{(i)}$ using quantile regression. The rationale for this selection of data points with separation values below 5 NM is that there is no ambiguity on the loss of separation for these points, and the linear trend of the median obtained with this data is robust. The intersection of this line with the horizontal axis $Y = 0$ determines the threshold value for $D$, for the considered quantile of $t_{CPA}$.

## 3.7. Catalogue construction

All retained events are encoded into a structured catalogue containing the deviating aircraft, its deviation geometry, the counterfactual trajectory, the involved neighbouring traffic, and the contextual parameters of the encounter. This catalogue constitutes the main contribution of the paper: a large-scale empirical dataset of controller conflict-resolution actions suitable for analysis and model development.

# 4. Case study on Bordeaux area control centre

## 4.1. Description of the input dataset

The Aeronautical Information Regulation and Control (AIRAC) cycle is a standardized system for updating aeronautical information globally. Managed by the International Civil Aviation Organization (ICAO),

AIRAC cycles occur every 28 days to ensure that aviation charts, navigation databases, and operational procedures remain current and synchronized worldwide. These updates help maintain flight safety by providing accurate and timely information on airspace structures, waypoints, and other critical data. The table on the left in Fig. 2 lists the AIRAC cycles for the year 2022, with each cycle labelled using the format A22XX, where “22” represents the year 2022 and “XX” is the cycle number. The corresponding dates indicate when each cycle became effective. For example, A2201 started on January 27, 2022, and A2213, the last cycle of the year, was effective from December 29, 2022 and spanned over the first days of 2023. These cycles are essential for pilots, air traffic controllers, and flight planners to ensure consistency and accuracy in aeronautical operations.

ADS-B is a surveillance technology that relies on satellite navigation and onboard sensors to enable aircraft to automatically transmit their flight state data. This data includes the aircraft's unique ICAO identifier, the flight's callsign, as well as precise position and velocity information. The trajectory data used in this study were extracted from the OpenSky Network historical database (Schäfer et al., 2014). It contains ADS-B data from flights within the Bordeaux Area Control Centre (LFBBBDX), in southwestern France, illustrated on the right in Fig. 2. The dataset covers the period from January 27 to December 29, 2022, corresponding to AIRAC cycles A2201 to A2212.

We focused exclusively on en-route trajectory segments, with only portions of trajectories with a minimum altitude of 20,000 feet (Flight Level (FL) 200). An additional database containing flight plan information was provided by the French Air Navigation Services. This database includes the planned route for each identified flight, along with the corresponding navigation aids (navaids) that serve as key reference points along the trajectory to be followed.

We combined these datasets to uniquely identify each flight and its corresponding initial flight plan using the Python library traffic (Olive, 2019). To mitigate the inherent imperfections of ADS-B data, we apply a consistency-based filtering method (Olive et al., 2025) that constructs a graph of trajectory points based on vertical and horizontal consistency checks. The longest path in this graph represents the most coherent sequence of values, removing noisy or inconsistent data. Any unacceptable values are deleted from the dataset. All flights were then resampled at one-seconds intervals to ensure consistency in operations.

The complete filtered and resampled dataset contains portions from 745,555 different trajectories, which totals to 1,444,398,582 trajectory points.

## 4.2. Extraction of lateral deviations

To illustrate our lateral deviation extraction method, Fig. 3 compares two trajectories from the input dataset associated with the
<figure><img src="image_6.png" /><figcaption>Fig. 3. Example of two trajectories corresponding to the same flight plan. In (a) the aircraft bypasses several navaids but remains aligned with one from the plan, while in (b) the orange segment shows a deviation not aligned with any navaid from the flight plan.</figcaption></figure>

same flight plan (SOPIL BALAN EVPOK NARAK GAI LOMRA ROCAN PUMAL).

In Fig. 3(a), the aircraft bypasses several navaids in favour of a straighter route, but it remains aligned with one of the planned navaids (PUMAL). This is a routine deviation that is not considered abnormal.

In contrast, Fig. 3(b) highlights a trajectory segment (orange) where the aircraft's alignment no longer corresponds to any of its flight plan's navaids. According to our detection rule, this portion is extracted as a candidate lateral deviation to be examined as a candidate deconfliction situation.

## 4.3. Counterfactual analysis

While we attribute lateral deviations to unexpected or abnormal events, they are not always related to deconfliction manoeuvres. Trajectory deviations may also result from other factors, such as meteorological constraints (Olive and Basora, 2020). Determining whether a deviation was made to resolve a conflict requires analysing the trajectory in the context of surrounding traffic at the time of the deviation. Controllers evaluate the risk of conflict by forecasting future aircraft trajectories and their potential closest points of approach. To replicate this reasoning, we compare the observed deviated trajectory A with its counterfactual prediction $\hat{A}$, defined in Section 3.3, and examine its relation to neighbouring trajectory $B \in \mathcal{N}$.

Fig. 4 illustrates a clear case: trajectory A (blue) deviates from its flight plan (pink crosses) along the orange segment, likely to avoid trajectory B (green). The observed minimum distance between the two is 9.6 NM, above the regulatory threshold of 5 NM. However, the counterfactual prediction $\hat{A}$ (grey) results in a minimum separation of only 0.9 NM, which would have constituted a loss of separation.

In some cases, the identification of the neighbouring trajectory that led to A being deviated is ambiguous. In Fig. 5 for example, the blue trajectory A is deviated from its flight plan for about 7 min. The original navaids from the flight plan are represented by the pink crosses. The grey-dashed line represents the trajectory prediction over 20 min, starting right before the deviated portion. The position of the deviated aircraft A is plotted twice, at the times when the distances between the prediction and the two neighbouring trajectories are the smallest. In this case, the deviation in A increases the distance to these two different flights. Without the deviation, our prediction gives a loss of separation after 486 seconds with a distance of 0.20 NM, and a second one after 700 seconds with a distance of 4.25 NM, which are

<figure><img src="image_7.png" /><figcaption>Fig. 4. Example of a detected deconfliction. The blue trajectory is deviated on the orange portion, likely to resolve a conflict with the green trajectory. The dotted grey line represents the prediction of what the blue trajectory would have been without the deviation, following its flight plan, represented by pink crosses.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Example of a detected deconfliction with two potential conflicting aircraft. The blue trajectory is deviated on the orange portion, likely to resolve a conflict with one of the green trajectories, potentially both. The dotted grey line represents the prediction of what the blue trajectory would have been without the deviation, following its flight plan, represented by pink crosses.</figcaption></figure>

both under the minimum separation threshold of 5 NM. Thanks to the separation, the actual minimal distances are 7.51 NM and 10.36 NM. Given this ambiguity, we chose to keep track of several neighbouring aircraft instead of limiting this study to the closest neighbour. In the rest of this paper, we study each deviation in relation to its closest neighbours in $\mathcal{N}$. The number of closest neighbours is limited to 10 for clarity, but can of course be inferior to 10 if $|\mathcal{N}| < 10$.

After the deviation, A does not align directly to the closest navaid in its flight plan, but skips some of them to align with a navaid that is further away. As mentioned in Section 4.2, this is not an abnormal behaviour, but underlines the potential inexactitude of the flight plan-based prediction. While this method offers more nuance than a simple straight-line projection, it remains an approximation and may still lack accuracy in certain scenarios.

Though the situation depicted in Fig. 5 is a clear example of a deconfliction manoeuvre, most of the deviations we extracted from the original dataset do not show such an obvious pattern. For instance, in some cases, the deviation actually seems to reduce the distance between the closest aircraft rather than increase it. In other cases, $\hat{A}$ and B are initially too far apart to suggest any significant risk of a loss of separation. Following this logic, to be seen as a conflict resolution, a manoeuvre must follow at least these two criteria:

$$ \hat{d}_{min} < d_{min} \text{ and } \hat{d}_{min} \le D \qquad (4) $$
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Difference between actual and predicted minimum distance as a function of the predicted closest distance. Each blue point (left panel) represents one situation. The black curve shows the KNN-median regression, the green dashed line corresponds to the 5 NM regulatory minimum, and the vertical red dashed line marks the empirically inferred threshold at 8 NM. The right panel displays the distribution of deviations across predicted distance intervals, highlighting the asymmetry below the 8 NM threshold.</figcaption></figure>

Here, $d_{min}$ is the observed minimum distance between the two aircraft during the actual (deviated) trajectory, while $\hat{d}_{min}$ is the predicted minimum distance had the aircraft continued along its original flight plan. The threshold $D$ represents the minimum separation typically enforced by air traffic controllers — below this value, a resolution manoeuvre is expected to be issued to avoid conflict. In an ideal scenario, with no uncertainties related to either physical constraints or inherent to the controllers' practices, a deconfliction manoeuvre would be issued in instances where the minimum distance was predicted to fall below 5 NM. A threshold close to this minimum value would reflect a very high risk tolerance from the controller. On the other hand, a cautious controller would set this threshold to a much higher value to minimize the risk. In practice, the value of $D$ may differ depending on the person in charge and on the specific traffic configuration of the airspace. Operational tools typically issue alerts well before the minimum separation, for example the User Request Evaluation Tool<fnref n="3" /> projects potential conflicts up to 20 min in the future, with red alerts for a predicted minimum separation below 5 NM and yellow alerts below approximately 12 NM.

Finally, note that the progressive implementation of Free Route Airspace (FRA) in France does not fundamentally affect our methodology (Section 3.3), since flight plans are already treated as waypoint sequences. FRA primarily reduces the number of intermediate navaids, simplifying trajectory prediction.

## 4.4. Empirical thresholds and patterns

### 4.4.1. Threshold on closest distance at CPA

In Fig. 6, we present a study on all extracted situations involving deviations lasting 30 seconds or more, using the KNN-median regression as described in 3.6.1. Each point in the scatter plot on the left represents a situation including a deviated aircraft and a neighbouring aircraft, with the x-axis showing the predicted closest distance and the y-axis indicating the increase between the actual and predicted closest distances. On the right, a density plot represents the distribution of these values. This graph uses a colour gradient to indicate the concentration of deviations for each interval of the predicted minimum distance: darker colours represent higher concentrations of deviations, while lighter colours indicate lower concentrations. This plot shows a significantly higher concentration of points on the right side compared to the left. For small values of $\hat{d}_{min}$, the dispersion is asymmetric and

notably wider, whereas for larger values of $\hat{d}_{min}$, the distribution is more symmetrical, tightly clustered around zero, with low variability. While this may appear counter-intuitive compared to what we can see on the left figure, where the dispersion seems greater for large values of $\hat{d}_{min}$, the discrepancy is explained by the smaller number of points associated with small values of $\hat{d}_{min}$.

The black line represents the median of the distance increase according to the predicted closest distance, as described in the methodology above. The green-dashed line corresponds to the equation $y = 5, NM - x$, so all points above this line indicate cases where $d_{min} > 5$ NM, meaning the distance remains above 5 NM. Conversely, points below this line suggest losses of separation. Closer examination reveals that most points below this threshold are likely inconsistencies due to data noise rather than genuine instances where $d_{min} < 5$ NM.

The vertical red-dashed line marks the approximate point where the median falls to zero, intersecting the x-axis at a threshold value $D$ around 8 NM. Below this threshold, the median difference follows a linear trend approximated by the equation $y = 8, NM - x$, while for predicted distances above 8 NM, the median stabilizes around zero. This observation supports the hypothesized pattern and establishes a threshold of $D = 8$ NM. This finding also corroborates the results of Gaume et al. (2023), where a similar conclusion was drawn using a much smaller dataset. For the remainder of this study, we consider $D$ as indicative of acceptable risk from the controller's perspective, suggesting that deviations below this threshold most likely result from deconfliction actions.

However, as previously mentioned, we expect that this threshold likely depends on the specific context in which the conflict occurs. In particular, there may be a relationship between the time to CPA $t_{CPA}$, and the threshold at which a situation is deemed risky. This is because uncertainties increase over time; the further away the potential conflict, the greater the positional uncertainties for all involved aircraft. To test this hypothesis, we examine the $D$ threshold across different $t_{CPA}$ intervals.

In Fig. 7, each panel represents the same dataset of extracted deviations, this time filtered according to the value of $t_{CPA}$. The deviations corresponding to the first quartile of $t_{CPA}$ are shown in the top left and the ones at the bottom right correspond to the last quartile. As in Fig. 6, each blue point in the scatter plot represents one extracted deviation. Instead of using a KNN median regression to visually interpret the result, we use a linear quantile regression based on deviations where $\hat{d}_{min} < 5$ NM. The median is represented as an orange straight line on the graphs, with the intersection in yellow. This approach enables us to work precisely with defined threshold values, avoiding any potential bias that could complicate direct comparisons. Given the mandatory

<footnote n="3">³ https://automation.forthillgroup.com/story/URET, https://www.faa.gov/air_traffic/publications/media/pcg_4-03-14.pdf</footnote>
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Threshold *D* as a function of time to closest point of approach (*t*<sub>CPA</sub>). Each panel corresponds to a quartile of *t*<sub>CPA</sub>, with blue points representing individual situations. The orange line is the linear quantile regression on cases with *d̂*<sub>min</sub> < 5 NM. The yellow dot marks its intersection with the x-axis (inferred *D*), while the red dashed line at 8 NM serves as reference. From top-left to bottom-right, *D* increases from 7.12 NM to 10.19 NM, showing that larger margins are applied when conflicts are further ahead.</figcaption></figure>

minimum separation of 5 NM for aircraft at the same Flight Level, deviations below this threshold are highly likely to be related to deconfliction manoeuvres. The threshold is determined at the intersection of this regression with the x-axis and is marked by a yellow point.

We observe a significant variation in the threshold value, between 7.12 NM for the first quartile and 10.19 NM for the last quartile, confirming our intuition. This trend reflects how controllers adapt their separation margins depending on the temporal distance to the potential conflict. When the time to CPA is short, controllers can predict the geometry of the encounter with relatively high certainty, since the aircraft are already close and their trajectories are less affected by longer-term uncertainties such as changes in wind, pilot response, or speed adjustments. In this case, smaller safety margins (around 7 NM) are considered acceptable. By contrast, when the potential conflict lies further in the future, prediction errors accumulate, making it harder to anticipate the exact geometry of the encounter. Controllers therefore tend to apply more conservative thresholds (up to about 10 NM) to ensure that, even if uncertainties materialize, the residual separation will remain above the regulatory minimum of 5 NM. In other words, the variation of *D* with *t*<sub>CPA</sub> captures the operational intuition that the longer the look-ahead, the larger the buffer needed to hedge against uncertainty.

Fig. 8 goes into more detail. On the x-axis, we plot every decile value Di for t<sub>CPA</sub>, with on the y-axis every value of D corresponding to each interval. For values of t<sub>CPA</sub> under 32 s (between D0 and D1), the median of d<sub>min</sub> - d̂<sub>min</sub> does not intersect with the x-axis, making this interval unexploitable with this method, which is why D0 does not appear on the graph.

It is important to note that the time to CPA measures only the interval between the start of the deviation and the closest point of approach, without accounting for the pilot's reaction time. This limitation can be important to consider when discussing time-related uncertainties, as the exact moment the manoeuvre was issued by the controller is unknown.

Determining the *D* threshold enables us to uncover patterns in how controllers perceive risk and to identify a value consistent with real-world controllers' practices. Additionally, variations in this threshold

relative to the time to CPA provide further insight into controllers' perception of uncertainty over time. However, this threshold alone is insufficient to confirm whether a deviation was issued specifically for deconfliction purposes. To enhance the accuracy of this method and filter out irrelevant cases, we can extend our analysis to other easily accessible variables.

4.4.2. Characterization of manoeuvres according to their duration

Building on the results from the median regression in determining separation thresholds, we now explore whether a similar approach could establish a minimum duration threshold for deviations to qualify as relevant candidates for conflict resolution. This duration, denoted Δt, corresponds to t<sub>2</sub> - t<sub>1</sub>. In the following, we will refer to the corresponding threshold on duration as ΔT.

Following the same logic, we assume that standard changes in a direction unrelated to deconfliction manoeuvres should have little to no impact on the minimum separation between aircraft. Therefore, we would expect a median separation change close to zero for deviations of short duration.

In Fig. 9, we represent the difference in minimum separation made by the deviation according to its duration, with the median regression on 200 neighbours as a black line.

Unlike what we observe in Fig. 6, the median values plotted in this figure remain close to zero, showing little variation with respect to duration. We observe two distinct, roughly symmetrical clusters: a narrow one for small values of Δt < 2 min and a broader one for larger values. We hypothesize that the dense cloud at smaller Δt represents routine turns in the trajectory, unrelated to deconfliction manoeuvres. In contrast, the broader distribution at larger Δt likely corresponds to persistent deviations from the flight plan, which are more often the result of deliberate controller actions and therefore more likely linked to deconfliction.

However, this second cluster does not exhibit a significant shift in the median that would indicate a systematic increase in separation between aircraft. This is likely due to the way the dataset is constructed: for each detected deviation, up to ten different data points describe
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Evolution of the *D* threshold across deciles of time to closest point of approach (*t*<sub>CPA</sub>). Blue dots mark the inferred threshold values in each decile interval [*D*<sub>n</sub>, *D*<sub>n+1</sub>], and the dashed line highlights the increasing trend. No threshold is obtained for *t*<sub>CPA</sub> < 32 s (*D*<sub>0</sub>), as the regression does not intersect the x-axis in this interval.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Difference between actual and predicted minimum distance (*d*<sub>min</sub> − *d̂*<sub>min</sub>) as a function of the deviation duration *Δt*, considering all deviations in the dataset. Each orange point represents one situation; the black line shows the KNN-median regression. Two distinct clusters are visible: short deviations (*Δt* < 2 min), and longer, more persistent deviations. The right panel shows the corresponding density distribution.</figcaption></figure>

the relationship between the deviated flight and its closest neighbours. Given the dataset's breadth, it is expected that many of these data points correspond to aircraft pairs that were never in conflict. Unlike the predicted minimum distance between aircraft, the duration of a deviation alone does not reliably indicate whether a manoeuvre was intended for deconfliction.

The density plot highlights that the vast majority of detected deviations are short. Across all deviation durations, the distribution remains symmetrical, reinforcing the idea that duration alone is not a strong enough criterion to reliably identify deconfliction manoeuvres.

In Fig. 10, we consider only the closest neighbour in terms of predicted minimum distance for each deviation. With this approach, we observe a clearer pattern: around 200 s, the median values begin to increase, suggesting that prolonged deviations may indeed contribute

to greater separation between aircraft. This trend was less apparent in the previous figure due to the inclusion of multiple neighbouring aircraft per deviation, many of which were not in conflict. The small cluster seen in the earlier figure, likely corresponding to routine turns, still appears here, but does not correspond to an increase in the distance between aircraft.

This time, the figure on the right reveals an asymmetrical distribution for larger deviation durations, confirming a tendency for aircraft to increase their separation. However, for shorter durations, deconfliction-related manoeuvres remain difficult to distinguish. Their statistical contribution is too small to noticeably impact the overall distribution, which stays symmetrical and centred around zero.

To explore this further and mitigate this issue, we apply a median regression analysis on deviation durations in high-risk scenarios where
<figure><img src="image_13.png" /><figcaption>Fig. 10. Difference between actual and predicted minimum distance ($d_{min} - \hat{d}_{min}$) as a function of the deviation duration $\Delta t$, considering only the closest neighbour for each deviation. Orange points represent individual situations, while the black line shows the KNN-median regression. Around 200 s, the median begins to rise, indicating that longer deviations tend to increase aircraft separation. The right panel displays the density distribution, which becomes asymmetrical for large $\Delta t$, confirming that prolonged deviations are more often associated with deliberate deconfliction manoeuvres.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11. Difference between actual and predicted minimum distance ($d_{min} - \hat{d}_{min}$) as a function of the deviation duration $\Delta t$, restricted to cases where $\hat{d}_{min} < 8$ NM. Orange points represent individual situations, while the black line shows the KNN-median regression. The vertical red-dotted line marks $\Delta t = 2$ min. The median is consistently positive across all durations. Two clusters are visible: short turns around 30 s and longer, persistent deviations, both shown to contribute to deconfliction. The right panel shows the density distribution of deviations, which is spread out and asymmetrical.</figcaption></figure>

the predicted closest separation $\hat{d}_{min}$ falls below a designated threshold. This increases the likelihood of analysing relevant neighbouring aircraft in each situation. After applying an 8NM threshold, a significant shift becomes evident in Fig. 11.

In this filtered dataset, most points now lie above the x-axis, resulting in a consistently positive median across the entire plot — significantly higher than in the previous graph. The distinct clusters previously identified remain: one for short deviations around 30 s and another for longer deviations, primarily between 2 min and approximately 800 s. However, unlike before, these clusters are no longer symmetrical. While deviations exceeding 800 s are less frequent, they still tend to increase the distance between aircraft in high-risk scenarios.

This observation supports our earlier finding that filtering by the predicted distance at CPA, $\hat{d}_{min}$, helps isolate deviations more likely to increase aircraft separation. Additionally, the persistence of these two clusters, now associated with higher median values, reinforces the

idea that even standard turns can contribute to conflict resolution. Notably, the extraction of small deviations using this approach was demonstrated previously in Gaume et al. (2023).

The density plot on the right reveals a more balanced dataset compared to previous analyses, particularly in the distribution of deviation durations. While short deviations still account for a significant portion of cases, the distribution is now more spread out and no longer centred around zero. This suggests that even minor deviations can contribute to increased aircraft separation, highlighting their potential role in conflict resolution. Deviations around 2 min correspond to the smallest values of $d_{min} - \hat{d}_{min}$. Although the median remains positive and the distribution asymmetrical in this range, these instances occupy an interesting middle ground between brief, routine turns and persistent deviations. For long deviation durations above 800 s, the density profile degrades due to sparse data.
<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Examples of short “direct-to” manoeuvres. The blue trajectory shows the deviated aircraft, with the orange segment marking the deviation and pink crosses representing its flight plan. Conflicting trajectories are shown in green. Both deviations (43 s on the left and 36 s on the right) increase separation that would otherwise have fallen below 5 NM.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 13.** Difference between actual and predicted minimum distance $d_{min} - \hat{d}_{min}$ as a function of the time to CPA $t_{CPA}$, using all deviations in the dataset. Green points represent individual deviations, the black line shows the KNN-median regression, and the right panel displays the distribution of values. For very small $t_{CPA}$, the median remains close to zero, indicating that such deviations are less likely to correspond to conflict-resolution manoeuvres.</figcaption></figure>

<figure><img src="image_17.png" /></figure>

While it is true that most small deviations are unrelated to de-confliction actions, this filtering of the dataset leaves us with the few standard turns that are likely to have been used by the controllers as deconfliction manoeuvres. In Fig. 12, we illustrate this phenomenon with two small deviations of 43 and 36 seconds. In these instances, the closest neighbouring aircraft did not deviate. Without the detected deviation, a loss of separation would have occurred, with a minimum distance of 2.0 NM on the left and 2.2 NM on the right.

These traffic situations likely correspond to “direct-to” instructions issues by air traffic controllers to adjust an aircraft’s trajectory towards a specific waypoint from the flight plan. Unlike the previously observed persistent deviations, “direct-to” manoeuvres are typically brief course adjustments designed to resolve potential conflicts while also optimizing routing. The presence of small deviations in conflict-resolution scenarios highlights their role as a proactive, efficient tool for ensuring safe separation with minimal disruption to flight efficiency. In operational practice, we expect that such instructions often lead the deviating aircraft to pass behind the non-touched aircraft. Our extraction, however, does not enforce this criterion and retains both front and behind cases. In future work, the catalogue could also be used to verify this behaviour statistically.

Filtering according to the duration highlights an interesting pattern in the data regarding the use of both short and long deviations. However, it is still impossible to assert that all deviations in Fig. 11 are

due to deconfliction actions. We can observe some points in the scatter plot having very small or even negative values of $d_{min} - \hat{d}_{min}$, which are most probably not related to deconfliction actions. These irrelevant points can be easily filtered out by introducing an additional positive threshold $\epsilon$, and removing points for which $d_{min} - \hat{d}_{min} \le \epsilon$.

### 4.4.3. Threshold on time to CPA

Intuitively, we assume that, in most cases, controllers aim to resolve conflicts well before a potential loss of separation, accounting for uncertainties such as pilot reaction times and manoeuvres durations. We hypothesize that deviations with low values of time to CPA are likely to be false positives. Fig. 13 displays the median of $d_{min} - \hat{d}_{min}$ as a function of time to CPA, based on all deviations in the dataset without any filtering. For very small time-to-CPA values, the median effect of deviations on the increase in separation $d_{min} - \hat{d}_{min}$ is close to zero, as indicated by the nearly horizontal alignment around the x-axis in this region. Similar to what we observed with deviation duration, the wide distribution of values in this plot likely results from the fact that many deviations in the dataset were not performed in response to a potential loss of separation. Time to CPA alone is not a sufficient indicator of whether a deviation was intended for deconfliction. No distinct threshold naturally emerges to separate deconfliction-related deviations from routine trajectory adjustments. Instead, deviations occur across the entire range of time to CPA values, with a significant
<figure><img src="image_18.png" /><figcaption>**Fig. 14.** Difference between actual and predicted minimum distance $d_{min} - \hat{d}_{min}$ as a function of the time to CPA $t_{CPA}$, restricted to cases where $\hat{d}_{min} < 8$ NM. Green points represent individual deviations, the black line shows the KNN-median regression, and the right panel displays the distribution of values. With this filtered dataset, the median grows steadily with $t_{CPA}$, showing that earlier interventions tend to produce larger increases in separation.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 15.** Examples of short “direct-to” manoeuvres unrelated to deconfliction. The blue trajectory is the deviated aircraft, with the orange segment marking the deviation and pink crosses its flight plan; nearby aircraft are shown in green. The left panel shows a 43 s deviation likely simplifying the route by bypassing navaids. The right panel shows a 22 s deviation that shortens the trajectory but slightly reduces the minimum separation (from 7.49 NM to 7.40 NM). Such brief deviations reflect routine adjustments rather than conflict-resolution actions.</figcaption></figure>

proportion producing little to no change in separation distance. In addition to this, the density plot reveals that a very large proportion of the extracted deviations are associated to a value of $t_{CPA} < 100$ s. For instances with higher $t_{CPA}$ values, the density profile remains flat and symmetrical, making it difficult to derive any meaningful insights.

Additional filtering, such as focusing on deviations where separation distances were critically low, may help isolate patterns that are more representative of controller-initiated conflict resolution.

Similarly to our study of the effect of the duration on $d_{min} - \hat{d}_{min}$, we plot the same graph, but only for situations where $\hat{d}_{min} < 8$ NM, in Fig. 14. The median curve shows a gradual increase in separation as the time to CPA grows. This trend suggests that deviations introduced earlier relative to the CPA time tend to result in larger increases in minimum separation between the two aircraft. Although it is completely expected that a significant increase in the distance between the aircraft would take more time, this figure helps us rule out the occurrences that are most likely to be simple standard turns.

In this case, the density distribution changes significantly: although the distribution for values under 100 s remains narrow and centred

around zero, it is much less dense compared to the rest of the distribution, becoming asymmetrical and biased positively. This suggests that the interval still contains relevant instances. The densest intervals occur for values of $t_{CPA}$ between approximately 300 s and 600 s. As $t_{CPA}$ increases and the intervals become sparser, the distributions flatten, but they remain positive.

The takeaway from these graphs is that deviations shorter than approximately 50 seconds are less likely to be associated with deconfliction actions. Fig. 15 presents two examples of short deviations, with $t_{CPA}$ values of 43 seconds (left) and 22 seconds (right). In both cases, these small deviations do not appear to have been used for deconfliction.

On the left, given the flight plan information and the prior alignment of IBE32TV, it is unlikely that a conflict with FHBOC was a concern. Instead, the deviation seems to facilitate a more direct route, bypassing several navaids. Similarly, on the right, the deviation simplifies the trajectory of RYR28LC, though it slightly reduces the minimum separation with IBE30JU, from 7.49 NM to 7.40 NM.
<figure><img src="image_20.png" /><figcaption>Fig. 16. Summary of the methodology used to produce the catalogue.</figcaption></figure>

# 5. Extraction of the catalogue

## 5.1. Process overview

The catalogue's extraction processed is summarized in Fig. 16. Then process integrates ADS-B and flight plan data to identify and isolate meaningful deviation events. After denoising and resampling trajectories, successive filtering steps, based on $\hat{d}_{min}$, and $t_{CPA}$, progressively narrow down the dataset. Our analysis of $\Delta t$ enables us to distinguish between persistent deviations, typically associated with standard deconfliction manoeuvres, and shorter “direct-to” instructions. Both forms are preserved within the final catalogue. This structured approach is designed to maximize the retention of relevant lateral deviations while minimizing the presence of false positives.

## 5.2. Extraction heuristics

Since $D$ is influenced by the value of $t_{CPA}$, two heuristic strategies can be considered. The first is a simple global threshold, applying a constant value of $D = 8$ NM regardless of $t_{CPA}$. The second approach is more refined and adapts $D$ according to the quartile in which $t_{CPA}$ falls.

Since some deviations lead to only negligible increases in aircraft separation, we introduce an additional threshold, $\epsilon$, to avoid capturing trivial non-zero values of $d_{min} - \hat{d}_{min}$. This criterion helps prevent our heuristics from incorrectly flagging insignificant cases as meaningful deviations.

$$ \text{Fixed-threshold heuristic: } (t_{CPA} > T_{CPA}) \ \& \ (d_{min} - \hat{d}_{min} > \epsilon) \ \& \ (\hat{d}_{min} < D) $$

where:

$$ \epsilon = 0.1 \text{ NM} $$

$$ T_{CPA} = 50 \text{ s} $$

$$ D(q) = 8 \text{ NM} $$

$$ \text{Flexible-threshold heuristic: } (t_{CPA} > T_{CPA}) \ \& \ (d_{min} - \hat{d}_{min} > \epsilon) \ \& \ (\hat{d}_{min} < D(q)) \text{ with } q = \text{quartile}(t_{CPA}) $$

where $D(q)$ is a threshold that depends on the quartile $q$ of $t_{CPA}$.

where:

$$ \epsilon = 0.1 \text{ NM} $$

$$ T_{CPA} = 50 \text{ s} $$

$$ D(q) = \begin{cases} 7.12 \text{ NM}, & \text{if } t_{CPA} < 444 \text{ s } (q1) \\ 7.83 \text{ NM}, & \text{if } 444 \le t_{CPA} < 610 \text{ s } (q2) \\ 8.82 \text{ NM}, & \text{if } 610 \le t_{CPA} < 810 \text{ s } (q3) \\ 10.19 \text{ NM}, & \text{if } t_{CPA} \ge 810 \text{ s } (q4) \end{cases} $$

This tiered heuristic allows the minimum distance threshold to scale with the temporal proximity of the CPA, potentially improving the relevance of selected events. In both cases, we then filter by $t_{CPA}$ to minimize false positives. According to Fig. 14, we choose a threshold of 50 s.

Each situation will also be labelled based on the duration of the deviation to distinguish between standard turns (potentially representing a “direct-to” deconfliction instruction) and persistent deviations.

From the 964,010 lateral deviations initially detected in the Bordeaux 2022 dataset, only a small fraction are consistent with conflict-resolution manoeuvres according to our heuristics. Applying the fixed-threshold heuristic yields 21,217 retained events (2.2% of all deviations), while the flexible-threshold heuristic retains 21,201 events (also 2.2%). This confirms that the overwhelming majority of lateral deviations in daily traffic are unrelated to conflict resolution.

It is important to emphasize that these figures do not represent the full share of conflict-related manoeuvres in operations. Our method does not attempt to capture all deviations, but only those that fit the specific lateral-deconfliction patterns defined by our heuristics. In particular, vertical manoeuvres and mixed vertical-lateral resolutions are outside the scope of the present study. The number of conflicts not accounted for due to the exclusion of vertical deconfliction is therefore unknown.

## 5.3. Format of the catalogue

The extracted catalogue of deconfliction situations is stored in a structured format encapsulating relevant information essential for replaying and studying the scenarios in detail. To enable users to develop and test their own detection methods, the catalogue also includes situations beyond the scope of our heuristics. Specifically, the dataset contains cases where at least one neighbouring aircraft is predicted to approach within $\hat{d}_{min} < 15$ NM of the deviated aircraft, at the same flight level. Only cases where the observed distance exceeds the predicted distance, i.e., $d_{min} - \hat{d}_{min} > 0$, are included. Each instance is tagged based on both heuristic criteria and the duration of the deviation. Every extracted situation is saved as a JSON file, which contains, for each situation, the information described in Table 1. All times are given in Unix time format.

## 5.4. Visual validation of the extracted catalogue

To further evaluate the reliability of the extraction process, we performed a manual visual inspection of a representative subset of the catalogue. For each AIRAC cycle included in the dataset, we randomly selected 10 detected deconflictions, resulting in a total of 120. These were plotted and examined qualitatively to assess whether the identified deviations plausibly corresponded to conflict resolution manoeuvres, or whether they were more likely the result of unrelated flight dynamics, trajectory noise, or heuristic misclassification.

Each plot displays the actual and predicted trajectories of the deviating aircraft, its deviation segment, nearby navigation points, and neighbouring aircraft considered as conflicting with the deviated flight. This visual context helps interpret the spatial dynamics of each situation and verify whether the deviation plausibly served to increase lateral separation.
<table><caption>**Table 1**
Format of the extracted catalogue of deconfliction cases.</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>sector</td><td>The sector that was open at the time of the conflict.<br>opening_time: opening time of the sector<br>closing_time: closing time of the sector<br>area: area within the external boundaries of the sector (square meters)<br>external_boundaries: external boundaries (WKB hexadecimal format)<br>designator: designator or name of the sector<br>decomposition: decomposition with each unitary sector's designator<br>extruded_polygons: extruded polygons for each unitary sector</td></tr><tr><td>deviated aircraft</td><td>The trajectory A that is detected as involved in a separation loss situation and subject to deviation.<br>flight_id: flight ID of A<br>start_deviation: start time of the deviated portion<br>stop_deviation: stop time of the deviated portion<br>flight_plan: list of navaids in the original flight plan.<br>aircraft_nb_at_start: number of aircraft in the sector at the start of the deviation<br>predicted trajectory: the predicted trajectory A&#770;</td></tr><tr><td>actual pairwise</td><td>The relationship between the deviated trajectory and every other trajectory in the neighbourhood, corresponding to all aircraft in the neighbourhood intersecting the sector between the beginning of the deviation and the time at which A leaves the sector.<br>time_at_cpa: timestamp at actual CPA<br>lateral_dist_at_tcpa: lateral distance at actual t<sub>CPA</sub> (NM)<br>vertical_dist_at_tcpa: vertical distance at actual t<sub>CPA</sub> (NM)</td></tr><tr><td>predicted pairwise</td><td>The relationship between the predicted deviation-free trajectory and every other trajectory in the neighbourhood.<br>time_at_cpa: timestamp at predicted CPA<br>lateral_dist_at_tcpa: lateral distance at predicted t<sub>CPA</sub><br>vertical_dist_at_tcpa: vertical distance at predicted t<sub>CPA</sub><br>nb_aircraft_at_tcpa: number of aircraft at predicted t<sub>CPA</sub><br>fixed_heuristic: boolean flag for whether the fixed-threshold heuristic is met<br>'short' if the heuristic is met with a deviation &le; 2 min<br>'long' if the heuristic is met with a deviation &gt; 2 min<br>'false' if the heuristic is not met:<br>flexible_heuristic: boolean flag for whether the flexible-threshold heuristic is met<br>'short' if the heuristic is met with a deviation &le; 2 min<br>'long' if the heuristic is met with a deviation &gt; 2 min<br>'false' if the heuristic is not met</td></tr><tr><td>trajectories</td><td>The collection of all neighbouring trajectories at a relevant altitude with, for each data point:<br>timestamp: a Unix timestamp in seconds<br>latitude: in degrees, WGS84<br>longitude: in degrees, WGS84<br>altitude: in feet<br>trackangle: in degrees, relative to the true geographic North<br>ground speed: in kts<br>vertical rate: in ft/min</td></tr></tbody></table>

### 5.4.1. Examples of correct detections

Fig. 17 presents two examples where the extracted deviations appear to correspond to clear deconfliction manoeuvres. In both cases, the predicted trajectory (dashed grey line) would have brought the aircraft in close proximity with a neighbouring flight. Instead, the actual flown trajectory (solid blue), incorporating a distinct deviation segment (orange), results in significantly increased lateral separation. In the first example, the predicted distance is 5.5 NM and the actual separation reaches 8.0 NM. Similarly, in the second case, the predicted minimum distance is just 0.6 NM, while the actual separation achieved is 7.8 NM. Both examples are consistent with controller-initiated lateral manoeuvres to mitigate conflict risk.

### 5.4.2. Examples of misclassified or ambiguous events

Despite the overall robustness of the extraction pipeline, some situations were found to be false positives, i.e., deviations not evidently related to a conflict or not resulting in significant added separation. These errors may stem from trajectory prediction inaccuracies, sector constraints, or manoeuvres intended for other operational reasons (e.g., sequencing, weather avoidance, or direct routing).

Fig. 18 illustrates two examples of false positive situations flagged by the heuristics as potential deconfliction manoeuvres, but which, upon visual inspection, appear unlikely to result from conflict resolution.

In the first example (left), although the predicted trajectory brings the aircraft within 0.2 NM of another flight, the deviation segment detected, a turn to the left just before entering the sector, does not show a clearly targeted lateral avoidance. Instead, additional deviations occurring later in the trajectory seem more consistent with an actual conflict resolution manoeuvre. In this case, it is likely that one of the subsequent deviations would also be detected and stored as a separate entry in the catalogue.

The second example (right) illustrates a different type of misclassification. In this case, the predicted and actual minimum separation values are nearly identical (7.4 NM vs. 7.5 NM), and the closest point of approach occurs when the deviated aircraft is already nearly realigned with its original flight plan. This timing suggests that the recorded deviation is unlikely to be a response to the detected neighbouring aircraft. It may instead reflect routine flight path variability or a deconfliction manoeuvre aimed to solve a different, undetected conflict. In either case, the lack of a clear geometric change or significant increase in separation due to the detected deviation undermines the interpretation of the event as a controller-initiated deconfliction.

### 5.4.3. Performance assessment

Across the 120 visually inspected cases, the majority of sampled situations were consistent with genuine deconfliction manoeuvres. This confirms the effectiveness of our heuristic-based extraction process and its practical relevance in identifying controller-initiated deviations. Out
<figure><img src="image_21.png" /><figcaption>**Fig. 17.** Examples of visually confirmed deconfliction manoeuvres. The actual flown trajectory is shown in blue, with the deviation segment in orange, the predicted (non-deviated) trajectory in dashed grey, and the conflicting trajectory in green. Black crosses mark flight plan navaids. In both cases, the deviation significantly increases lateral separation.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. 18.** Examples of false positives in the catalogue. The actual trajectory is shown in blue, with the deviation segment in orange, the predicted (non-deviated) trajectory in dashed grey, and the neighbouring trajectory in green. Black crosses mark flight plan navaids. On the left, the detected deviation is likely unrelated to conflict resolution, which instead stems from later manoeuvres. On the right, the predicted and actual separations are nearly identical, indicating that the deviation is not linked to the neighbouring aircraft.</figcaption></figure>

of the 120 samples, only 12 were flagged as false positives, yielding an estimated false positive rate of 10%. This is a promising result, especially given the complexity of real-world air traffic data and the unsupervised nature of the extraction pipeline.

False positives typically arose in ambiguous situations, such as minor course corrections, early deviations followed by returns to the flight plan, or proximity to multiple nearby aircraft, where the operational intent behind the manoeuvre is unclear. These cases highlight the inherent difficulty in inferring intent from trajectory data alone and suggest possible areas for refinement. In particular, improvements could be made by focusing on the most recent deviation before the predicted closest point of approach, as this is most likely to reflect an actual conflict resolution. Similarly, long deviations that end well before the CPA may be better excluded, as subsequent trajectory segments can dilute the relevance of the original manoeuvre.

In addition to false positives, it is equally important to acknowledge the presence of false negatives, which are genuine deconfliction manoeuvres that our pipeline fails to capture. These omissions are inherently difficult to quantify, since by definition they leave no trace in the catalogue, yet their existence is unavoidable. Certain manoeuvres may fall outside the scope of our heuristics, and the complexity of surrounding traffic can obscure the connection between a deviation and the conflict it resolves. Moreover, this work deliberately restricts its focus to lateral deconflictions, excluding those relying on vertical manoeuvres or speed adjustments. Unsurprisingly, the number of detected deconflictions remains small relative to the overwhelming volume of routine en-route traffic.

Identifying deconflictions in operational data is comparable to searching for a needle in a haystack: although controllers apply them as standard practice, they are statistically rare once dispersed across
<figure><img src="image_23.png" /><figcaption>Fig. 19. Actual minimum distance as a function of predicted minimum distance. Each point represents one extracted event. The actual separations $d_{min}$ remain mostly above 6 NM, indicating that controllers typically apply safety buffers beyond the regulatory 5 NM minimum.</figcaption></figure>

millions of uneventful flights. This rarity, compounded by the noisy and incomplete nature of surveillance data, makes reliable detection especially challenging. The resulting catalogue should thus be seen not as exhaustive, but as a curated set of infrequent yet operationally significant events, valuable precisely because of their scarcity and the insight they provide into real-world conflict resolution practices.

Future work could benefit from incorporating additional contextual cues, such as weather data, sector constraints, or sequencing demands. A more systematic annotation process, possibly involving expert air traffic controllers, would also help further validate and refine the catalogue. Despite these limitations, the overall robustness make the extracted dataset a strong foundation for further analysis or model development.

## 5.5. Example of usage

To illustrate the analytical possibilities enabled by the extracted catalogue, we provide a brief exploratory analysis focusing on situations that match the fixed-threshold heuristic. This preliminary overview highlights how simple statistical examinations can already offer insight into pilot behaviour and traffic complexity.

Fig. 19 shows the relationship between the actual minimum distance ($d_{min}$) and the predicted minimum distance ($\hat{d}_{min}$). We observe that for all values of the predicted minimum distance ($\hat{d}_{min}$), the actual minimum distance ($d_{min}$) mostly remains above approximately 6 NM. This shows that controllers tend to apply an additional margin, rather than strictly adhering to the predicted minimum value of 5 NM. There are however individual differences among the controllers. Some of them might be less risk-averse or more accurate in their predictions than others, as indicated by the few lateral deviations resulting in a minimum distance between 5 and 6 NM. So reducing the prescribed minimum separation to 4 NM in the hope that most controllers would actually target a minimal distance of 5 NM would probably not be safe. Such a reduction would likely produce cases with minima close to 4 NM, under the 5 NM standard separation which accounts for the positional errors in radar tracking.

<figure><img src="image_24.png" /><figcaption>Fig. 20. $t_{CPA}$ as a function of $\hat{d}_{min}$. Each cell shows the number of situations (colour scale), with darker shades indicating higher density. The trend shows that as $\hat{d}_{min}$ decreases, $t_{CPA}$ increases, suggesting critical situations are addressed earlier.</figcaption></figure>

In Fig. 20, we plot the time to CPA $t_{CPA}$ as a function of the predicted minimum distance $\hat{d}_{min}$. The general trend of the heatmap tends to show that the most critical conflicts (with small values of the predicted minimum distance $\hat{d}_{min}$) are identified and deconflicted earlier (i.e. with greater values of $t_{CPA}$) than less critical ones. This suggests that the more critical the situation, the sooner it is identified and addressed.

Fig. 21 shows a simple distribution of the duration of the deviations in the dataset, showing that the majority of deviations last between 2 to 10 min. As the duration increases beyond 10 min, the frequency of situations decreases significantly, suggesting that longer deviations are less common.

Finally, Fig. 22 explores the geometrical configuration of the deviations by showing the distribution of relative track angles between the deviating aircraft and its predicted closest neighbour (identified based on $\hat{d}_{min}$) at the onset of the deviation. This angle reflects the relative orientation of the two aircraft at the onset of the deviation, potentially indicating whether their trajectories were head-on, crossing, or parallel. Smaller angles suggest near-parallel flight paths, 90° represents a perpendicular crossing, and larger angles indicate more convergent or head-on interactions. Two illustrations are included to help visualize some of the most common configurations. The scarcity of angles beyond 90° suggests that head-on or directly converging paths are relatively rare or are managed differently.

# 6. Conclusion

In this paper, we introduced a data-driven methodology for identifying and cataloguing air traffic deconfliction manoeuvres using historical ADS-B and flight plan data. By focusing on lateral deviations in en-route airspace and leveraging both KNN-median and quantile
<figure><img src="image_25.png" /><figcaption>**Fig. 21.** Distribution of deviation durations in the dataset. Most deviations last between 2 and 10 min, while longer deviations become increasingly rare beyond 10 min.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Fig. 22.** Distribution of relative track angles between the deviating aircraft and its predicted closest neighbour at the start of the deviation. Small angles correspond to near-parallel trajectories, 90° to perpendicular crossings, and larger angles to more convergent encounters. Insets illustrate two typical configurations (parallel and crossing).</figcaption></figure>

regression techniques, we proposed a systematic approach to differentiate between deviations likely caused by conflict resolution and those due to other operational factors. The introduction of threshold-based heuristics, both fixed and variable with respect to time to CPA, allowed us to capture a broad range of resolution strategies, including brief “direct-to” instructions and more persistent deviations.

Our analysis confirms that controllers tend to act preemptively in the face of potential conflicts, applying varying safety margins depending on temporal proximity. These behavioural patterns, reflected in the dataset we constructed, could provide a useful empirical basis for refining the design and calibration of automated conflict detection and resolution tools.

The resulting catalogue is made available in a structured and interpretable format to support further research. As this study focused exclusively on lateral deviations, vertical manoeuvres and altitude-based resolutions were not considered, meaning some controller actions may not have been captured. Expanding the methodology to include vertical dynamics, speed changes, and environmental data such as weather could offer a more comprehensive view of real-world deconfliction strategies. The catalogue also opens the possibility of studying how the timing of conflict resolution relates to sector traffic load, an aspect that could provide valuable insights but has not yet been explored in this work. In addition, access to controller-specific data would make it possible to refine the analysis further and investigate variations in deconfliction practices at the individual or sector level.

## Glossary

*navaid* Short for navigational aid; a device (physical or electronic) used by aircraft for position determination and navigation (e.g., VOR, NDB, GPS).

*conflict* A situation in which two or more aircraft are predicted to come closer than the minimum separation standards, requiring intervention from a controller to maintain safe distances.

*standard separation* The prescribed minimum distance between aircraft to ensure safety, maintained by controllers through ATC procedures.

*callsign* A unique alphanumeric identifier assigned to an aircraft for radio communication and tracking, often reflecting the airline and flight number.

*LOS* *Loss Of Separation*, An event where the actual distance between aircraft falls below the applicable separation minima.

*CPA* *Closest Point of Approach*, The point at which the predicted distance between two aircraft will be the smallest, based on their current trajectories.

*ICAO* *International Civil Aviation Organization*, A United Nations agency that sets global aviation safety and standardization rules.
**AIRAC**
Aeronautical Information Regulation and Control,
A system for standardized and scheduled updates to aeronautical information.

**CPA**
Closest Point of Approach,
The point at which an aircraft is predicted to come nearest to another.

**FL**
Flight Level
Aircraft altitude, expressed in hundreds of feet (e.g., FL350 corresponds to 35,000 ft).

**ADS-B**
Automatic Dependent Surveillance-Broadcast,
A technology where aircraft broadcast their position and velocity to improve tracking.

**NM**
Nautical Miles,
A unit of distance used in aviation and maritime navigation, equal to 1,852 meters.

**KNN**
k-Nearest Neighbours,
An unsupervised machine learning algorithm that classifies samples based on their nearest neighbours.

## Notations

$LLT_{CPA}$
Threshold for Time to Closest Point of Approach, under which we consider the manoeuvre to not be a deconfliction.

$\Delta t$
Duration of the deviation — time in seconds between the start and the end of the deviation.

$\Delta T$
Threshold on duration differentiating small deviations (standard turns) from longer, persistent deviation manoeuvres.

$d_{min}$
Observed lateral distance at the closest point of approach between two aircraft during the actual (deviated) trajectory.

$\hat{d}_{min}$
Predicted lateral distance at the closest point of approach if the aircraft had followed its original flight plan.

$D$
Estimated acceptable risk threshold for lateral distance between aircraft at CPA.

$t_1$ Start of the deviation.

$t_2$ End of the deviation.

$\tau$
Maximum duration between the start of the deviation and the end of the trajectory taken into account in our analysis.

$A$
Actual (deviated) trajectory of the considered flight for which a lateral deviation from the planned route is observed.

$\hat{A}$
Counterfactual trajectory reconstructed from a sequence $Q$ of points based on the planned route and from the ground speed estimated at $t_1$. $\hat{A}$ is an approximation of the trajectory that the flight would have followed if it had not been deviated from its planned route.

$P_0$ Last recorded position of the trajectory before $t_1$.

$N_j$ The $j$th navaid from the flight plan after $t_1$.

$Q$
Ordered sequence of points used for trajectory prediction, $Q = (P_0, N_1, \dots, N_m)$.

$P(t)$
Interpolated horizontal position along the counterfactual trajectory at time $t$, obtained by great-circle interpolation between successive waypoints in $Q$.

## CRediT authorship contribution statement

**Kim Gaume:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation,

Conceptualization. **Xavier Olive:** Writing – review & editing, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization. **David Gianazza:** Writing – review & editing, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization. **Richard Alligier:** Writing – review & editing, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization. **Nicolas Durand:** Writing – review & editing, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization.

## Funding

The research presented in this paper was fully funded by the federation ONERA ISAE/SUPAERO ENAC.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

The data is available at a link specified in the document.

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