Journal of Advanced Transportation

Volume 2018, Article ID 7964641, 9 pages

https://doi.org/10.1155/2018/7964641

## A SVM Approach of Aircraft Conflict Detection in Free Flight

^{1}Air Traffic Control and Navigation College, Air Force Engineering University, Xi’an 710051, China^{2}National Key Laboratory of Air Traffic Collision Prevention, Xi’an 710051, China^{3}Nuclear Power Institute of China, Chengdu 610051, China

Correspondence should be addressed to Xiang-xi Wen; moc.361@yjaxxw

Received 2 May 2018; Accepted 13 November 2018; Published 6 December 2018

Guest Editor: Ali Tizghadam

Copyright © 2018 Xu-rui Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Probabilistic conflict detection methods typically require high computational burden to deal with complex multiaircraft conflict detection. In this article, aircraft conflict detection is considered as a binary classification problem; therefore, it can be solved by a pattern recognition method. A potential conflict would be identified, as long as its flight data features are extracted and fed to a classifier which has been trained by a large number of flight datasets. Based on this, a new method based on support vector machine (SVM) is employed to detect multiaircraft conflict in “Free Flight” airspace and to estimate the conflict probability. For that purpose, the current positions, velocity vectors, and predicted look-ahead time are selected as detection factors, and the detection model is established by SVM to detect aircraft conflict within look-ahead time during short and medium terms. Moreover, conflict probabilities are determined by the sigmoid function mapping method. Nevertheless, false alarm rate is always a first and foremost problem that troubles air traffic controllers. For the purpose of reducing false alarm rates, Synthetic Minority Over-sampling Technique (SMOTE) method is used to handle imbalanced datasets. Extensive simulation results are presented to illustrate the rationality and accuracy of this method.

#### 1. Introduction

Nowadays, the demand for air travel continues to grow at a rapid rate with air traffic becoming more and more complex. In this case, collision avoidance (CA), whose task is to maintain a separation between aircraft in air traffic management (ATM), is challenged by increased flight flow. In future, a number of automated decision support technologies, such as Conflict Detection and Resolution (CDR), will be required to enable continued provision of safe and efficient services in increasingly congested skies. Particularly in Free Flight, pilots will have the freedom to choose their trajectory and speed in real time to maximize their flight objectives while maintaining safe separation from neighboring traffic [1], therefore, seeking a fast conflict detection method in Free Flight, which is suitable in both the terminal areas and en-route areas, is extremely significant.

Conflict prediction is based on inexact trajectory prediction [2, 3]. Deterministic trajectory of an aircraft is influenced by a large number of parameters, particularly due to the wind and also due to the tracking, navigation, and control error, making the trajectory prediction inexact, and random patterns have to be considered. That makes conflict detection become a probability problem, and a number of conflict detection methods based on stochastic process have been proposed. Russel et al. [4] presented a method to estimate mid-term conflict probability of a pair of aircrafts for level flight; in his paper, a coordinate transformation was used to derive an analytical solution. They extended this method to nonlevel flight in [5]. Hu [6] proposed a short-term conflict detection algorithm based on Brownian motion (BM) for level flight. D. Li [7] used J. Hu’s [6] algorithm and improved the algorithm to reduce the rate of false alarms. Jilkov et al. [8] proposed a more accurate method for estimating the conflict probability by utilizing the information from multiple model aircraft trajectory prediction. However, previous work on multiaircraft conflict detection in Free Flight is still rare. It is shown in H. Blom’s research [9] that the interacting particle system (IPS) algorithm is efficient when more complex air traffic scenarios and more advanced conflict zones have to be taken into account. Damien Jacquemart et al. [10] proposed an adaptive algorithm to significantly increase the convergence rate. Moreover, some hierarchical IPS algorithms proposed in research are considered for Free Flight modeling described by advanced stochastic Petri nets [11]. In 2013, Damien Jacquemart [12] also used Markov chain model to simulate aircraft trajectories and applied the important splitting method to estimate conflict probabilities to overcome the flaw of Monte Carlo method which is not efficient to estimate small probabilities. In 2015, Qiao et al. [13] proposed Hidden Markov model-based Trajectory Prediction (HMTP) method to overcome the difficulty of describing the position and behavior of moving objects in a network-constraint environment. Yang et al. [14] proposed a probabilistic reachability analysis approach. In particular, ellipsoidal probabilistic reach sets are determined by formulating a chance-constrained optimization problem and solving it via a simulation-based method called scenario approach. Conflict detection is then performed by verifying if the ellipsoidal reach sets of different aircraft intersect. Their method gives this paper a great inspiration. However, most of the above methods have a common shortcoming, which is every pair of aircraft conflict detection requires a corresponding trajectory prediction.

Actually, the essence of conflict detection is a two-class classification problem: conflict or nonconflict. In this paper, we introduce SVM to solve the problem of aircraft conflict detection. Support vector machine (SVM) is an excellent two-class classification algorithm, which has been successfully applied in many domains ranging from digit recognition [15] and face recognition [16] to network anomaly detection [17] because of solid theoretical foundation and appealing classification performance. However in air traffic management operation, air traffic controllers (ATCs) expect conflict probability to estimate collision risk and to direct the pilots to avoid the conflicts according to the conflict levels. Standard SVM is a binary classifier: for sample , the output of the SVM, is . Some researchers [18, 19] modified the SVM outputs into posterior probabilities, and this method is widely applied in many areas [20, 21]. The calibrated posterior probabilities still inherit the sparseness of the SVM; moreover, they can provide probabilistic prediction decisions. In this paper, we choose Platt’s method to evaluate the conflict probability. On these bases, aircraft conflict during short-term to medium-term look-ahead time is predicted, which is suitable for the case of uncertain trajectory prediction error in Free Flight. At the same time, conflict probability can be estimated for ATCs to make a quick decision.

The remainder of the paper is organized as follows. In Section 2, some basic theories used in this paper: the SVM classifier, Platt’s probabilistic output, and ellipsoidal protected zone model are introduced. The whole conflict detection process based on SVM is presented. In Section 3, trajectory prediction model based on Brownian motion is introduced to simulate different flight scenarios. Conflict detection experiments on these scenarios are worked out to verify the proposed method. Finally, we conclude in Section 4.

#### 2. Probabilistic Conflict Detection Model Based on SVM

##### 2.1. SVM Classifier

Support Vector Machine is a statistical learning method with a good performance [22–27]. Given a dataset in the form of , standard SVM for the binary classification problem maps the feature vector into a high (possibly infinite) dimensional Euclidean space, , using a nonlinear mapping function : . The goal of support vector machines is to find the optimal separating hyperplane , which maximizes the margin, and it can be obtained by solving the convex optimization problem:over , , and the nonnegative slack variable . In the above, is a parameter that balances the size of and the sum of . It is well known that the numerical computation of Problem (1) is achieved through its dual formulation. Suppose is the Lagrange multiplier corresponding to the inequality, then the dual of (1) can be shown to bewhere the kernel function andWith (3), the expression of the hyperplane can be changed intoand serves as the decision function. The predicted class can be defined asThe predicted class is +1 if and -1 otherwise.

##### 2.2. Platt’s Probabilistic Output

Air traffic controllers (ATCs) expect conflict probability to estimate collision risk; however, standard SVM produces an uncalibrated value that is not a probability. Platt [18] came over this shortcoming and mapped into through sigmoid function, providing probabilistic information from standard SVM output. Suppose and are the numbers of positive () and negative () samples, respectively, in dataset* D*. The Platt’s probability output [28] iswhere is the SVM output given by (4) and the parameters* A* and* B* are found by minimizing the negative log likelihood of the training data, which is a cross-entropy error function, in the form ofwith if and if . Hereafter, refers to the estimated posterior probability belonging to class +1 given obtained from (7), while refers to the true but typically unknown posterior probability belonging to class given .

##### 2.3. Ellipsoidal Protected Zone Model

The SVM needs training samples to establish the detection model. To identify the potential conflicts, ellipsoidal protected zone is introduced. In Free Flight, aircrafts are surrounded by an imaginary cylindrical volume called the protected zone (PZ). The radius of the PZ is half (2.5 NM) the required horizontal separation standards and the height is equal to the vertical separation (1000 ft). The two aircrafts are said to be in conflict if their PZs overlap. In this paper, an imaginary cylindrical volume is replaced by an ellipsoidal-shaped conflict volume [29, 30], which can be shown in Figure 1.