## 1 Introduction
Also, these drones are relatively new in the market, compared to long-life large aircraft; as such, the fault modes are not well understood and identified. Therefore, a data-driven scheme that does not explicitly rely on the physics-based model of the vehicles can be a promising solution to anomaly detection of swarm of small-sized drones. Several noticeable studies have been performed to take advantage of data-driven machine-learning techniques for fault and/or anomaly detection of aerial vehicles. A multivariate Gaussian mixture model (mGMM) was proposed to detect and monitor airborne abnormalities in aircraft systems in real time [35], and a recurrent neural networks (RNN) method was proposed to identify events and trends that may reduce safety margins of the system out of the data collected from the flight data recorder (FDR) and/or flight operational quality assurance (FOQA) data [36]. A K nearest neighbor (KNN)-based method was presented to estimate the cause of failure and potential degradation of UAV performance on the fly [37]. Research carried out kernel principal component analysis(KPCA)-based sensor anomaly detection using drone sensor signals [38]. It should be noted that these previous studies mostly dealt with health management of a single UAV; there has not been a systematic machine learning-based methodology proposed to effectively detect anomaly in swarm flights, addressing the aforementioned difficulty in behavior of multiple vehicles. As such, this work presents a learning-based data-driven approach for anomaly detection in swarm flights. The approach primarily tries to tackle the issue of a lack of labeled data in swarm flights, and imbalance in the normal and abnormal data. A sequence of unsupervised learning methods is first applied: a principal component analysis (PCA) [39] procedure first reduces the dimensionality of the time series of flight data, and a \(K\)-means clustering groups the data and label them into four categories--true anomaly, uncertain anomaly, uncertain normal, and true normal. Then, a deep neural network, which is concatenation of a one-dimensional convolutional neural network (1D-CNN) [40] and a multi-layer perceptron for logistic regression, is trained to extract features and to detect anomaly. In general, supervised learning methods have better classification performance than unsupervised methods; a very recent form of self-supervised learning that outperforms the fully supervised method is reported in the context of anomaly detection [41]. While the authors of [41] devised highly sophisticated self-supervised framework that performs best, they also pointed out that the fully supervised method ranks the second by dominating all other unsupervised methods. The present paper is in line with this observation that the supervised learning approach is still a viable top-performing framework if a sufficient amount of labeled data is available and/or appropriate labeling procedure can be accompanied. The proposed method in this paper is tested against real flight data to demonstrate its accuracy in detection of anomaly and also applicability as an online monitoring scheme. The main contributions of this paper are: (a) to propose a systematic procedure of data-driven anomaly detection for swarm flights, and (b) to validate the method against real flight test data.