## 2 Problem Description  
Anomaly detection (AD) for swarm flights considered in this work involves two decisions: (a) to detect symptom of anomaly of the overall swarm, and (b) to identify which particular drone behaves in an abnormal manner. The anomaly detection scheme makes these decisions by monitoring the time series of the kinematic variables (i.e., position and velocity) of the drones. In particular, this AD scheme lies in the ground station that manages the overall health and flight status of the swarm vehicles; in other words, if implemented in practice, transmitted data from the drones down to the ground station go through the AD scheme to indicate the normality of the flights. This work aims at developing such an AD scheme by learning from the data collected in real flight tests. The swarm flight data on which this work is based was collected via a series of flight tests of swarm drones; this swarm system features the use of real-time kinematic (RTK) global positioning system (GPS)-based precision navigation methods proposed in [42]. The flight test data utilized in this work were obtained from a series of swarm flights completed between 26 April 2018 and 22 June 2018; as many as 30 quadcopter drones were used in these flight tests. About 60 tests were conducted, including individual and several groups of test vehicles. From these test results, data were selected that could be used as learning data suitable for the purpose of detecting abnormal behavior during the performance of a swarm mission. Figure 1 illustrates an example mission of the swarm drones (left) and the RTK-GPS navigation architecture of the swarm system (right). The output data from each flight sortie consists of 248 parameters, and the data are in the form of time series of these parameters some of which include multiple measurements. In this study, the following parameters that are thought to be crucial in monitoring anomalies in motion are chosen: three position coordinates and their set point values, three velocity components of the vehicles, and the vehicle status. The position coordinates (\(x_{a}\), \(y_{a}\), \(z_{a}\)) and the velocity components in three axes are obtained from RTK-GPS measurements whose accuracy was verified in [42]; the set point values (\(x_{s}\), \(y_{s}\), \(z_{s}\)) in three coordinates generated from the mission controller are also considered as anomalies that are likely to be associated with the errors between the desired and the actual behavior in vehicle motion, i.e., the following three terms:  
\[x=x_{a}-x_{s},y=y_{a}-y_{s},z=z_{a}-z_{s} \tag{1}\]  
Accelerometer and gyro reads obtained from the inertial navigation system (INS) are also considered as mechanical defects in drone systems that may typically yield abrupt and unpredictable  
Figure 1: Swarm-drones flight-test and system configuration diagram. behavior in acceleration and angular rates. The vehicle status parameter is included for basic checks for data compatibility and calibration. It should be noted that this work tries to devise an anomaly-detection scheme that is not dependent on the specific type and characteristics of a particular drone; as such, the data is not labeled with vehicle IDs. The characteristics of the parameters used in this study are tabulated in Table 1. The vehicle status variables are used to extract data that are collected during the flight when the navigation state is not \"manual\" and the arming state is \"armed\" indicating every device in the drone is fully powered. The data is collected with a 10 Hz rate. It should be pointed out that these kinematic variables may not be the complete and comprehensive set of variables needed to detect all possible anomalies in swarm flights. However, these are certainly critical variables in detecting anomalies caused by some types of failures and faults. Thus, this work expresses the anomaly detection problem as the detection and identification of abnormal behavior on the basis of kinematic variables, and focuses on such a problem.