In general, commercial UAVs have some essential sensors implemented for their avionics. These is at least an IMU, i.e., gyroscopes, accelerometers and magnetometers to measure the attitude, as well as a GNSS system to determine the position. The flight controller (or autopilot) processes the measured data for either stabilizing the UAV to hold the position in hover state (together with the data from the GNSS) or flying predefined trajectories. Actuator outputs of the autopilot are the rotor speeds.

For our purpose of wind field measurements with a fleet of UAVs in the ABL, we chose the Holybro QAV250 quadrotor frame in combination with the Pixhawk^® 4 Mini flight controller as shown in Fig. . This system has multiple advantages and meets most of the requirements that were defined.

All raw output data of the IMU should be accessible, which requires an open-source solution such as the Pixhawk flight controller and the PX4 software. With the PX4 software, the raw sensor data are available at 100 Hz. For wind measurement, we average the data to 1 Hz in this study. The selection of an open-source solution has the further advantage that the system allows software adjustment and the possibility of implementing additional sensors.

Choosing a quadrotor before multirotors with more than four rotors has several advantages such as easy kinematics, smaller frame sizes and price. Nevertheless, there are disadvantages such as the safety issues in case of motor failure, as flying with three remaining rotors is not possible. Furthermore, the ability to respond to side wind could be smoother and more defined for hexa- or octocopters. Furthermore, the potential payload is typically higher for multirotors with more than four rotors, but since we are not planning to add heavy payloads to the system, we do not consider that relevant for our purpose.

In addition to the onboard sensors of the flight controller, a temperature and humidity sensor of type HYT271 is integrated in every quadrotor. Specifications of the sensors are listed in Table  in the Appendix. Fleet communication is realized by a Wi-Fi router to which all quadrotors and the ground station computer are connected. The important system parameters are listed in Table .

We will refer to the fleet of Holybro QAV250 quadrotors as the SWUF-3D (Simultaneous Wind measurement with Unmanned Flight Systems in 3D) fleet corresponding to the name of the project.

The Pixhawk 4 Mini autopilot features the PX4 software. Specific parameter settings for the quadrotor are set to optimize flight behavior and to realize fleet flights. In order to align the quadrotor to the wind direction, the “weather-vane” mode is enabled. In that mode, the yaw angle is used as a control variable to minimize the roll angle amplitude, and hence the quadrotor will always face in upwind direction. The minimum roll angle for weather-vane controller to demand a yaw rate is set to 1∘.

Control of the fleet is realized by the software © QGroundControl. QGroundControl is an open-source software developed by the Dronecode Foundation . The current release of the software allows us to control 15 drones simultaneously; however, with minor changes in the source code this number can be increased. This ground station software is used to launch and monitor the fleet. The flight paths are planned a priori in global coordinates and are uploaded to the single quadrotors. This allows complete freedom in the design of possible flight patterns. However, it has to be guaranteed by design that flight paths do not cross and thus no collision of UAVs is possible. All flight data that are logged by the autopilot to the internal SD card can be transferred to the ground station through an interface in QGroundControl.

The motion of the quadrotor can be described by the fundamental mechanic equation of force and moment equilibrium. For the definition of the motion of the system, the frames of reference need to be introduced.

The well-known aerodynamic Rayleigh equation for calculating aerodynamic forces from the wind velocity Vw takes the projected front area A and the dimensionless drag coefficient cd into account. The variation of the density of air can be neglected for the low vertical extent of the flight profiles; it is assumed to be constant (ρ=1.2 kg m-3). 12Fw=ρ2cdAVw2 In a stable hover state, we assume that inertial forces on the left-hand side of Eq. () can be neglected and thus 13Fw,x=mgsin⁡θ. By taking Eq. () into account, Eq. () leads to the following equation for wind speed in the direction the quadrotor is facing: 14ρ2cdAVw,x2=Fw,x15Vw,x=2Fw,xcdAρ. The term cdA is unknown and requires calibration. The drag coefficient and the projected area vary with the attitude of the quadrotor. 16cdA=cd,0A0+f(θ), where cd,0A0 is the drag coefficient and area at zero pitch angle. In this study we assume that the function f(θ) is a linear function.

In order to calculate the wind velocity with the introduced method, the UAVs have to maintain a hover state. In order to evaluate the validity of the assumption of negligible linear and angular motion, we can look at the variance of the measured positions from GNSS data. The mean horizontal standard deviation of horizontal movement over all 76 flights of the campaign for all quadrotors results in σp,h=0.19 m. The vertical stability appears to be slightly lower with σp,v=0.85 m. These measured standard deviations are within the accuracy of the GNSS measurement, which is estimated to be of the order of ϵh=0.6 m in the horizontal direction and ϵv=0.8 m in the vertical direction by the avionic system. This means that actual movements can be slightly larger than the measured standard deviations but are still very small. These findings are also confirmed by visual inspection of the flights.

In the first step, each quadrotor is calibrated individually against the reference with all drone tower flights. Besides the determination of the parameters cd,0A0 and cp, an offset for the pitch angle is introduced as Δθ. This is necessary because of misalignment in the installation of the IMU in the quadrotor frame and slight differences in the mass distribution of the individual systems. Once the offset is calibrated it is applied to the measured pitch angle before any further processing. The pitch offset is obtained from the following calibration of the wind speed with the reference anemometer measurements. The optimal calibration function is obtained by solving a defined nonlinear least-squares problem. In particular, bounds were defined and the minimization was performed by the trust region reflective algorithm . The bounds were chosen in order to guide the minimization in physical plausible values. The resulting wind speed for this calibration is plotted in Fig. . One single data point represents the time-averaged wind speed of a single flight of one quadrotor in comparison to the corresponding average of the tower reference measurement. Due to some technical issues with quadrotor no. 4, it is not taken into consideration in the further calibration procedure. The root-mean-square deviations (σrms) of the calculated wind speed against the reference as well as a bias (ΔVw) are determined from all single flights for the individual quadrotors and listed in the left column of Table . In the present case the calibration dataset is equal to the validation data; therefore, the deviation is expected to be relatively small, and remaining differences include the atmospheric variability in mostly convective ABLs. For this calibration, the averaged bias between quadrotor wind speed measurements and the reference wind speed is ΔVw<0.01 m s-1. The random deviation for time-averaged data is σrms=0.23 m s-1 on average over all flights. The accuracies of each UAV are listed in Table . This kind of calibration with many flights in different conditions and individual coefficients for each UAV is considered the best possible calibration and the benchmark for more simplified calibration procedures with reduced calibration datasets and calibration parameters that are common for the whole fleet.

The aim of the study is to implement a robust calibration for a large number of UAVs in a fleet. In a large number of drones it will not always be possible to obtain as many calibration flights. Quadrotors of the same build should however have very similar aerodynamic characteristics. In order to achieve this requirement, one common set of parameters cd,0A0 and cp with sufficiently reasonable accuracy for all regarded quadrotors shall therefore be determined in this section. Only the pitch offset remains as an individual calibration parameter for each quadrotor. By using the dataset of 34 flights the following function is obtained by taking the mean of the parameters of all quadrotors to minimize the overall error (Eq. ). 18cdA=0.03-0.047×θ Figure  demonstrates that the obtained curve fits well with the individual data points of all quadrotors. The result of the calibration with common parameters is shown in the right column of Table . In comparison to the individual calibration, the accuracy is still reasonably high (σrms=0.25 m s-1). The obtained value for cd,0A0 is in the range of the expected value as it would be calculated from an approximated surface area A≈0.25⋅0.05 m2 and the drag coefficient of a long flat plate cd=2. Estimation of the constant parameter cd,0A0 from these parameters leads to a value of 0.025 m2. Of course, the drag coefficient and surface area of the quadrotor with running rotors can not be measured this simply, which is why the calibration is considered necessary. Comparing this result with the mentioned studies in literature (see Introduction), different functions were obtained for the relation between wind speed and quadrotor attitude. In our study the relation is more complex but could roughly be described as a root function.

Having established aerodynamic parameters which appear to be universally applicable to the SWUF-3D fleet, it is still necessary to calibrate the pitch offset Δθ for each individual quadrotor. In this section, we evaluate how many calibration flights are necessary and how stable the calibration is, i.e., how large the errors grow if only fewer calibration flights are used. First, the full dataset of 34 flights is used to determine Δθ. Then, different calibration scenarios are performed with the present dataset, and the related rms deviations in comparison to the tower measurements are calculated. In order to use a common validation dataset, only drone tower flights of the second week (see Table ) are used to calculate rms deviations and wind speed bias. Four different calibration scenarios were performed. a.

All 34 drone tower flights are used to estimate individual values of Δθ. This should yield the best results for the accuracy estimation.

Additionally to the magnitude of the wind speed, the wind direction is obtained from the quadrotors. As mentioned in Sect. , the quadrotors were operated in weather-vane mode. Hence, the quadrotor is automatically yawed in the direction of the wind. Therefore, the corresponding wind direction can directly be obtained from the yaw angle ψ. Nevertheless, the magnetometer is not always perfectly oriented towards north and calibration deviations can occur, which makes an offset calibration of the yaw angle necessary. For this purpose, the same two flights as for the wind speed calibration are used (i.e., flight no. 31 and no. 56). The offset yaw angle ranges between Δψ=-2∘ and Δψ=22∘. The calibrated average wind direction for the drone tower flights of the second week is plotted in Fig. . The mean rms deviation results in σrms,ψ=7.5∘. The few outliers can be explained by low wind speed conditions, when roll angles above 1∘ are hardly reached and the weather-vane mode does not always correct the yaw angle fully into the wind direction.

The drone tower flight pattern which was also used for calibration is suitable for measurements of vertical profiles with the quadrotors. As an example, we present flights no. 61 and no. 62 (without UAV no. 4) of the campaign since they feature shear and some gustiness in the wind field and were performed in close succession. In Fig. a, only the quadrotor at 90 m is compared to the corresponding sonic measurement at the same height. It is evident from this plot that not only the 10 min averaged values are in good agreement with the reference instruments, but also the resolved time series of wind speed matches the sonic anemometer data very well. The variance of the velocity fluctuation of the 1 Hz data of the quadrotor σv,q2=1.76 m2 s-2 is thus in good agreement with the sonic data σv,s2=1.65 m2 s-2 for this particular case. However, some outliers occur in the time series plot in Fig. a. In this particular case at 13:40 UTC, the sonic anemometer data show high vertical wind up to 3.5 m s-1 that causes lift at the UAV, which leads to an increased altitude. In order to sustain the vertical position, the motor thrust is reduced to descend the UAV to the target altitude. To stabilize the descent, the pitch angle is controlled to a more horizontal position. This causes an underestimation of the wind speed due to small pitch angle. The same situation applies at 13:16 UTC, where UAV measurements also underestimate the reference wind speed. Figure b and c show the time series of the vertical profile for cup anemometers on the mast and seven quadrotors respectively. The data from the cup anemometers are only available as 1 min average values, which is why the complete met-mast data are shown in the contour plot with a resolution of 1 min and thus significantly less structure in the flow field is seen compared to the SWUF-3D fleet. Nevertheless, periods of higher wind speeds and stronger shear are present and match well between SWUF-3D and mast. To show the shear profile more clearly, Fig.  gives the averaged vertical profiles for the two 10 min periods. The differences between UAVs and mast measurements are of the same order as the previously determined rms deviations.

With the 1 Hz resolution of the quadrotor measurements, a significant part of the turbulent fluctuations can theoretically be resolved. In order to evaluate the capability to measure wind speed variance, we compare all flights at 50 and 90 m with the corresponding sonic anemometers. Figure  shows the scatterplot of this comparison. The mean rms deviation of the variance is σrms,σ2=0.37 m2 s-2. Given the convective nature of the ABL in which most of the flights were performed, we consider the agreement satisfactory. Further detailed analyses of the scales that are resolved with the quadrotor are out of the scope of this study and will be handled in a separate study.

The long-range lidar was used for further validation of the possibility to resolve horizontal structures in the atmospheric boundary layer with the SWUF-3D fleet. In one scenario, the lidar was set to measure continuously at a fixed elevation (7∘) and azimuth angle (280∘). Eight quadrotors were placed along the line of sight in the same spacing as the range gate separation of the lidar, which was set to 20 m with the closest range gate 80 m from the lidar (see also Fig. ). As the lidar is measuring with a nonzero elevation angle, there is a height difference of 18 m between the position of the first range gate at 10 m a.g.l. (meters above ground level) and the last range gate at 28 m a.g.l. Figure  shows the comparison of the time series of the interpolated horizontal line. It is evident how both measurement systems measure the same variations in wind speed. A significant gust occurred at 13:27 UTC for example, which is observed with both systems. The lidar measurements show smoother gradients in wind speed variations along the line of sight which can be attributed to the volume averaging effect that is inherent to the method and can also explain the lower maximum values of the lidar measurements.

In order to evaluate the performance of the UAV fleet to measure wind fields and their spatial distribution, flights were performed in a 3 × 3 grid, in the measurement plane of a lidar RHI (range–height indicator) scan. Figure  shows the resulting time series of one 10 min flight. The lidar data are linearly interpolated to the quadrotor location, and the horizontal wind component is reconstructed by division through the cosine of the elevation angle (vh=vrcos⁡ϕ). The 1 Hz quadrotor data points are centered at the time when the lidar beam crossed the quadrotor location and the wind component in line with the RHI plane was calculated from quadrotor wind speed and wind direction. It shows that the main features of the flow are captured similarly with a quadrotor and lidar. At the location of the central quadrotor, the lidar showed some hard target reflections that were probably caused by the quadrotor and lead to some gaps in the data for this location. As for the previous validation measurements, a good agreement with the reference system is found with deviations between quadrotor and lidar that are of the order of the previously determined accuracies. This example gives some confidence that spatial structures can be well captured with the SWUF-3D fleet even though the convective nature of the ABL in this experiment is extremely challenging for a direct comparison to the reference instruments.