To simulate drone movements, we referred to one of the most popular drones, DJI’s Mavic 2 Pro, as shown in Figure 1. The drone has two types of propellers, clockwise (CW) and counterclockwise (CCW), that are mirror-symmetric to each other. The centers of the propellers were located in a bilateral symmetric structure. In addition, the RCS patterns of a propeller made of carbon fiber and one made of a perfect electric conductor (PEC) are similar [8]. Because the micro-Doppler effects caused by the relative movement of the radar and drone mainly occur in the propeller, only the PEC propeller was modeled to estimate the dynamic RCS. When a drone is hovering, the net thrust of all propellers pushing the drone up must be equal to the gravitational force pulling it down. In other words, all the propellers have identical rotation rates. Ascending (or descending) drones have a higher (or lower) rotation rate than hovering drones. To fly forward, the rear propellers must rotate faster than the front propellers.

Figure 1: 
DJI’s Mavic 2 Pro: (a) overall view and (b) propeller dimensions

By referring to the Robin Radar System ELVIRA, the operating frequency was determined as 9.65 GHz. The RCS and radar return signals were simulated at 9.65 GHz. Furthermore, the propeller’s mesh was divided based on an operating frequency of 9.65 GHz. The propeller length was 20.32 cm, or approximately 6.54λ at 9.65 GHz.

To obtain the dynamic RCS of a moving drone, first, the electric field scattered from the drone with respect to the time step must be simulated. The method of moments (MoM), a numerical analysis technique, is commonly used to accurately estimate the RCS [9]. We adopted the MoM introduced in [10] to simulate the dynamic scattered field because it has a fast computation time. In [11], the results were obtained for each frame using the MoM, which applied a core principle similar to ours, and practically valid results were obtained. As shown in Figure 1 (b), the propeller CAD model is segmented by triangular meshes based on the operating frequency, and the MoM using the Rao–Wilton–Glisson basis function is applied to the propeller meshes to calculate the electric field of a single rotating propeller. The electric field of a single propeller is synthesized into the electric field of multiple propellers using the far-field approximation, as shown in Figure 2. The RCS is defined as

Figure 2: 
Flowchart of the process followed to estimate the dynamic electric field of multiple propellers

where R is the distance between the radar and target, and Eⁱ and E^s are the incident and scattered fields, respectively. Substituting the dynamic electric field into Equation (1) yields the dynamic RCS.

The spectrogram was obtained as a micro-Doppler signature from the dynamic electric field. As shown in Figure 3, first, a window function is applied to the dynamic electric field data, and the fast Fourier transform (FFT) is used to obtain a magnitude spectrum over time. Then, the squared spectrum becomes the spectrogram, which allows for the determination of the rotation rate and approximate magnitude of the micro-Doppler frequency over time.

Figure 3: 
Procedure used to obtain a spectrogram from a dynamic electric field

Finally, for a more realistic dataset, additive white Gaussian noise (AWGN) is added to the dynamic electric field according to various signal-to-noise ratios (SNRs). This results in micro-Doppler signature images with various SNR values.

For the dataset, the elevation angle (θⁱ) was changed from 0° to 90° in 1° step intervals, and the azimuth angle (ϕⁱ) was changed from 0° to 180° in 5° step intervals. A total of 6,552 images were generated for each movement. To account for the noise effect, the AWGN was added to the radar return signal, so that the SNR varied from 0 dB to -15 dB with a -5 dB interval.

CNN transfer learning was used to classify the drone movement using the micro-Doppler signatures of the spectrogram in a supervised manner. The signature images used in this study have corresponding labels to identify the movement to which they are associated. The pre-trained CNN was AlexNet. In the training, stochastic gradient descent with momentum was used as the optimization technique. By considering the number of datasets, training was performed with a MiniBatch size of 64 and an epoch of 10. The initial learning rate was set to 0.01.

Figure 4: 
Coordinate and incident angles for dataset generation

Figure 5 shows the spectrogram of the drone when θⁱ = 90°, ϕⁱ = 180°, and SNR = 0 dB. The x- and y-axes are the micro-Doppler frequency and time, respectively. The upper and lower points in the spectrogram are the points at which the Doppler frequency shift is maximized. The maximum Doppler frequency can be calculated as follows:

Figure 5: 
Spectrogram when the drone is (a) descending, (b) hovering, (c) ascending, and (d) going forward for an SNR of 0 dB

where r is the radius of the propellers, ω is the rotation angular velocity, and λ is the wavelength of the operating frequency. Accordingly, as the rotation rate increases, the length of the propeller and the operating frequency increase. Furthermore, the micro-Doppler frequency increases. The movement of the drone changes according to the rotation rate of the propellers, and various micro-Doppler signatures appear according to the movement. In the case of vertical movement, as the rotation rates of all propellers used in one drone are all the same, components with identical micro-Doppler frequencies superpose and appear strongly in the spectrogram. The descending case had the lowest rotation rate, and showed the smallest micro-Doppler frequency. However, as the rotation rate increased from the descending to hovering movement and from the hovering to ascending movement, the micro-Doppler frequency increased. In addition, when moving forward, as the front and rear propellers have different rotation rates, components with large and small micro-Doppler frequencies appear together. Figures 5 (a), 5 (b), and 5 (c) show that the maximum micro-Doppler frequency increases as the rotation rate increase. Because the propellers of the drone that is moving forward have two different rotation rates, the maximum micro-Doppler frequency is similar to the case of ascending via faster rotating propellers; however, the micro-Doppler signature of the horizontal axis appears more complicated owing to intermodulation by two rotation rates.

As the noise component increases, the spectrograms in Figure 5 change, as shown in Figure 6. Because the dynamic RCS level of the propellers is low, it is difficult to determine the micro-Doppler patterns even with noise of -15 dB SNR.

Figure 6: 
Spectrogram when the drone is (a) descending, (b) hovering, (c) ascending, and (d) moving forward for an SNR of - 15 dB

The drone movement was categorized into four types according to the rotation rate of the propellers: ascending, hovering, descending, and moving forward. A total of 65,520 images were randomly divided into three groups: training images, validation images, and images used to test for transfer learning. The classification performance is summarized in Table 1. When the elevation angle was small (0–1°), the accuracy was less than 60%. As the elevation angle increased, the accuracy increased significantly. The average accuracy for all elevation angles was 98.94%.

If the radar is located directly above or below the drone (θⁱ = 0º), the distance between the radar and propellers is always maintained as constant in the radar direction. Consequently, a micro-Doppler signal is barely generated. These results can be seen in Figure 7.

Figure 7: 
Spectrogram when the drone is (a) descending, (b) hovering, (c) ascending, and (d) moving forward for θⁱ = 0° and ϕⁱ = 180°