In recent years, the application of civil drones has expanded rapidly across various sectors, including agriculture, surveillance, emergency response, and environmental monitoring. As these unmanned aerial vehicles become integral to critical operations, assessing their flight performance through precise trajectory measurement is essential for ensuring safety, efficiency, and compliance with industry standards. This article delves into the methodologies for evaluating key flight trajectory parameters—specifically, path control accuracy, altitude stability, and maximum level flight speed—for civil drones. By leveraging advanced measurement techniques and conducting empirical experiments, I aim to provide a comprehensive framework for accurate performance assessment, highlighting challenges and proposing improvements for future testing protocols.
The proliferation of civil drones in diverse fields necessitates robust evaluation methods to quantify their flight characteristics. Flight trajectory parameters serve as critical indicators of a drone’s navigation and control systems, directly influencing operational safety and task effectiveness. For instance, path control accuracy reflects the drone’s ability to follow predefined routes, which is vital for applications like precision agriculture or infrastructure inspection. Similarly, altitude stability and maximum speed are pivotal for missions requiring consistent performance under varying environmental conditions. In this study, I focus on civil drones, employing a combination of global navigation satellite systems (GNSS) and inertial measurement units (IMU) to achieve high-precision trajectory data. The integration of these technologies allows for real-time kinematic (RTK) and deep coupling approaches, enhancing measurement reliability even in challenging environments.
To establish a foundation for trajectory measurement, it is essential to understand the underlying principles. Traditional methods, such as photoelectric theodolite tracking, involve ground-based instruments that calculate position using azimuth, elevation, and slant range measurements. For example, the coordinates (X, Y, Z) in a local coordinate system can be derived as follows: $$ X = R \cos E \cos A $$ $$ Y = R \sin E $$ $$ Z = R \sin E \cos A $$ where R is the slant range, E is the elevation angle, and A is the azimuth angle. However, this method often requires multiple stations for cross-bearing measurements, leading to complexities in setup and susceptibility to environmental interference, especially for small civil drones.
In contrast, GNSS-based techniques, particularly RTK, offer a more scalable solution for civil drone trajectory measurement. RTK utilizes carrier phase differentials to achieve centimeter-level accuracy by mitigating errors such as ionospheric delays and clock biases. The fundamental equation for carrier phase observation is: $$ \Phi^{(s)}_u = \lambda^{-1} \left[ r^{(s)}_u + I^{(s)}_u + T^{(s)}_u \right] + f \left[ \delta t_u – \delta t^{(s)} \right] + N^{(s)}_u + \epsilon^{(s)}_{\phi u} $$ Here, \( \Phi^{(s)}_u \) represents the carrier phase measurement, \( \lambda \) is the wavelength, \( r^{(s)}_u \) is the geometric distance, \( I^{(s)}_u \) and \( T^{(s)}_u \) are ionospheric and tropospheric delays, \( \delta t_u \) and \( \delta t^{(s)} \) are receiver and satellite clock errors, \( N^{(s)}_u \) is the integer ambiguity, and \( \epsilon^{(s)}_{\phi u} \) is noise. Through single and double differencing, these errors are minimized, enabling precise relative positioning for civil drones. For instance, the double-difference equation simplifies to: $$ \Phi^{(ij)}_{br} = -\lambda^{-1} ( \mathbf{l}^{(j)}_b – \mathbf{l}^{(i)}_b ) \cdot [x_r – x_b \quad y_r – y_b \quad z_r – z_b]^T + (N^{(j)}_{br} – N^{(i)}_{br}) + (\epsilon^{(j)}_{\phi br} – \epsilon^{(i)}_{\phi br}) $$ This enhances the accuracy of trajectory data for civil drones, making RTK a preferred method in many applications.
To address issues like signal occlusion or interference, deep coupling of GNSS and IMU technologies provides a resilient solution. This integration corrects inertial navigation system (INS) errors using GNSS data while aiding satellite signal acquisition through IMU-derived predictions. The deep coupling mechanism ensures continuous and reliable trajectory measurement for civil drones, even in adverse conditions. A schematic representation of this process involves feedback loops where GNSS signals refine IMU outputs, and vice versa, resulting in a robust system capable of maintaining high accuracy during dynamic flights of civil drones.
In designing the measurement setup for civil drones, I employed a lightweight, high-precision trajectory acquisition device weighing approximately 72 grams, which minimizes impact on the drone’s performance. The core components include a GNSS-RTK module and an IMU operating in deep coupling mode, with data sampled at 10 Hz. This setup is versatile enough to accommodate various civil drone types, such as multi-rotor and vertical take-off and landing (VTOL) fixed-wing models. The measurement environment was selected to ensure open spaces with minimal obstacles and electromagnetic interference, adhering to short-baseline RTK conditions for optimal accuracy. For instance, experiments were conducted in regions like the Nagqu area of Tibet and the Hutuo River in Shijiazhuang, where baseline coordinates were calibrated to WGS84 standards with sub-centimeter precision.
Statistical methods for evaluating trajectory parameters are crucial for objective assessment. Path control accuracy, denoted as \( \sigma_R \), is computed based on deviations from predefined paths. For linear segments, the deviation \( \Delta R_i \) is given by: $$ \Delta R_i = \frac{a N_i + b E_i + c}{\sqrt{a^2 + b^2}} $$ where \( a, b, c \) are parameters of the line equation, and \( N_i, E_i \) are the north and east coordinates in a local frame. For circular paths, the deviation is: $$ \Delta R_i = \sqrt{(N_i – N_0)^2 + (E_i – E_0)^2} – R_0 $$ with \( N_0, E_0 \) as the circle center and \( R_0 \) as the radius. The root mean square (RMS) path accuracy is then: $$ \sigma_R = \sqrt{\frac{1}{n} \sum_{i=1}^n \Delta R_i^2} $$ Altitude stability, \( \sigma_U \), is derived from height deviations: $$ \Delta U_i = U_i – U_{\text{set}} $$ $$ \sigma_U = \sqrt{\frac{1}{n} \sum_{i=1}^n \Delta U_i^2} $$ where \( U_{\text{set}} \) is the target altitude. Maximum level flight speed, \( v_{\text{max}} \), is determined by averaging the peak ground speeds from multiple flight segments, reducing wind-induced biases.
Experiments involved testing several civil drone prototypes, including a six-rotor industrial model, a four-rotor consumer-grade unit, and two VTOL fixed-wing drones. Flight trajectories were programmed or manually controlled to include patterns like circles, straight lines, and hover phases. For example, the six-rotor civil drone followed a path combining circles and折线, while the VTOL fixed-wing models executed long-distance往返 or large-radius circles. Data collected from the onboard measurement system were processed using post-processing software to extract precise trajectory information. The results were then analyzed to compute the key parameters, as summarized in the table below.
| Civil Drone Model | Path Control Accuracy, \( \sigma_R \) (m) | Altitude Stability, \( \sigma_U \) (m) | Maximum Level Flight Speed, \( v_{\text{max}} \) (m/s) |
|---|---|---|---|
| Six-Rotor Industrial Civil Drone | 1.80 | 0.29 | 10.92 |
| Four-Rotor Consumer Civil Drone | 0.07 | 0.04 | 15.57 |
| VTOL Fixed-Wing Civil Drone 1 | 0.81 | 3.52 | 27.13 |
| VTOL Fixed-Wing Civil Drone 2 | 3.31 | 6.76 | 24.06 |
The analysis reveals that multi-rotor civil drones generally exhibit superior path control and altitude stability compared to fixed-wing variants, owing to their hover capabilities and stabilization algorithms. For instance, the four-rotor civil drone achieved a path accuracy of 0.07 m and altitude stability of 0.04 m, attributed to its laser-based height sensor. In contrast, VTOL fixed-wing civil drones showed larger deviations due to higher speeds and aerodynamic sensitivities, with path accuracy up to 3.31 m and altitude variations reaching 6.76 m. Speed assessments indicated that fixed-wing civil drones attain higher maximum speeds (e.g., 27.13 m/s) than multi-rotor models, aligning with their design for endurance and coverage. These findings underscore the importance of selecting appropriate measurement techniques tailored to the specific characteristics of civil drones.
Despite the advancements, several challenges persist in trajectory measurement for civil drones. Route planning discrepancies arise from inherent errors in ground station maps, which, if uncalibrated, can lead to significant deviations and safety risks during testing of civil drones. Additionally, the installation of measurement equipment on civil drones must account for weight and aerodynamic effects; even minor additions can alter the center of gravity and introduce uncertainties. This is particularly critical for consumer-grade civil drones with limited payload capacities. Furthermore, the reference truth value for trajectory data relies on measurement instruments with精度 that must exceed the drone’s specified accuracy by a factor of three or more. However, as civil drones achieve centimeter-level claims, current RTK technologies—with optimal accuracy of ±(12 + 1×D) mm, where D is the baseline length in km—may fall short, necessitating further research into enhanced reference systems for civil drones.
To illustrate the impact of these factors, consider the uncertainty in height measurements for civil drones. The combined standard uncertainty \( u_c \) can be modeled as: $$ u_c = \sqrt{u_{\text{GNSS}}^2 + u_{\text{IMU}}^2 + u_{\text{inst}}^2} $$ where \( u_{\text{GNSS}} \), \( u_{\text{IMU}} \), and \( u_{\text{inst}} \) represent uncertainties from GNSS, IMU, and installation effects, respectively. For civil drones, minimizing these uncertainties requires rigorous calibration and environmental controls.
In conclusion, this study demonstrates the efficacy of GNSS-RTK and deep coupling technologies for measuring flight trajectory parameters in civil drones. The experimental results validate the quantifiability of path control accuracy, altitude stability, and maximum speed, providing a reliable basis for performance evaluation. Future work should focus on addressing the identified issues, such as improving map calibration techniques and developing lighter measurement systems, to enhance the accuracy and applicability of trajectory assessment for civil drones. As the adoption of civil drones continues to grow, refining these methodologies will be crucial for ensuring safe and efficient operations across various industries.
The evolution of civil drone technology demands continuous improvement in testing protocols. By integrating advanced sensors and algorithms, we can overcome current limitations and achieve more precise trajectory measurements for civil drones. This will not only bolster safety standards but also unlock new possibilities for civil drone applications in complex environments. Ultimately, a standardized approach to flight performance evaluation will foster innovation and trust in the burgeoning civil drone market.