# An RTK UAV-Based Method for Radial Velocity Validation of Weather Radar
## 2 Materials and Methods
### Time Synchronized Radial Velocity Comparison between the UAV and the Radar  
When the UAV is in a stable state of motion, its radar cross-section tends to remain constant, indicating minimal fluctuations in radar intensity values within a narrow range. When affected by environmental factors such as ambient winds, the three Euler angles of the UAV can be disturbed. It caused changes in the effective radar cross section, which is exposed to electromagnetic waves, resulting in abrupt numerical changes in radar intensity. Therefore, this approach uses the maxima stable dBZ value of the UAV as a reference criterion for selecting radar-validated data. At the same time, the reference values for the UAV velocity are synchronously selected based on the time of the validated data.  
The radar system records the velocity values of the UAV during both stationary hover and constant motion along the radar radial direction. A comparison is then made between these recorded velocities and the reference values of the UAV velocity. This paper refers to the evaluation method of validation for point targets and analyzes the results according to two validation criteria: relative accuracy and absolute accuracy. The relative accuracy of the velocity validation results is assessed based on the standard deviation of the radar-measured values of the UAV velocity [15; 19; 20].  
\[\Delta R=\sqrt{\frac{\Sigma\left(V_{Ri}-\overline{V_{R}}\right)^{2}}{N-1}} \tag{15}\]  
The equation defines \(\Delta R\) as the relative validation accuracy, \(V_{Ri}\) as the radar-measured velocity, \(\overline{V_{R}}\) as the average radar-measured velocity, and \(N\) as the number of valid data points.  
Theoretically, absolute validation accuracy is typically used to explain the absolute differences between measured and reference values. The absolute validation accuracy of the radial velocity is determined by taking the difference between the radar velocity values obtained from the base data and their reference values, using the maximum absolute value of these differences as an indicator [15].  
\[\Delta A=Max\{|V_{Ri}-V_{i}|\} \tag{16}\]  
Considering that the absolute accuracy indicators are currently used mainly for satellite or airborne SAR, theoretically, the validation results could not be affected by reference targets fixedly deployed on the ground. However, a weather radar is ground-based, and the reference target can only be an airborne target such as a UAV, and as such, it will inevitably be subject to interference caused by the instability of the moving target itself. Moreover, the UAV velocity reference values are derived from the average velocity based on RTK position information, so its proximity to the instantaneous velocity is related to the frequency of positioning updates and the stability of the UAV flight state. To reduce the impact of internal and external environmental factors on the UAV velocity stability, this study, based on valid data pairs, uses the minimum deviation between measured and reference values as the optimal absolute accuracy for validating radar radial velocity.  
\[\Delta OA=Min\{|V_{Ri}-V_{i}|\} \tag{17}\]  
where \(\Delta OA\) is the optimum absolute accuracy, \(V_{Ri}\) is the radar-measured velocity values, and \(V_{i}\) is the time-synchronized UAV velocity reference values.