## 2 Materials and Methods
### Air Quality Data Correction Model  
The movement of UAVs can induce airflow disturbances, affecting the accuracy of sensor data. To mitigate these errors, this study employs a motion compensation algorithm based on an Inertial Navigation System (INS), complemented by a Backpropagation (BP) neural network for sensor data correction. The INS integrates gyroscopes, accelerometers, and high-precision GPS to provide real-time motion state information of the UAV, including velocity, acceleration, and rotation angles. Specifically, the BP neural network was employed to correct the disturbances in air quality measurements caused by the UAV's airflow during flight. These disturbances arise from the complex and hard-to-quantify air currents generated by the UAV's movement. Given that airflow is closely tied to the UAV's dynamic behavior, we utilized internal flight data, capturing nine motion indicators: velocity and acceleration in the x, y, and z directions, as well as roll, yaw, and pitch angles. The relationship between these motion parameters and the resulting sensor errors is highly non-linear, making it difficult to model using traditional physical approaches. Therefore, we selected the BP neural network for its robustness in handling non-linear relationships and its proven effectiveness in correcting measurement errors caused by external disturbances like airflow [20,21]. The BP neural network is particularly suited for this task because of its ability to model and learn the intricate dependencies between UAV motion and data distortions, thus enhancing the accuracy of the air quality measurements. The network operates in two phases--forward propagation and backpropagation--continually optimizing its performance. During forward propagation, information flows smoothly from the input layer through the hidden layers to the output layer. In backpropagation, information flows in reverse to adjust network parameters, including weights (w) and biases (b), to achieve optimal prediction results. This operational process is distinctly divided into two phases, as depicted in Figure 2.  
The core structure of this system consists of input, hidden, and output layers (as illustrated in Figure 3). In this study, the correction model specifically considers nine input factors: roll angle, yaw angle, and pitch angle, as well as velocities and accelerations in the x, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Category**} & **Measurement Resolution** & \multirow{2}{*}{**Measurement Range**} & \multirow{2}{*}{**Measurement Accuracy**} \\ \hline CO\({}_{2}\) & 1 ppm & 400–5000 ppm & \(\pm\)3\% \(\pm\) 50 ppm or \(\pm\)10\% \\ PM\({}_{2.5}\) & 1 ug/m\({}^{3}\) & 0–999 ug/m\({}^{3}\) & \(\pm\)10\% or \(\pm\)10 \\ Temperature & 0.01 \({}^{\circ}\)C & \(-\)40–100 \({}^{\circ}\)C & \(\pm\)1 \({}^{\circ}\)C \\ Humidity & 0.04\% & 0–100\% & \(\pm\)3\%RH \\ PM\({}_{2.5}\) & 1 ug/m\({}^{3}\) & 0–999 ug/m\({}^{3}\) & \(\pm\)10\% or \(\pm\)10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The specific parameters of sensors carried by the unmanned aerial vehicle (UAV). Figure 2: The BP neural network model. The network uses weights (W), biases (b), and activation functions (indicated by curved lines) to process the input data. The “+” symbol denotes the summation operation in each layer. y, and z directions. The output layer is responsible for providing corrected values of various air quality indices, which will be used for the dynamic correction of measured values. For the UAV motion parameters used here, there are two main sources. * Regarding acceleration and tilt angle, they come from the IMU sensor inside the flight control, specifically the following model: ICM-42688-P (TDK InvenSense, Tokyo, Japan). The main characteristics are listed in Table 2.  
* The velocities in the x, y, and z directions come from the GPS carried by the aircraft, specifically signaled as with the Holybro M9N GPS (Holybro, Shenzhen, China), and the main characteristics are listed in Table 3.