# Tilt-Induced Error Compensation with Vision-Based Method for Polarization Navigation
## 4 Discussion  
### Validation of Horizon Attitude Estimation Algorithm  
In order to verify the validity and reliability of the horizon attitude estimation method proposed in this paper, an airborne experiment was carried out with a UAV equipped with a high-resolution camera and a polarization camera. In total, 2278 image frames were collected during the flight for analysis and validation. In addition, the IMU-KVH1750 integrated navigation system, with high-precision fiber/satellite, serves as a reference, offering pitch and roll angle accuracy of 0.015\({}^{\circ}\) and heading angle accuracy of 0.035\({}^{\circ}\). The experimental equipment is shown in Figure 8, and the camera parameters are shown in Table 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Parameter** \\ \hline Resolution & 1280 \(\times\) 720 \\ Focus distance (mm) & 3.24 \\ Sensor format (inch) & 1/2.5 \\ Field of view (\({}^{\circ}\)) & 90 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Camera parameters.  
This UAV platform was selected due to its stable flight performance and sufficient payload capacity, allowing for the effective integration of the necessary sensors. Furthermore, its ability to execute diverse tilt maneuvers made it well-suited for testing the proposed tilt-induced error compensation method under realistic dynamic conditions. However, one limitation of this platform is its moderate resistance to environmental disturbances, such as wind gusts, which may introduce additional motion noise.  
The proposed horizon attitude estimation algorithm in this paper is compared with the following methods: traditional horizon attitude estimation approaches, optical flow-based attitude estimation algorithms, isomorphic matrix attitude estimation methods based on SIFT feature points, and reference data. After the UAV completes its flight mission, the attitude estimation results and error curves for all methods are generated using MATLAB R  
The pitch and roll angle attitude estimation results indicate that the isomorphic matrix attitude estimation method based on SIFT feature points exhibits significant systematic bias in both pitch and roll angle calculations, along with pronounced numerical fluctuations. The optical flow-based method displays reduced error fluctuations and superior overall stability compared to the SIFT-based isomorphic matrix approach, though periodic oscillations persist under motion blur interference. The traditional horizon attitude estimation algorithm shows substantial attitude angle deviations at three sampling nodes (609, 1296, and 1668) due to hazy conditions. In contrast, the proposed horizon attitude estimation method achieves optimal accuracy in both pitch and roll angle calculations, with enhanced overall stability, thereby validating the effectiveness of the proposed algorithm.  
Tables 4 and 5 present a comprehensive performance analysis by detailing the Root Mean Square Error (RMSE) and Standard Deviation (STD) of pitch and roll angle estimation errors for each algorithm. As shown in the tables, the proposed attitude estimation method outperforms the other methods in both error metrics.