# Tilt-Induced Error Compensation with Vision-Based Method for Polarization Navigation
## 5 Conclusions  
This paper proposes a method to estimate the UAV's horizontal attitude angle using horizon computation, aiming to compensate for significant heading errors in polarized light navigation under tilted conditions. Firstly, a dehazing-enhancement method integrating Retinex theory and dark channel prior is proposed, improving the algorithm's adaptability under low illumination and hazy conditions. Secondly, an HSV-based dynamic threshold image segmentation method is developed, significantly enhancing the robustness of horizon extraction. Then, an improved adaptive bilateral filtering Canny operator is employed for edge detection, which not only detects fine edges but also effectively suppresses noise. Finally, the progressive probabilistic Hough transform is employed for line extraction, substantially reducing computational complexity and memory requirements. Subsequent to horizon extraction, the horizontal attitude angle of the UAV is calculated from the horizon parameters. Sensor measurements are converted from the body frame to the navigation frame using coordinate transformation, thereby compensating for polarized light heading errors. Airborne experiments are conducted to validate the efficacy of the suggested method. The experimental results show that the horizontal attitude angle estimation method based on the horizon in this paper has high accuracy. Furthermore, the implementation of the polarization orientation error compensation method proposed in this paper substantially improves the course accuracy and effectively mitigates errors.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **RMSE (\({}^{\circ}\))** & **STD (\({}^{\circ}\))** & **Mean (\({}^{\circ}\))** \\ \hline pre-compensation & 5.0869 & 5.0633 & 0.5005 \\ post-compensation & 1.1485 & 1.1441 & \(-\)0.1039 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison table of error before and after heading compensation.  
While the proposed algorithm achieves high accuracy, it possesses specific limitations. Firstly, in urban or densely forested areas, the horizon is often occluded, causing failure in vision-based horizontal attitude angle estimation. Secondly, horizon detection relies on computationally intensive image processing algorithms, complicating the fulfillment of real-time requirements. Additionally, when the UAV undergoes large roll or pitch angles, errors in the polarized light heading compensation model increase significantly, degrading compensation performance. Future research might involve multi-source sensor fusion for attitude estimation to reduce reliance on single-source visual information while optimizing image processing algorithms to enhance real-time performance. Additionally, the polarized light heading compensation model requires refinement to improve stability under large-angle conditions.  
Conceptualization, M.Y. and X.W.; methodology, M.Y.; software, M.Y.; validation, M.Y., X.W. and X.L.; formal analysis, M.Y.; investigation, M.Y.; data curation, M.Y.; writing--original draft preparation, M.Y.; writing--review and editing, M.Y. and X.L.; visualization, M.Y.; supervision, C.W. and X.L.; project administration, C.W.; funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by Key research and development project of Shanxi Province (202202020101002), in part by the Shanxi Province Basic Research Program (202303021211150), in part by the Aviation Science Foundation (202400080U0001), in part by the Shanxi province key laboratory of quantum sensing and precision measurement (201905D121001), in part by the Shanxi Province Graduate Student Innovation Practice Project (2024 SJ244), in part by the Scientific and technological breakthrough of \"Light of the Taihu Lake\" (basic research) (K20241058).  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflicts of interest.