# Tilt-Induced Error Compensation with Vision-Based Method for Polarization Navigation
[16] employed GRU (Gated Recurrent Unit) neural networks to fuse MARG (Magnetic, Angular Rate, and Gravity) sensor data with optical flow measurements, enhancing the accuracy of 3D attitude estimation. The RMSE (Root Mean Square Error) of roll, pitch, and yaw angles are 1.51\({}^{\circ}\), 2.07\({}^{\circ}\), and 0.87\({}^{\circ}\), respectively. [PERSON] et al. [17] devised a novel straight-line detection method based on deep convolutional neural networks, which improves detection precision with an accuracy of 93.03% on the dataset, while incurring greater computational complexity. [PERSON] et al. [18] proposed a minimal human interaction horizon detection approach with an average computational error within 2 pixels; nevertheless, its performance is vulnerable to image quality degradation and exhibits cumulative error characteristics. [PERSON] et al. [19] enhanced optical flow sensors using a gimbal stabilization system, achieving robustness through sliding mode control at the cost of introducing high-frequency vibrations and demanding strict hardware stability requirements. While each of these solutions has distinct advantages, they all present significant limitations in practical deployment scenarios. In contrast, horizon detection methods establish an absolute horizontal reference for attitude estimation by recognizing the physical boundary between the sky and the ground. This approach inherently displays superior robustness against textureless environments and dynamic disturbances. Consequently, our study adopts this horizon-based methodology for the estimation of UAV horizontal attitude angles. Early studies on polarized light navigation primarily concentrated on orientation under horizontal conditions, neglecting the impact of tilt on navigation accuracy [20]. The growing demand for dynamic navigation in mobile platforms like UAVs and ground robots has made tilt-induced polarization angle error correction a critical bottleneck limiting the practical application of polarized light navigation technology. Consequently, developing efficient and robust methods for rectifying tilt-induced errors in polarized light is crucial for enhancing the practicality and reliability of polarized light navigation systems. [PERSON] et al. [21] addressed the solar meridian ambiguity problem by using a biologically constrained sensor array and introduced a gating function that compensates for tilt errors by receiving sensor tilt information and modulating the response of the solar layer. Under tilted conditions, this method reduced the overall average compass error from 65.78\({}^{\circ}\) to 10.47\({}^{\circ}\). [PERSON] et al. [22] utilized attitude angles from an inertial navigation system (INS) to determine the zenith direction during platform tilt in motion, achieving an RMSE of 1.58\({}^{\circ}\) in heading angle. However, this method exhibits linear error growth with distance, leading to significant cumulative positional inaccuracies. [PERSON] et al. [23] investigated the incident light path of a polarized light compass before and following a tilt, computing the sky polarization pattern using horizontal attitude angles and dynamically identifying the zenith region in the skylight image to extract the solar meridian. The advantage of this approach lies in its constant use of polarization information from the zenith region to calculate the vehicle's heading. Under a tilt angle of 30\({}^{\circ}\), this method achieved a heading estimation accuracy with an RMSE of 1.19\({}^{\circ}\). [PERSON] et al. [24] proposed an efficient extreme learning machine (EELM)-based method to model and compensate for tilt-induced heading errors in polarized compasses during practical applications. It has an improvement of the RMSEby 86% compared with prior arts. This method employs nonlinear fitting to accurately establish the relationship between tilt angle and heading error, hence improving orientation performance considerably. [PERSON] et al.