Navigation by Skylight Polarization via Rayleigh Model Optimization on a Road Vehicle

Ben Potter, Eslam Mounier, Aboelmagd Noureldin, Yahia Antar, Muhammad Alam · N/A · 2026

Summary

Reliable absolute heading estimation is critical for road-vehicle navigation, particularly when magnetic, inertial, or GNSS-based references are degraded.

Abstract Summary

Reliable absolute heading estimation is critical for road-vehicle navigation, particularly when magnetic, inertial, or GNSS-based references are degraded. This paper presents a skylight polarization navigation method that estimates vehicle heading by globally optimizing a Rayleigh sky model against measurements from a division-of-focal-plane polarimetric camera. The proposed framework combines a pinhole camera model, a single-scattering Rayleigh polarization model, and a solar position algorithm to synthesize the expected full image angle of polarization distribution for candidate vehicle states. A degree of polarization weighted root mean square error objective function compares measured and simulated polarization patterns, allowing the estimator to use all available sky information while attenuating low confidence pixels caused by clouds, buildings, foliage, and other depolarizing occlusions. Experimental evaluation is performed using three urban road vehicle trajectories collected with a roof mounted polarimetric camera and a high precision dual-antenna GNSS/INS reference system. Results show sub-degree RMS yaw error across all trajectories, ranging from $0.718^{\circ}$ to $0.889^{\circ}$. Compared with representative feature-based and model-based polarization navigation methods, the proposed approach reduces RMS heading error by up to 87% and demonstrates improved robustness to partial sky occlusion.

Key Points

Reliable absolute heading estimation is critical for road-vehicle navigation, particularly when magnetic, inertial, or GNSS-based references are degraded.
This paper presents a skylight polarization navigation method that estimates vehicle heading by globally optimizing a Rayleigh sky model against measurements from a division-of-focal-plane polarimetric camera.
The proposed framework combines a pinhole camera model, a single-scattering Rayleigh polarization model, and a solar position algorithm to synthesize the expected full image angle of polarization distribution for candidate vehicle states.
A degree of polarization weighted root mean square error objective function compares measured and simulated polarization patterns, allowing the estimator to use all available sky information while attenuating low confidence pixels caused by clouds, buildings, foliage, and other depolarizing occlusions.
Experimental evaluation is performed using three urban road vehicle trajectories collected with a roof mounted polarimetric camera and a high precision dual-antenna GNSS/INS reference system.

Theory of Skylight Polarization for Navigation

The horizontal coordinate system, denoted the $n$-frame, has axes $E$, $N$, and $U$, with an origin located at the observer, $O$. Following the convention for horizontal coordinate systems, its axes are aligned with the cardinal east and north directions with the $U$ axis pointing upward. All other coordinate systems are placed relative to the $n$-frame.

The camera body coordinate system, denoted the $b$-frame, has axes $X^{b}$, $Y^{b}$, and $Z^{b}$, with an origin located at the observer, $O$.

Model Optimization

We propose a method of absolute heading estimation from skylight polarization based on optimization of the Rayleigh sky model. Our method combines a pinhole camera model with the Rayleigh model to simulate images of the skylight polarization pattern given the state (i.e., position, time, and orientation) of a virtual camera.

We define an objective function that encodes the proximity of an estimated state of a virtual camera to the true state of a given measured image using this simulation. Fig.

Model Optimization — Navigation by Skylight Polarization via Rayleigh Model Optimization on a Road Vehicle — (b)

Instrumentation and Dataset

Our dataset is constructed using a modified consumer road vehicle, shown in Fig. 7 . The modifications to the road vehicle are made to support advanced multi-sensor navigation research. The on-board reference system has been applied to previous navigation research by Araujo et al. [ 42 ] .

The reference navigation solution is generated using a NovAtel PwrPak7 integrated system, configured with dual GNSS antennas and a high-performance NovAtel IMU-µIMU-IC.

Instrumentation and Dataset — Navigation by Skylight Polarization via Rayleigh Model Optimization on a Road Vehicle — (a) Measured AoP in Superpixel Frame

Results

The performance of the model optimization method is summarized in Table I . We include the performance of Lu’s method [ 24 ] and Wang’s method [ 30 ] for comparison. We provide the RMS, P95, and maximum absolute error as measures of algorithm performance. The P95 error represents the lowest error that contains $95\text{\,}\mathrm{\%}$ of all estimates.

Following, we explain our choices for the model optimization algorithm’s hyperparameters.

Results — Navigation by Skylight Polarization via Rayleigh Model Optimization on a Road Vehicle — (b) Measured AoP in Ray Frame

Sources and Demonstrations

Figures are reproduced from Potter et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.