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

Ben Potter; Eslam Mounier; Aboelmagd Noureldin; Yahia Antar; Muhammad Alam

cs.ROOct 14, 2026

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

Authors: Ben Potter, Eslam Mounier, Aboelmagd Noureldin, Yahia Antar, Muhammad Alam

Organizations: Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON K7L 3N6, Canada · Department of Computer and Systems Engineering, Ain Shams University, Cairo 11535, Egypt · Department of Electrical and Computer Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada · School of Computing, Queen’s University, Kingston, ON K7L 2N8, Canada ·

Abstract

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.

Figures & tables

Panel of Figure 1 — Fig. 1: Rayleigh-model geometry for skylight polarization. (a) Predicted e-vector orientations over the sky form a structured pattern around the solar point. (b) A single-scattering event defines the scattered ray observed at $P$ and the corresponding e-vector orientation orthogonal to the scattering plane.

Panel of Figure 2 — Fig. 2: Example measured and simulated polarization images used by the proposed model-optimization framework. The measured angle of polarization is shown in the superpixel frame and after transformation to the ray frame, alongside the measured degree of polarization and the Rayleigh-model angle of polarization prediction generated from the reference state.

Panel of Figure 3 — Fig. 3: High-level flow for evaluating the model-optimization objective function. Candidate orientation, position, and time are used to simulate the expected skylight polarization image, which is then compared with the measured polarimetric image.

Fig. 4: Pinhole camera geometry used to map image-plane coordinates to sky-ray directions. The focal length

f

determines the relationship between each sensor location and its corresponding ray in the camera body frame.

Fig. 5: Division-of-focal-plane polarimeter superpixel structure. Four micro-polarizers measure intensities at orthogonal linear polarization angles, which are used to reconstruct the Stokes vector, angle of polarization, and degree of polarization.

Panel of Figure 6 — Fig. 6: Relationship between the ray-frame $X^{r}_{i}$ axis and the superpixel-frame $X^{s}_{i}$ axis for the $i^{th}$ pixel under level and tilted camera orientations. The angle between these axes defines the rotation required to compare measured sensor-frame angle of polarization values with Rayleigh-model predictions in the ray frame.

Panel of Figure 7 — Fig. 7: Diagram of the experimental instrumentation we use to record the dataset. The polarization camera is highlighted with a close-up image for clarity. Instruments that are part of the reference system are distinguished using the yellow color.

Panel of Figure 8 — Fig. 8: Urban road-vehicle trajectories used for experimental evaluation in Kingston, Ontario. Red points denote the reference-system position measurements, arrows indicate the direction of travel, and green markers identify the start and end locations. Basemap tiles attribution: Esri World Street Map.

Fig. 9: Distribution of available sky pixels for each trajectory. Example polarimetric images illustrate different levels of sky visibility, with red overlays indicating pixels classified as obstruction.

Test Case		Yaw Error (°)
Method	Trajectory	RMS	P95	Max. Abs.
Lu’s [ 24 ]	Trajectory 1	2.930	5.279	20.415
	Trajectory 2	4.357	7.301	27.458
	Trajectory 3	5.688	8.597	20.059
Wang’s [ 30 ]	Trajectory 1	1.787	2.980	11.049
	Trajectory 2	2.673	4.483	7.162

TABLE I: Summary of error in yaw estimate

Fig. 10: Yaw-estimation error for Lu’s method, Wang’s method, and the proposed full-image model-optimization method across the three vehicle trajectories. Time-series plots show frame-by-frame error, and box plots summarize each method’s error distribution.

Fig. 11: Absolute yaw error as a function of available sky pixels. Points show the mean error for each sky-visibility bin and error bars indicate the 95% confidence interval, demonstrating the proposed method’s robustness under partial sky occlusion.

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PolarVis: A Dataset and Diffusion Framework for RGB-to-Polarization Perception in Adverse Driving Scenes

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Polarimetric Imaging Image-to-Image Translation Autonomous Driving Perception Diffusion Models

Open paper AskPDF arXiv

Reflections, glare, transparent structures, and material-dependent appearance variations can introduce ambiguity into RGB-based visual perception in vehicle-relevant environments. Polarization provides complementary reflection- and material-sensitive information, but its acquisition requires dedicated sensing hardware. This paper presents RGB-P Wild, a real-world dataset containing 10,000 paired RGB and four-angle linear-polarization image sets, together with PolarVis, a diffusion-based framework for recovering polarization representations from a single RGB image. PolarVis combines hierarchical RGB feature extraction, diffusion-based feature refinement, four angle-specific decoders, and multi-scale attention recalibration to reconstruct polarization intensity images at

0^\circ

45^\circ

90^\circ

, and

135^\circ

. On RGB-P Wild, PolarVis achieves a normalized-domain MSE of 0.0465, a PSNR of 27.83 dB, and an SSIM of 0.8597. Compared with the released PolarAnything model under the adopted evaluation protocol, PolarVis obtains an AoLP error of

25.66^\circ

and a DoLP MAE of 0.0404, compared with

46.03^\circ

and 0.1084, respectively. Cross-dataset evaluation on vehicle-mounted imagery further examines transfer beyond the training domain. In downstream evaluation, a frozen PCDNet achieves AP50/AP50:95 of 86.3%/59.1% on 990 RGBP-Car test images using PolarVis-generated polarization, compared with 87.0%/59.8% using measured polarization. These results indicate that RGB-derived polarization retains useful polarimetric information for the evaluated perception tasks, while remaining distinct from calibrated physical polarization measurements.

Abstract

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