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 · Electrical Engineering Department, Royal Military College of Canada, Kingston, ON K7K 7B4 Canada
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∘ to 0.889∘. 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
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.
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.
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.
Fig. 6: Relationship between the ray-frame Xir axis and the superpixel-frame Xis axis for the ith 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.
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.
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.
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∘, 45∘, 90∘, and 135∘. 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∘ and a DoLP MAE of 0.0404, compared with 46.03∘ 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.
Ruilin Huang, Jue Wang, Zhen Tian +2
School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China · Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen 518107, China · Department of Electrical Engineering, Carleton University, Ottawa, Ontario K1S 5B6, Canada
PairUAV relative localization maps two UAV images to a polar navigation command. Although heading and range share the same pairwise pose context, treating them as homogeneous coordinates forces both outputs to use the same decoder evidence and optimization state. Controlled readout probes reveal a different structure: the two axes favor different decoder-depth combinations, their best checkpoints disagree on 80.8% of a validation trajectory, and range errors exhibit a distinct high-error tail. We introduce method, Polar Axis-Conditioned Estimation, which retains a shared Reloc3r-style pair representation while assigning axis-specific readout interfaces. Heading uses mid/late relational evidence, whereas range remains attached to a direct late metric path. On the official hidden test, the strongest released raw predictor scores 0.002460; the complementary PAAER predictor scores 0.002514 with a slightly lower angle error. Deterministic challenge packaging, reported separately from learned estimation, yields the final score of 0.001874. Code, checkpoints, predictions, and reconstruction tools are available at https://github.com/zerong7777-boop/PairUAV-PACE.
Vision-based navigation complements Global Navigation Satellite Systems, but certification demands integrity guarantees that account for faulty measurements. Previous work presented a probabilistic computer vision pipeline for runway-based pose estimation with fault detection inspired by Receiver Autonomous Integrity Monitoring. This work extends that framework by deriving protection levels, which provide probabilistic bounds on pose error that remain valid under undetected faults. We present an algorithm for computing protection levels for the nonlinear Perspective-n-Point problem applied to an aviation setting. The algorithm covers all six degrees of freedom of the aircraft pose (position and orientation) directly. We analyze the effect of measurement redundancy, pixel-level prediction uncertainty, and runway distance on the resulting protection levels. To make the results tangible, we demonstrate tradeoffs in the protection levels on an illustrative runway example.
Olivia Beyer Bruvik, Romeo Valentin, Marc R. Schlichting +2
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305 USA · A3 by Airbus LLC, Sunnyvale, CA 94086 USA