CredibleDFGO: Differentiable Factor Graph Optimization with Credibility Supervision

2026-05-07

AI Summary

This work addresses the unreliability of covariance estimates produced by GNSS positioning solvers in urban canyons, a challenge overlooked by existing methods that focus solely on improving point estimates while neglecting uncertainty calibration. The authors propose CredibleDFGO, a novel framework that explicitly treats covariance credibility as a trainable objective by integrating differentiable factor graph optimization to jointly learn position and uncertainty. A weight-generation network is introduced to predict satellite reliability, and the east–north predictive distribution is end-to-end supervised using a proper scoring rule combining negative log-likelihood and energy score. Evaluated across three UrbanNav urban scenarios, the method significantly enhances both localization accuracy and uncertainty reliability; notably, in the challenging Mong Kok area, it reduces the average positioning error from 13.77 m to 11.68 m, the negative log-likelihood from 40.63 to 6.59, and the energy score from 12.31 to 9.05.

Abstract

Global navigation satellite system (GNSS) positioning is widely used for urban navigation, but the covariance reported by the GNSS solver is often unreliable in urban canyons. Existing differentiable factor graph optimization (DFGO) methods already learn measurement weighting through the solver, but they still use position-only objectives. As a result, the mean estimate may improve while the reported covariance remains too small, too large, or wrong in shape. In this work, we propose CredibleDFGO (CDFGO), a differentiable GNSS factor graph framework that makes covariance credibility an explicit training target. The Weighting Generation Network (WGN) predicts per-satellite reliability weights. The differentiable Gauss--Newton solver maps these weights to a position estimate and posterior covariance, and proper scoring rules supervise the East--North predictive distribution end-to-end. We study negative log-likelihood (NLL), Energy Score (ES), and their combination. Results on three UrbanNav test scenes show consistent gains in uncertainty credibility. Positioning accuracy also improves on the medium-urban and harsh-urban scenes, and the mean horizontal error and 95th-percentile error improve on the deep-urban scene. On the harsh-urban Mong Kok (MK) scene, CDFGO-Combined reduces the mean horizontal error from 13.77\,m to 11.68\,m, reduces NLL from 40.63 to 6.59, and reduces ES from 12.31 to 9.05. The case studies link the MK improvement to better axis-wise consistency, more credible local covariance ellipses, and satellite-level reweighting.

Problem

• GNSS positioning
• covariance credibility
• urban canyons
• uncertainty calibration
• factor graph optimization

Innovation

• Differentiable Factor Graph Optimization
• Covariance Credibility
• Proper Scoring Rules
• GNSS Positioning
• Uncertainty Estimation