# CredibleDFGO: Differentiable Factor Graph Optimization with Credibility Supervision

arXiv: https://arxiv.org/abs/2605.06100 · HTML: https://mlsanity.com/paper/2605.06100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 53 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Differentiable Factor Graph Optimization for Learning Smoothers](https://mlsanity.com/paper/2105.08257/) (2021)
- [Improving GNSS Positioning using Neural Network-based Corrections](https://mlsanity.com/paper/2110.09581/) (2021)
- [Towards Robust GNSS Positioning and Real-time Kinematic Using Factor Graph Optimization](https://mlsanity.com/paper/2106.01594/) (2021)
- [GNSS Outlier Mitigation Via Graduated Non-Convexity Factor Graph Optimization](https://mlsanity.com/paper/2109.00667/) (2021)
- [pyrtklib: An open-source package for tightly coupled deep learning and GNSS integration for positioning in urban canyons](https://mlsanity.com/paper/2409.12996/) (2024)
- [Credible Uncertainty Quantification under Noise and System Model Mismatch](https://mlsanity.com/paper/2509.03311/) (2025)

## Abstract (arXiv)

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 learn measurement weighting through the solver, but they still use position-only objectives. As a result, the position estimate may improve while the reported covariance remains too small, too large, or incorrectly oriented. We propose CredibleDFGO (CDFGO), a differentiable GNSS factor graph framework that makes covariance credibility an explicit training target. A Weighting Generation Network (WGN) predicts per-satellite reliability weights, and a differentiable Gauss-Newton solver maps these weights to a position estimate and a Hessian-derived posterior covariance. We use proper scoring rules to supervise the East-North predictive distribution end to end. We study negative log-likelihood (NLL), the energy score (ES), and their combination. Results on three UrbanNav test scenes show consistent gains in covariance credibility. Positioning accuracy also improves on the medium-urban and harsh-urban scenes; on the deep-urban scene, both the mean horizontal error and the 95th-percentile error improve. 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 relative to DFGO (MAE). Case studies link the MK improvement to better axis-wise consistency, more credible local covariance ellipses, and satellite-level reweighting.