Organizations: Department of Aeronautical and Aviation Engineering The Hong Kong Polytechnic University, Hong Kong, China
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 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.
In Global Navigation Satellite System (GNSS)-degraded environments, pseudolites (PLs) provide additional signal sources to enhance positioning performance, but their integration in optimization-based frameworks remains limited. This paper presents a loosely coupled factor graph optimization (FGO) framework that fuses the GNSS/PL least-squares (LS) solutions with inertial measurement unit (IMU) data. The evaluation considers low GNSS visibility scenarios with four high-elevation GNSS satellites and up to two PL transmitters over an 80~s window. FGO achieves a 22.8% to 41.3% reduction in mean 3D error compared to standard LS methods. Compared to a GNSS-IMU baseline, incorporating PL transmitters further improves positioning accuracy, with performance depending on geometry.
To address cumulative localization drift of unmanned ground vehicles in structured road environments under severe Global Navigation Satellite System signal occlusion, this paper proposes a robust route-constrained state estimation method. During periods without satellite signals, the proposed method establishes the correspondence between the historical dead reckoning trajectory and local segments of the mission route extracted from a high-definition map, and estimates a route-referenced position via a two-dimensional rigid transformation. The estimated position is then formulated as a pseudo-position observation and incorporated into an Extended Kalman Filter update. In this way, route constraints at the road level can be continuously injected into a unified state estimation framework, thereby suppressing position deviation relative to the mission route while indirectly improving azimuth estimation. To enhance practical applicability, engineering strategies, such as trigger control, matching quality validation, route offset compensation, and single update correction limiting, are further introduced. Experiments in three representative scenarios, including a long tunnel, a multi-segment tunnel, and a curved tunnel, show that the proposed method effectively suppresses error accumulation during satellite outages, reduces the risk of large maximum deviation, and improves localization continuity and road-level usability.
Reliable online autonomy is critical for quadrotor operation in urban airspaces, where global navigation satellite systems (GNSS) measurements suffer from multipath, blockage, and latency issues, introducing non-stationary, temporally correlated errors that degrade conventional GNSS-IMU fusion. This paper presents a belief-adaptive online autonomy framework that augments an extended Kalman filter (EKF) with explicit GNSS trust modelling, second-order online belief adaptation, and latency-aware out-of-sequence measurement handling. GNSS trust is represented as a latent belief state that modulates measurement weighting and multipath bias uncertainty, and is updated online using EKF consistency signals. Unlike reactive covariance tuning, the proposed approach enables proactive and stable sensor trust adaptation without prior environmental knowledge or offline training. Evaluation in simulated urban air mobility scenarios with correlated multipath, stochastic latency, and obstacle constraints demonstrates improved belief convergence, smoother trajectories, and reduced estimation and tracking errors compared to naive, adaptive, and first-order baselines. The framework preserves classical GNSS-IMU fusion structure and can be integrated directly into existing flight control pipelines, supporting robust online autonomy in GNSS degraded environments.