Two stage GNSS outlier detection for factor graph optimization based GNSS-RTK/INS/odometer fusion

Reliable GNSS positioning in complex environments remains a critical challenge due to non-line-of-sight (NLOS) propagation, multipath effects, and frequent signal blockages. These effects can easily introduce large outliers into the raw pseudo-range measurements, which significantly degrade the performance of global navigation satellite system (GNSS) real-time kinematic (RTK) positioning and limit the effectiveness of tightly coupled GNSS-based integrated navigation system. To address this issue, we propose a two-stage outlier detection method and apply the method in a tightly coupled GNSS-RTK, inertial navigation system (INS), and odometer integration based on factor graph optimization (FGO). In the first stage, Doppler measurements are employed to detect pseudo-range outliers in a GNSS-only manner, since Doppler is less sensitive to multipath and NLOS effects compared with pseudo-range, making it a more stable reference for detecting sudden inconsistencies. In the second stage, pre-integrated inertial measurement units (IMU) and odometer constraints are used to generate predicted double-difference pseudo-range measurements, which enable a more refined identification and rejection of remaining outliers. By combining these two complementary stages, the system achieves improved robustness against both gross pseudo-range errors and degraded satellite measuring quality. The experimental results demonstrate that the two-stage detection framework significantly reduces the impact of pseudo-range outliers, and leads to improved positioning accuracy and consistency compared with representative baseline approaches. In the deep urban canyon test, the outlier mitigation method has limits the RMSE of GNSS-RTK/INS/odometer fusion from 0.52 m to 0.30 m, with 42.3% improvement.

Credible Uncertainty Quantification under Noise and System Model Mismatch

State estimators often provide self-assessed uncertainty metrics, such as covariance matrices, whose reliability is critical for downstream tasks. However, these self-assessments can be misleading due to underlying modeling violations like noise or system model mismatch. This letter addresses the problem of estimator credibility by introducing a unified, multi-metric evaluation framework. We construct a compact credibility portfolio that synergistically combines traditional metrics like the Normalized Estimation Error Squared (NEES) and the Noncredibility Index (NCI) with proper scoring rules, namely the Negative Log-Likelihood (NLL) and the Energy Score (ES). Our key contributions are a novel energy distance-based location test to robustly detect system model misspecification and a method that leverages the asymmetric sensitivities of NLL and ES to distinguish optimism covariance scaling from system bias. Monte Carlo simulations across six distinct credibility scenarios demonstrate that our proposed method achieves high classification accuracy (80-100%), drastically outperforming single-metric baselines which consistently fail to provide a complete and correct diagnosis. This framework provides a practical tool for turning patterns of credibility indicators into actionable diagnoses of model deficiencies.