arXiv subjects

Penggao Yan

Publications and source records attributed to Penggao Yan.

10 recordsLinked to original sources

arXiv2026

Certifiable Alignment of GNSS and Local Frames via Lagrangian Duality

Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task rely on abundant satellites unavailable in GNSS-degraded environments, or use local optimization methods which cannot guarantee the optimality of a solution. This work introduces a globally optimal solver that transforms raw pseudo-range or Doppler measurements into a convexly relaxed problem. The proposed method is certifiable, meaning it can numerically verify the correctness of the result, filling a gap where existing local optimizers fail. We first formulate the original frame alignment problem as a nonconvex quadratically constrained quadratic program (QCQP) problem and relax the QCQP problem to a concave Lagrangian dual problem that provides a lower cost bound for the original problem. Then we perform relaxation tightness and observability analysis to derive criteria for certifiable optimality of the solution. Finally, simulation and real world experiments are conducted to evaluate the proposed method. The experiments show that our method provides certifiably optimal solutions even with only 2 satellites with Doppler measurements and 2D vehicle motion, while the traditional velocity-based VOBA method and the advanced GVINS alignment technique may fail or converge to local optima without notice. To support the development of GNSS-based navigation techniques in robotics, all code and data are open-sourced at https://github.com/Baoshan-Song/Certifiable-Doppler-alignment.

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arXiv2026

CredibleDFGO: Differentiable Factor Graph Optimization with Credibility Supervision

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.

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arXiv2026

Logistic-aided Huber M-estimator for robust GNSS positioning

This paper develops a logistic-aided Huber (LAH) M-estimator for robust GNSS positioning under long-tailed, multipath-affected measurement errors. The key idea is to leverage a logistic measurement error assumption and establish a one-to-one approximation between the logistic-based loglikelihood (i.e., quasi-log-cosh) and the Huber kernel by matching their score functions. This yields closed-form tuning rules for the scale and threshold parameters in the Huber estimator, grounded on logistic error statistical properties. We further show that the proposed LAH estimator preserves comparable efficiency and robustness to the connected logistic-based least quasi-log-cosh (LQLC) estimator. Both Monte Carlo simulations with long-tailed measurement errors and a one-hour urban GNSS dataset confirm that the proposed logistic-statistics-based tuning improves positioning accuracy and precision while suppressing large error spikes. Specifically, LAH reduces the 2D RMSE/STD by 28.03%/38.83% versus conventional 95%-efficiency-based Huber tuning in simulation, and reduces the overall 3D RMSE/STD by 4.85%/16.68% in real-world experiments while suppressing large positioning error spikes by up to 51%.

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arXiv2026

Credible Uncertainty Quantification under Noise and System Model Mismatch

State estimators often provide self-assessed uncertainty metrics, such as covariance matrices, whose credibility is critical for downstream tasks. However, these self-assessments can be misleading due to underlying modeling violations like noise model mismatch (NMM) or system model misspecification (SMM). This letter addresses this problem by developing a unified, multi-metric framework that integrates noncredibility index (NCI), negative log-likelihood (NLL), and energy score (ES) metrics, featuring an empirical location test (ELT) to detect system model bias and a directional probing technique that uses the metrics' asymmetric sensitivities to distinguish NMM from SMM. Monte Carlo simulations reveal that the proposed method achieves excellent diagnosis accuracy (80-100%) and significantly outperforms single-metric diagnosis methods. The effectiveness of the proposed method is further validated on a real-world UWB positioning dataset. This framework provides a practical tool for turning patterns of credibility indicators into actionable diagnoses of model deficiencies.

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arXiv2026

Jackknife ARAIM: Efficient GNSS Integrity Monitoring for Simultaneous Faults under Non-Gaussian Errors

Legacy and advanced receiver autonomous integrity monitoring (RAIM/ARAIM) rely on Gaussian error models that can be overly conservative for real-world non-Gaussian errors. This paper proposes an extended jackknife detector capable of detecting multiple simultaneous faults with non-Gaussian nominal errors. Furthermore, an integrity monitoring algorithm, jackknife ARAIM, is developed by systematically exploiting the properties of the jackknife detector in the range domain. We prove that the proposed method has equivalent monitoring performance with the solution separation (SS) ARAIM, but is significantly computationally efficient for single-fault cases with non-Gaussian nominal errors, while maintaining similar efficiency to SS ARAIM for multiple-fault cases. The proposed method is examined in worldwide simulations, with the nominal measurement error simulated based on authentic experimental data, which reveals different findings in existing research. In a single Global Positioning System (GPS) constellation setting, the proposed method can reduce the 99.5 percentile vertical protection level (VPL) below 45 m, outperforming 50 m VPL produced by the ARAIM algorithm using Gaussian nominal error models. In GPS-Galileo dual-constellation setting, while these Gaussian-based ARAIM algorithms suffer VPL inflation over 60 m due to Galileo's heavy-tailed errors, the proposed method maintains VPL below 40 m, achieving over 92% normal operations for 35 m Vertical Alert Limit. Moreover, we tentatively implement the SS ARAIM using non-Gaussian overbounds and compare it with the proposed Jackknife ARAIM method regarding computation efficiency. The proposed method achieves up to 59.4% reduction in median processing time compared to SS ARAIM in single-constellation scenarios.

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arXiv2026

Improved GNSS Positioning in Urban Environments Using a Logistic Error Model

A Gaussian error assumption is commonly adopted in the pseudorange measurement model for global navigation satellite system (GNSS) positioning, which leads to the conventional least squares (LS) estimator. In urban environments, however, multipath and non-line-of-sight (NLOS) receptions produce heavy-tailed pseudorange errors that are not well represented by the Gaussian model. This study models urban GNSS pseudorange errors using a logistic distribution and derives the corresponding maximum likelihood estimator, termed the Least Quasi-Log-Cosh (LQLC) estimator. The resulting estimation problem is solved efficiently using an iteratively reweighted least squares (IRLS) algorithm. Experiments in light, medium, and deep urban environments show that LQLC consistently outperforms LS, reducing the three-dimensional (3D) root mean square error (RMSE) by approximately 11%-31% and the 3D error standard deviation (STD) by approximately 27%-61%. A controlled scale-mismatch analysis further shows that LQLC is more sensitive to severe underestimation than to overestimation of the logistic scale, indicating that the practical tuning requirement is to avoid overly small scale values rather than to achieve exact scale matching. In addition, the computational cost remains compatible with real-time positioning. These results indicate that logistic modeling provides a simple and practical alternative to Gaussian-based urban GNSS positioning.

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arXiv2026

Cauchy-Gaussian Overbound for Heavy-tailed GNSS Measurement Errors

Overbounds of heavy-tailed measurement errors are essential to meet stringent navigation requirements in integrity monitoring applications. This paper proposes to leverage the bounding sharpness of the Cauchy distribution in the core and the Overbounds of heavy-tailed measurement errors are essential for meeting stringent navigation requirements in integrity-monitoring applications. This paper proposes to leverage the bounding sharpness of the Cauchy distribution in the core and the Gaussian distribution in the tails to tightly bound heavy-tailedglobal navigation satellite system measurement errors. We develop a procedure to determine the overbounding parameters for both symmetric unimodal (SU)and non-symmetric unimodal (NSU) heavy-tailed errors and prove that the over-bounding property is preserved through convolution. Experiment results on both simulated and real-world data sets reveal that our method can sharply boundheavy-tailed errors in both the core and tail regions. In the position domain, the proposed method reduces the average vertical protection level by 15% for SU heavy-tailed errors compared with the single-cumulative-density-function Gaussian overbound and by 21%-47% for NSU heavy-tailed errors compared with the navigation discrete envelope and two-step Gaussian overbounds.

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arXiv2025

An Efficient Detector for Faulty GNSS Measurements Detection With Non-Gaussian Noises

Fault detection is crucial to ensure the reliability of navigation systems. However, mainstream fault detection methods are developed based on Gaussian assumptions on nominal errors, while current attempts at non-Gaussian fault detection are either heuristic or lack rigorous statistical properties. The performance and reliability of these methods are challenged in real-world applications. This paper proposes the jackknife detector, a fault detection method tailored for linearized pseudorange-based positioning systems under non-Gaussian nominal errors. Specifically, by leveraging the jackknife technique, a test statistic is derived as a linear combination of measurement errors, eliminating the need for restrictive distributional assumptions while maintaining computational efficiency. A hypothesis test with the Bonferroni correction is then constructed to detect potential faults in measurements. Theoretical analysis proves the equivalence between the jackknife detector and the solution separation (SS) detector, while revealing the former's superior computational efficiency. Through a worldwide simulation and a real-world satellite clock anomaly detection experiment--both involving non-Gaussian nominal errors--the proposed jackknife detector demonstrates equivalent detection performance to the SS detector but achieves a fourfold improvement in computational efficiency. These results highlight the jackknife detector's substantial potential for real-time applications requiring robust and efficient fault detection in non-Gaussian noise environments.

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arXiv2025

Online IMU-odometer Calibration using GNSS Measurements for Autonomous Ground Vehicle Localization

Accurate calibration of intrinsic (odometer scaling factors) and extrinsic parameters (IMU-odometer translation and rotation) is essential for autonomous ground vehicle localization. Existing GNSS-aided approaches often rely on positioning results or raw measurements without ambiguity resolution, and their observability properties remain underexplored. This paper proposes a tightly coupled online calibration method that fuses IMU, odometer, and raw GNSS measurements (pseudo-range, carrier-phase, and Doppler) within an extendable factor graph optimization (FGO) framework, incorporating outlier mitigation and ambiguity resolution. Observability analysis reveals that two horizontal translation and three rotation parameters are observable under general motion, while vertical translation remains unobservable. Simulation and real-world experiments demonstrate superior calibration and localization performance over state-of-the-art loosely coupled methods. Specifically, the IMU-odometer positioning using our calibrated parameters achieves the absolute maximum error of 17.75 m while the one of LC method is 61.51 m, achieving up to 71.14 percent improvement. To foster further research, we also release the first open-source dataset that combines IMU, 2D odometer, and raw GNSS measurements from both rover and base stations.

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arXiv2025

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.

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