Penggao Yan

Baoshan Song, Matthew Giamou, Penggao Yan et al.

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.

Penggao Yan, Ronghe Jin, Junyi Zhang et al.

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.

Liang Qian, Penggao Yan, Penghui Xu et al.

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.

Penggao Yan, Xingqun Zhan, Rui Sun et al.

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.