A Machine Learning Framework for Weighted Least Squares GNSS Positioning based on Activation Functions
Authors: Pin-Hsun Lee, Harry Leib
Organizations: Department of Electrical and Computer Engineering, McGill University, Montreal, QC, Canada
Abstract
Global Navigation Satellite Systems (GNSS) are widely used to provide position, velocity, and timing (PVT) information for various applications, including transportation, location-based communication services, and intelligent agriculture. In urban canyons, high-rise buildings and narrow streets can cause signal obstruction, non-line-of-sight (NLOS) reception, and multipath effects that introduce errors in GNSS pseudorange measurements. Although multi-constellations GNSS effectively increase the number of available satellites, the inclusion of degraded signals can lead to severe positioning errors. This study proposes a machine learning framework for the weighted least squares (WLS) algorithm incorporating activation functions to enhance positioning accuracy. Several signal quality indicators are employed as training features for ensemble learning algorithms to identify poor quality signals by providing quality scores. Then, activation functions are employed to transform the machine learning predicted scores to appropriate weights for WLS positioning. To evaluate the performance of our approach, experiments are conducted using real-world datasets from Hong Kong and Tokyo urban areas. Comparative analysis of activation functions reveals that sigmoid functions consistently yield the greatest improvements with different machine learning algorithms and GNSS constellation configurations. The proposed algorithm demonstrates substantial reductions in positioning errors for both single- and multiconstellation scenarios. Furthermore, our results indicate that the proposed algorithm exhibits strong geographical transferability. The proposed algorithm maintains comparable level of performance when trained on data from other regions with similar levels of urbanization.
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.
Global navigation satellite system (GNSS) interference poses a serious threat to reliable positioning, especially in indoor and multipath-rich environments where source localization is highly challenging. In this paper, we formulate GNSS interference localization as an active sensing problem and propose a reinforcement learning (RL) framework in which an agent sequentially explores the environment to infer the position of an emitter source from radio frequency (RF) observations acquired with a 2x2 patch antenna. The localization task is modeled as a partially observable decision process, since single-snapshot measurements are often ambiguous under multipath propagation and changing channel conditions. To address this, the proposed framework combines high-dimensional RF sensing with deep RL and recurrent policy learning. We investigate both value-based and policy-based approaches, namely Deep Q-Networks (DQN) and Proximal Policy Optimization (PPO), and study their behavior under domain shift. The approach is evaluated on a simulated dataset generated with the Sionna ray-tracing module, which provides realistic propagation effects and diverse environment configurations. Experimental results show that the proposed method achieves a localization success rate of 80.1, demonstrating the potential of RL for adaptive GNSS interference localization. Overall, the results highlight simulation-assisted training as a promising direction for robust interference localization in challenging propagation environments.
M. Shamail J. Khan, Nisha L. Raichur, Lucas Heublein +5
Maintaining accurate navigation during GNSS outages remains a significant challenge for autonomous systems relying on low-cost inertial sensors. While classical smoothing methods, such as the two-filter smoother and Rauch-Tung-Striebel smoother, exploit measurements collected before and after an outage, their performance remains limited by the accuracy of conventional GNSS measurements. This paper presents Bayesian learning-enhanced navigation with deep smoothing (BLENDS), a transformer-based framework that augments Bayesian smoothing with learned covariance adaptation and state correction. The proposed method preserves the statistical foundations of Bayesian estimation while leveraging data-driven learning to improve navigation accuracy. Evaluations on the quadrotor dataset with GNSS outages demonstrate that BLENDS consistently outperforms both model-based smoothers, achieving up to 25.6% improvement in the position root mean square error while also reducing estimation uncertainty. Furthermore, BLENDS learns to compensate for the systematic bias between conventional GNSS positioning and RTK ground truth, enabling accuracy beyond that achievable with conventional GNSS measurements alone. The results demonstrate the potential of learning-enhanced Bayesian smoothing for resilient and high-accuracy navigation in GNSS-challenged environments.