This paper presents research findings on handling faulty measurements (i.e., outliers) of global navigation satellite systems (GNSS) for vehicle localization under adverse signal conditions in field applications, where raw GNSS data are frequently corrupted due to environmental interference such as multipath, signal blockage, or non-line-of-sight conditions. In this context, we investigate three strategies applied specifically to GNSS pseudorange observations: robust statistics for error mitigation, machine learning for faulty measurement prediction, and Bayesian inference for noise distribution approximation. Since previous studies have provided limited insight into the theoretical foundations and practical evaluations of these three methodologies within a unified problem statement (i.e., state estimation using ranging sensors), we conduct extensive experiments using real-world sensor data collected in diverse urban environments. Our goal is to examine both established techniques and newly proposed methods, thereby advancing the understanding of how to handle faulty range measurements, such as GNSS, for robust, long-term vehicle localization. In addition to presenting successful results, this work highlights critical observations and open questions to motivate future research in robust state estimation.

This short paper presents research findings on two learning-based methods for quantifying measurement uncertainties in global navigation satellite systems (GNSS). We investigate two learning strategies: offline learning for outlier prediction and online learning for noise distribution approximation, specifically applied to GNSS pseudorange observations. To develop and evaluate these learning methods, we introduce a novel multisensor state estimator that accurately and robustly estimates trajectory from multiple sensor inputs, critical for deriving GNSS measurement residuals used to train the uncertainty models. We validate the proposed learning-based models using real-world sensor data collected in diverse urban environments. Experimental results demonstrate that both models effectively handle GNSS outliers and improve state estimation performance. Furthermore, we provide insightful discussions to motivate future research toward developing a federated framework for robust vehicle localization in challenging environments.

State estimation methods using factor graph optimization (FGO) have garnered significant attention in global navigation satellite system (GNSS) research. FGO exhibits superior estimation accuracy compared with traditional state estimation methods that rely on least-squares or Kalman filters. However, only a few FGO libraries are specialized for GNSS observations. This paper introduces an open-source GNSS FGO package named gtsam\_gnss, which has a simple structure and can be easily applied to GNSS research and development. This package separates the preprocessing of GNSS observations from factor optimization. Moreover, it describes the error function of the GNSS factor in a straightforward manner, allowing for general-purpose inputs. This design facilitates the transition from ordinary least-squares-based positioning to FGO and supports user-specific GNSS research. In addition, gtsam\_gnss includes analytical examples involving various factors using GNSS data in real urban environments. This paper presents three application examples: the use of a robust error model, estimation of integer ambiguity in the carrier phase, and combination of GNSS and inertial measurements from smartphones. The proposed framework demonstrates excellent state estimation performance across all use cases.

This paper presents an efficient method for updating particles in a particle filter (PF) to address the position estimation problem when dealing with sharp-peaked likelihood functions derived from multiple observations. Sharp-peaked likelihood functions commonly arise from millimeter-accurate distance observations of carrier phases in the global navigation satellite system (GNSS). However, when such likelihood functions are used for particle weight updates, the absence of particles within the peaks leads to all particle weights becoming zero. To overcome this problem, in this study, a straightforward and effective approach is introduced for updating particles when dealing with sharp-peaked likelihood functions obtained from multiple observations. The proposed method, termed as the multiple update PF, leverages prior knowledge regarding the spread of distribution for each likelihood function and conducts weight updates and resampling iteratively in the particle update process, prioritizing the likelihood function spreads. Experimental results demonstrate the efficacy of our proposed method, particularly when applied to position estimation utilizing GNSS pseudorange and carrier phase observations. The multiple update PF exhibits faster convergence with fewer particles when compared to the conventional PF. Moreover, vehicle position estimation experiments conducted in urban environments reveal that the proposed method outperforms conventional GNSS positioning techniques, yielding more accurate position estimates.

A global navigation satellite system (GNSS) is a sensor that can acquire 3D position and velocity in an earth-fixed coordinate system and is widely used for outdoor position estimation of robots and vehicles. Various GNSS/inertial measurement unit (IMU) integration methods have been proposed to improve the accuracy and availability of GNSS positioning. However, all these methods require the addition of a 3D attitude to the estimated state to fuse the IMU data. In this study, we propose a new optimization-based positioning method for combining GNSS and IMU that does not require attitude estimation. The proposed method uses two types of constraints: one is a constraint between states using only the magnitude of the 3D acceleration observed by an accelerometer, and the other is a constraint on the angle between the velocity vectors using the angular change measured by a gyroscope. The evaluation results with the simulation data show that the proposed method maintains the position estimation accuracy even when the IMU mounting position error increases and improves the accuracy when the GNSS observations contain multipath errors or missing data. The proposed method could improve positioning accuracy in experiments using IMUs acquired in real environments.

The global navigation satellite systems (GNSS) play a vital role in transport systems for accurate and consistent vehicle localization. However, GNSS observations can be distorted due to multipath effects and non-line-of-sight (NLOS) receptions in challenging environments such as urban canyons. In such cases, traditional methods to classify and exclude faulty GNSS observations may fail, leading to unreliable state estimation and unsafe system operations. This work proposes a deep-learning-based method to detect NLOS receptions and predict GNSS pseudorange errors by analyzing GNSS observations as a spatio-temporal modeling problem. Compared to previous works, we construct a transformer-like attention mechanism to enhance the long short-term memory (LSTM) networks, improving model performance and generalization. For the training and evaluation of the proposed network, we used labeled datasets from the cities of Hong Kong and Aachen. We also introduce a dataset generation process to label the GNSS observations using lidar maps. In experimental studies, we compare the proposed network with a deep-learning-based model and classical machine-learning models. Furthermore, we conduct ablation studies of our network components and integrate the NLOS detection with data out-of-distribution in a state estimator. As a result, our network presents improved precision and recall ratios compared to other models. Additionally, we show that the proposed method avoids trajectory divergence in real-world vehicle localization by classifying and excluding NLOS observations.

Accurate and robust vehicle localization in highly urbanized areas is challenging. Sensors are often corrupted in those complicated and large-scale environments. This paper introduces GNSS-FGO, an online and global trajectory estimator that fuses GNSS observations alongside multiple sensor measurements for robust vehicle localization. In GNSS-FGO, we fuse asynchronous sensor measurements into the graph with a continuous-time trajectory representation using Gaussian process regression. This enables querying states at arbitrary timestamps so that sensor observations are fused without requiring strict state and measurement synchronization. Thus, the proposed method presents a generalized factor graph for multi-sensor fusion. To evaluate and study different GNSS fusion strategies, we fuse GNSS measurements in loose and tight coupling with a speed sensor, IMU, and lidar-odometry. We employed datasets from measurement campaigns in Aachen, Duesseldorf, and Cologne in experimental studies and presented comprehensive discussions on sensor observations, smoother types, and hyperparameter tuning. Our results show that the proposed approach enables robust trajectory estimation in dense urban areas, where the classic multi-sensor fusion method fails due to sensor degradation. In a test sequence containing a 17km route through Aachen, the proposed method results in a mean 2D positioning error of 0.19m for loosely coupled GNSS fusion and 0.48m while fusing raw GNSS observations with lidar odometry in tight coupling.

Accurate localization is a core component of a robot's navigation system. To this end, global navigation satellite systems (GNSS) can provide absolute measurements outdoors and, therefore, eliminate long-term drift. However, fusing GNSS data with other sensor data is not trivial, especially when a robot moves between areas with and without sky view. We propose a robust approach that tightly fuses raw GNSS receiver data with inertial measurements and, optionally, lidar observations for precise and smooth mobile robot localization. A factor graph with two types of GNSS factors is proposed. First, factors based on pseudoranges, which allow for global localization on Earth. Second, factors based on carrier phases, which enable highly accurate relative localization, which is useful when other sensing modalities are challenged. Unlike traditional differential GNSS, this approach does not require a connection to a base station. On a public urban driving dataset, our approach achieves accuracy comparable to a state-of-the-art algorithm that fuses visual inertial odometry with GNSS data -- despite our approach not using the camera, just inertial and GNSS data. We also demonstrate the robustness of our approach using data from a car and a quadruped robot moving in environments with little sky visibility, such as a forest. The accuracy in the global Earth frame is still 1-2 m, while the estimated trajectories are discontinuity-free and smooth. We also show how lidar measurements can be tightly integrated. We believe this is the first system that fuses raw GNSS observations (as opposed to fixes) with lidar in a factor graph.