This letter extends the exactly sparse Gaussian variational inference (ESGVI) algorithm for state estimation in two complementary directions. First, ESGVI is generalized to operate on matrix Lie groups, enabling the estimation of states with orientation components while respecting the underlying group structure. Second, factors are introduced to accommodate heavy-tailed and skewed noise distributions, as commonly encountered in ultra-wideband (UWB) localization due to non-line-of-sight (NLOS) and multipath effects. Both extensions are shown to integrate naturally within the ESGVI framework while preserving its sparse and derivative-free structure. The proposed approach is validated in a UWB localization experiment with NLOS-rich measurements, demonstrating improved accuracy and comparable consistency. Finally, a Python implementation within a factor-graph-based estimation framework is made open-source (https://github.com/decargroup/gvi_ws) to support broader research use.

This work introduces a single-range-aided navigation observer that reconstructs the full state of a rigid body using only an Inertial Measurement Unit (IMU), a body-frame vector measurement (e.g., magnetometer), and a distance measurement from a fixed anchor point. The design first formulates an extended linear time-varying (LTV) system to estimate body-frame position, body-frame velocity, and the gravity direction. The recovered gravity direction, combined with the body-frame vector measurement, is then used to reconstruct the full orientation on $\mathrm{SO}(3)$, resulting in a cascaded observer architecture. Almost Global Asymptotic Stability (AGAS) of the cascaded design is established under a uniform observability condition, ensuring robustness to sensor noise and trajectory variations. Simulation studies on three-dimensional trajectories demonstrate accurate estimation of position, velocity, and orientation, highlighting single-range aiding as a lightweight and effective modality for autonomous navigation.

Onboard simultaneous localization and mapping (SLAM) methods are commonly used to provide accurate localization information for autonomous robots. However, the coordinate origin of SLAM estimate often resets for each run. On the other hand, UWB-based localization with fixed anchors can ensure a consistent coordinate reference across sessions; however, it requires an accurate assignment of the anchor nodes' coordinates. To this end, we propose a two-stage approach that calibrates and fuses UWB data and SLAM data to achieve coordinate-wise consistent and accurate localization in the same environment. In the first stage, we solve a continuous-time batch optimization problem by using the range and odometry data from one full run, incorporating height priors and anchor-to-anchor distance factors to recover the anchors' 3D positions. For the subsequent runs in the second stage, a sliding-window optimization scheme fuses the UWB and SLAM data, which facilitates accurate localization in the same coordinate system. Experiments are carried out on the NTU VIRAL dataset with six scenarios of UAV flight, and we show that calibration using data in one run is sufficient to enable accurate localization in the remaining runs. We release our source code to benefit the community at https://github.com/ntdathp/slam-uwb-calibration.

Radio-based methods such as Ultra-Wideband (UWB) and RAdio Detection And Ranging (radar), which have traditionally seen limited adoption in robotics, are experiencing a boost in popularity thanks to their robustness to harsh environmental conditions and cluttered environments. This work proposes a multi-robot UGV-UAV localization system that leverages the two technologies with inexpensive and readily-available sensors, such as Inertial Measurement Units (IMUs) and wheel encoders, to estimate the relative position of an aerial robot with respect to a ground robot. The first stage of the system pipeline includes a nonlinear optimization framework to trilaterate the location of the aerial platform based on UWB range data, and a radar pre-processing module with loosely coupled ego-motion estimation which has been adapted for a multi-robot scenario. Then, the pre-processed radar data as well as the relative transformation are fed to a pose-graph optimization framework with odometry and inter-robot constraints. The system, implemented for the Robotic Operating System (ROS 2) with the Ceres optimizer, has been validated in Software-in-the-Loop (SITL) simulations and in a real-world dataset. The proposed relative localization module outperforms state-of-the-art closed-form methods which are less robust to noise. Our SITL environment includes a custom Gazebo plugin for generating realistic UWB measurements modeled after real data. Conveniently, the proposed factor graph formulation makes the system readily extensible to full Simultaneous Localization And Mapping (SLAM). Finally, all the code and experimental data is publicly available to support reproducibility and to serve as a common open dataset for benchmarking.

Multi-robot localization is a crucial task for implementing multi-robot systems. Numerous researchers have proposed optimization-based multi-robot localization methods that use camera, IMU, and UWB sensors. Nevertheless, characteristics of individual robot odometry estimates and distance measurements between robots used in the optimization are not sufficiently considered. In addition, previous researches were heavily influenced by the odometry accuracy that is estimated from individual robots. Consequently, long-term drift error caused by error accumulation is potentially inevitable. In this paper, we propose a novel visual-inertial-range-based multi-robot localization method, named SaWa-ML, which enables geometric structure-aware pose correction and weight adaptation-based robust multi-robot localization. Our contributions are twofold: (i) we leverage UWB sensor data, whose range error does not accumulate over time, to first estimate the relative positions between robots and then correct the positions of each robot, thus reducing long-term drift errors, (ii) we design adaptive weights for robot pose correction by considering the characteristics of the sensor data and visual-inertial odometry estimates. The proposed method has been validated in real-world experiments, showing a substantial performance increase compared with state-of-the-art algorithms.

Accurate relative state observation of Unmanned Underwater Vehicles (UUVs) for tracking uncooperative targets remains a significant challenge due to the absence of GPS, complex underwater dynamics, and sensor limitations. Existing localization approaches rely on either global positioning infrastructure or multi-UUV collaboration, both of which are impractical for a single UUV operating in large or unknown environments. To address this, we propose a novel persistent relative 6D state estimation framework that enables a single UUV to estimate its relative motion to a non-cooperative target using only successive noisy range measurements from two monostatic sonar sensors. Our key contribution is an observability-enhanced attitude control strategy, which optimally adjusts the UUV's orientation to improve the observability of relative state estimation using a Kalman filter, effectively mitigating the impact of sensor noise and drift accumulation. Additionally, we introduce a rigorously proven Lyapunov-based tracking control strategy that guarantees long-term stability by ensuring that the UUV maintains an optimal measurement range, preventing localization errors from diverging over time. Through theoretical analysis and simulations, we demonstrate that our method significantly improves 6D relative state estimation accuracy and robustness compared to conventional approaches. This work provides a scalable, infrastructure-free solution for UUVs tracking uncooperative targets underwater.

To address the need for robust positioning, navigation, and timing services in lunar environments, this paper proposes a novel onboard clock phase jump detection framework for satellite constellations using range measurements obtained from dual one-way inter-satellite links. Our approach leverages vertex redundantly rigid graphs to detect faults without relying on prior knowledge of satellite positions or clock biases, providing flexibility for lunar satellite networks with diverse satellite types and operators. We model satellite constellations as graphs, where satellites are vertices and inter-satellite links are edges. The proposed algorithm detects and identifies satellites with clock jumps by monitoring the singular values of the geometric-centered Euclidean distance matrix (GCEDM) of 5-clique sub-graphs. The proposed method is validated through simulations of a GPS constellation and a notional constellation around the Moon, demonstrating its effectiveness in various configurations.

Ultra-wideband (UWB) technology has shown remarkable potential as a low-cost general solution for robot localization. However, limitations of the UWB signal for precise positioning arise from the disturbances caused by the environment itself, due to reflectance, multi-path effect, and Non-Line-of-Sight (NLOS) conditions. This problem is emphasized in cluttered indoor spaces where service robotic platforms usually operate. Both model-based and learning-based methods are currently under investigation to precisely predict the UWB error patterns. Despite the great capability in approximating strong non-linearity, learning-based methods often do not consider environmental factors and require data collection and re-training for unseen data distributions, making them not practically feasible on a large scale. The goal of this research is to develop a robust and adaptive UWB localization method for indoor confined spaces. A novelty detection technique is used to recognize outlier conditions from nominal UWB range data with a semi-supervised autoencoder. Then, the obtained novelty scores are combined with an Extended Kalman filter, leveraging a dynamic estimation of covariance and bias error for each range measurement received from the UWB anchors. The resulting solution is a compact, flexible, and robust system which enables the localization system to adapt the trustworthiness of UWB data spatially and temporally in the environment. The extensive experimentation conducted with a real robot in a wide range of testing scenarios demonstrates the advantages and benefits of the proposed solution in indoor cluttered spaces presenting NLoS conditions, reaching an average improvement of almost 60% and greater than 25cm of absolute positioning error.

--Cooperative localization in multi-agent robotic systems is challenging, especially when agents rely on limited information, such as only peer-to-peer range measurements. Two key challenges arise: utilizing this limited information to improve position estimation; handling uncertainties from sensor noise, nonlinearity, and unknown correlations between agents' measurements; and avoiding information reuse. This paper examines the use of the Unscented Transform (UT) for state estimation for a case in which range measurement between agents and covariance intersection (CI) is used to handle unknown correlations. This makes formulating a CI approach with ranging-only measurements a challenge. T o overcome this, UT is used to handle uncertainties and formulate a cooperative state update using range measurements and current cooperative state estimates. This introduces information reuse in the measurement update. Therefore, this work aims to evaluate the limitations and utility of this formulation when faced with various levels of state measurement uncertainty and errors. Cooperative localization has emerged as a viable strategy for increasing the accuracy and resilience of multi-robot systems' localization [1].

This paper introduces MILUV, a Multi-UAV Indoor Localization dataset with UWB and Vision measurements. This dataset comprises 217 minutes of flight time over 36 experiments using three quadcopters, collecting ultra-wideband (UWB) ranging data such as the raw timestamps and channel-impulse response data, vision data from a stereo camera and a bottom-facing monocular camera, inertial measurement unit data, height measurements from a laser rangefinder, magnetometer data, and ground-truth poses from a motion-capture system. The UWB data is collected from up to 12 transceivers affixed to mobile robots and static tripods in both line-of-sight and non-line-of-sight conditions. The UAVs fly at a maximum speed of 4.418 m/s in an indoor environment with visual fiducial markers as features. MILUV is versatile and can be used for a wide range of applications beyond localization, but the primary purpose of MILUV is for testing and validating multi-robot UWB- and vision-based localization algorithms. The dataset can be downloaded at https://doi.org/10.25452/figshare.plus.28386041.v1. A development kit is presented alongside the MILUV dataset, which includes benchmarking algorithms such as visual-inertial odometry, UWB-based localization using an extended Kalman filter, and classification of CIR data using machine learning approaches. The development kit can be found at https://github.com/decargroup/miluv, and is supplemented with a website available at https://decargroup.github.io/miluv/.