Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

FE-GUT: Factor Graph Optimization hybrid with Extended Kalman Filter for tightly coupled GNSS/UWB Integration

Qijia Zhao, Shaolin Lü, Jianan Lou, Rong Zhang

TL;DR

This work tackles the problem of tightly coupling GNSS and UWB sensors when UWB devices lack hardware-level time synchronization, by introducing FE-GUT—a hybrid architecture that combines Graphical State Space Modeling (GSSM) solved via Factor Graph Optimization (FGO) to estimate the invariant time-offset $t_d$, with an Extend Kalman Filter (EKF) that initializes new factors and compensates the offset. The approach leverages online temporal calibration to align asynchronous GNSS/UWB measurements, achieving significant localization improvements in simulation (horizontal RMSE down by 58.59%, vertical by 34.80%) and notably enhanced time-offset estimation (76.80%). FE-GUT demonstrates that integrating FGO for time-invariant parameters with EKF updates can yield higher-precision navigation in low-cost multi-sensor systems, and the authors provide open-source code for reproducibility. The work lays a foundation for real-world validation and further theoretical study on discretization effects in hybrid graphical–filtering architectures.

Abstract

Precise positioning and navigation information has been increasingly important with the development of the consumer electronics market. Due to some deficits of Global Navigation Satellite System (GNSS), such as susceptible to interferences, integrating of GNSS with additional alternative sensors is a promising approach to overcome the performance limitations of GNSS-based localization systems. Ultra-Wideband (UWB) can be used to enhance GNSS in constructing an integrated localization system. However, most low-cost UWB devices lack a hardware-level time synchronization feature, which necessitates the estimation and compensation of the time-offset in the tightly coupled GNSS/UWB integration. Given the flexibility of probabilistic graphical models, the time-offset can be modeled as an invariant constant in the discretization of the continuous model. This work proposes a novel architecture in which Factor Graph Optimization (FGO) is hybrid with Extend Kalman Filter (EKF) for tightly coupled GNSS/UWB integration with online Temporal calibration (FE-GUT). FGO is utilized to precisely estimate the time-offset, while EKF provides initailization for the new factors and performs time-offset compensation. Simulation-based experiments validate the integrated localization performance of FE-GUT. In a four-wheeled robot scenario, the results demonstrate that, compared to EKF, FE-GUT can improve horizontal and vertical localization accuracy by 58.59\% and 34.80\%, respectively, while the time-offset estimation accuracy is improved by 76.80\%. All the source codes and datasets can be gotten via https://github.com/zhaoqj23/FE-GUT/.

FE-GUT: Factor Graph Optimization hybrid with Extended Kalman Filter for tightly coupled GNSS/UWB Integration

TL;DR

This work tackles the problem of tightly coupling GNSS and UWB sensors when UWB devices lack hardware-level time synchronization, by introducing FE-GUT—a hybrid architecture that combines Graphical State Space Modeling (GSSM) solved via Factor Graph Optimization (FGO) to estimate the invariant time-offset , with an Extend Kalman Filter (EKF) that initializes new factors and compensates the offset. The approach leverages online temporal calibration to align asynchronous GNSS/UWB measurements, achieving significant localization improvements in simulation (horizontal RMSE down by 58.59%, vertical by 34.80%) and notably enhanced time-offset estimation (76.80%). FE-GUT demonstrates that integrating FGO for time-invariant parameters with EKF updates can yield higher-precision navigation in low-cost multi-sensor systems, and the authors provide open-source code for reproducibility. The work lays a foundation for real-world validation and further theoretical study on discretization effects in hybrid graphical–filtering architectures.

Abstract

Precise positioning and navigation information has been increasingly important with the development of the consumer electronics market. Due to some deficits of Global Navigation Satellite System (GNSS), such as susceptible to interferences, integrating of GNSS with additional alternative sensors is a promising approach to overcome the performance limitations of GNSS-based localization systems. Ultra-Wideband (UWB) can be used to enhance GNSS in constructing an integrated localization system. However, most low-cost UWB devices lack a hardware-level time synchronization feature, which necessitates the estimation and compensation of the time-offset in the tightly coupled GNSS/UWB integration. Given the flexibility of probabilistic graphical models, the time-offset can be modeled as an invariant constant in the discretization of the continuous model. This work proposes a novel architecture in which Factor Graph Optimization (FGO) is hybrid with Extend Kalman Filter (EKF) for tightly coupled GNSS/UWB integration with online Temporal calibration (FE-GUT). FGO is utilized to precisely estimate the time-offset, while EKF provides initailization for the new factors and performs time-offset compensation. Simulation-based experiments validate the integrated localization performance of FE-GUT. In a four-wheeled robot scenario, the results demonstrate that, compared to EKF, FE-GUT can improve horizontal and vertical localization accuracy by 58.59\% and 34.80\%, respectively, while the time-offset estimation accuracy is improved by 76.80\%. All the source codes and datasets can be gotten via https://github.com/zhaoqj23/FE-GUT/.
Paper Structure (11 sections, 35 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 35 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. TRADITIONAL DISCRETE-TIME STATE SPACE MODEL FOR TIGHTLY COUPLED GNSS/UWB INTEGRATION
  3. Continues-Time State Space Model for Tightly Coupled GNSS/UWB Integration
  4. TDTSSM of Tightly Coupled GNSS/UWB Integration
  5. A New Hybrid Architecture for Tightly Coupled GNSS/UWB Integration
  6. Graphical State Space Model for Tightly Coupled GNSS/UWB Integration
  7. The FE-GUT Architecture
  8. Results and Analysis
  9. Simulation Setup
  10. State-Estimation Performance
  11. Conclusion and future works

Figures (3)

  • Figure 1: The factor graph of tightly coupled GNSS/UWB integration modeled by GSSM.
  • Figure 2: The architecture in which FGO is hybrid with EKF for tightly coupled GNSS/UWB integration.
  • Figure 3: (a) The comparison of the horizontal and vertical positioning localization error between EKF and FE-GUT. (b) The comparative evaluation of the estimated time offset between EKF and FE-GUT. (c) The nominal and estimated trajectories.