[Paper Review] It is time for Factor Graph Optimization for GNSS/INS Integration: Comparison between FGO and EKF

Weisong Wen, Tim Pfeifer+2 more|arXiv (Cornell University)|Apr 22, 2020

GNSS positioning and interferenceEngineering47 references17 citations

TL;DR

This paper evaluates factor graph optimization (FGO) and extended Kalman filtering (EKF) for GNSS/INS integration in urban canyons, demonstrating FGO's superior performance through comparative analysis. It reveals that FGO outperforms EKF in positioning accuracy and robustness, especially under challenging signal conditions, and provides insights into optimal window size selection for FGO-based systems.

ABSTRACT

The recently proposed factor graph optimization (FGO) is adopted to integrate GNSS/INS attracted lots of attention and improved the performance over the existing EKF-based GNSS/INS integrations. However, a comprehensive comparison of those two GNSS/INS integration schemes in the urban canyon is not available. Moreover, the performance of the FGO-based GNSS/INS integration rely heavily on the size of the window of optimization. Effectively tuning the window size is still an open question. To fill this gap, this paper evaluates both loosely and tightly-coupled integrations using both EKF and FGO via the challenging dataset collected in the urban canyon. The detailed analysis of the results for the advantages of the FGO is also given in this paper by degenerating the FGO-based estimator to an EKF like estimator. More importantly, we analyze the effects of window size against the performance of FGO, by considering both the GNSS pseudorange error distribution and environmental conditions.

Motivation & Objective

• To provide a comprehensive comparison between factor graph optimization (FGO) and extended Kalman filtering (EKF) in GNSS/INS integration under urban canyon conditions.
• To investigate the impact of window size on FGO performance, particularly in relation to pseudorange error distribution and environmental factors.
• To analyze the trade-offs between loosely and tightly coupled integration schemes using both FGO and EKF.
• To evaluate the robustness and positioning accuracy of FGO under degraded GNSS signal conditions typical of urban environments.
• To determine whether FGO can be effectively tuned to outperform traditional EKF-based integration in real-world urban scenarios.

Proposed method

• The study uses a real-world dataset collected in a challenging urban canyon environment to evaluate both FGO and EKF-based GNSS/INS integration.
• FGO is implemented with a sliding window optimization framework, where states are estimated by minimizing a non-linear cost function over a sequence of measurements.
• The FGO formulation incorporates GNSS pseudorange and pseudorange-rate measurements, along with inertial measurements from the INS, into a factor graph structure.
• The EKF-based integration is implemented as a standard loosely and tightly coupled estimator, using standard state propagation and update steps.
• The FGO is degenerated into an EKF-like estimator to enable direct comparison and isolate the effects of optimization versus filtering.
• Performance is evaluated based on positioning error, consistency, and convergence under varying window sizes and environmental conditions.

Experimental results

Research questions

• RQ1 How does FGO-based GNSS/INS integration compare to EKF in terms of positioning accuracy and robustness in urban canyon environments?
• RQ2 What is the optimal window size for FGO in urban GNSS/INS integration, and how does it affect performance under varying signal conditions?
• RQ3 How do loosely and tightly coupled FGO and EKF integration schemes differ in performance and stability under multipath and non-line-of-sight conditions?
• RQ4 To what extent does the distribution of GNSS pseudorange errors influence FGO performance, and how can this be leveraged for window size tuning?
• RQ5 Can FGO be effectively degenerated into an EKF-like estimator to validate its advantages and understand the underlying performance gains?

Key findings

• FGO consistently outperforms EKF in positioning accuracy, especially in urban canyons with high multipath and non-line-of-sight conditions.
• The performance of FGO is highly sensitive to window size, with an optimal range that balances computational load and estimation accuracy.
• Tightly coupled FGO integration yields better positioning results than loosely coupled FGO, particularly when GNSS pseudorange errors are non-Gaussian.
• The study identifies that window sizes between 5 and 10 seconds provide the best trade-off between accuracy and computational cost in the tested urban environment.
• Degenerating FGO into an EKF-like estimator confirms that the primary performance gain of FGO comes from global optimization over a sliding window, not just state estimation.
• Environmental conditions such as signal blockage and multipath significantly degrade EKF performance but have a more moderate impact on FGO due to its ability to correct past states through optimization.