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Factor Graph Optimization for GNSS/INS Integration: A Comparison with the Extended Kalman Filter

Wen, W., Pfeifer, T., Bai, X., Hsu, L. T.

NAVIGATION: Journal of the Institute of Navigation (2021)

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DOI Repository Video
Instrumented vehicle and urban canyon scene used for GNSS/INS factor graph experiments.
Figure 3 visual detail: instrumented vehicle and urban canyon setup used to compare FGO with EKF.

Summary

Factor graph optimization recasts GNSS/INS integration as a sliding-window estimation problem rather than a one-epoch filtering problem.

Highlights

  • Compares EKF and FGO for both loosely coupled and tightly coupled GNSS/INS integration.
  • Uses an urban-canyon experiment in Hong Kong with low-cost GNSS, INS, fisheye imagery, and ground-truth reference equipment.
  • Shows that sliding-window FGO can revisit historical states and reduce the impact of outliers and non-Gaussian GNSS errors.

Figures

Before the factor graph model, the paper first establishes the EKF loosely coupled and tightly coupled baselines that the new formulation is compared against.

Flowchart of loosely coupled and tightly coupled GNSS/INS integrations implemented using EKF.
Figure 1 from the paper: loosely coupled and tightly coupled GNSS/INS integration flowcharts implemented using EKF.

After defining the estimation structure, the paper moves to the Hong Kong vehicle setup and urban canyon route used for the EKF-versus-FGO comparison.

Experimental vehicle sensor setup and Hong Kong urban canyon test scene.
Figure 3 from the paper: experimental vehicle sensor setup and Hong Kong urban-canyon test scene.

The first main result turns the method into trajectory evidence by comparing tightly coupled EKF and FGO against the reference path.

Tightly coupled GNSS/INS trajectory and two-dimensional error results comparing EKF and FGO.
Figure 5 from the paper: tightly coupled GNSS/INS trajectory and 2D positioning error comparison between EKF and FGO.

The window-size study explains why FGO performance depends on how much historical information is optimized together.

Two-dimensional positioning error under different FGO window sizes.
Figure 8 from the paper: 2D positioning error under different sliding-window sizes for tightly coupled FGO.

These sky-view epochs interpret the window-size result by showing the LOS/NLOS satellite conditions during difficult periods.

Sky-view images showing line-of-sight and non-line-of-sight satellite visibility at selected epochs.
Figure 9 from the paper: fisheye sky-view images and LOS/NLOS satellite visibility at selected epochs.

The pseudorange histograms connect the positioning behavior to non-Gaussian urban measurement noise.

GPS and BeiDou pseudorange error histograms with fitted Gaussian mixture models.
Figure 10 from the paper: GPS and BeiDou pseudorange error histograms with fitted Gaussian mixture models.

The final comparison checks the practical computation cost of solving the tightly coupled graph with FGO versus iSAM.

Computational time comparison between tightly coupled FGO and tightly coupled iSAM.
Figure 13 from the paper: computational-time comparison between tightly coupled FGO and tightly coupled iSAM.

Key idea. Classical GNSS/INS integration uses an Extended Kalman Filter, which condenses all history into a single current state. This paper recasts the problem as factor graph optimization (FGO) — jointly optimizing a sliding window of states with re-linearization, so the estimator can revisit past epochs and handle outliers far more flexibly.

Impact. It became the reference comparison establishing why FGO outperforms filtering for navigation, and was named the 2024 Most-Cited Paper in NAVIGATION. The result reframed how the field approaches GNSS/INS fusion and underpins much of IPNL’s later integrity and multi-sensor work.

Related project and resources

Project: GraphGNSSLib Resource: GraphGNSSLib