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Integrity-Constrained Factor Graph Optimization for GNSS Positioning in Urban Canyons

Xia, X., Wen, W., Hsu, L. T.

NAVIGATION: Journal of the Institute of Navigation (2024)

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UrbanNav trajectory comparisons under integrity-constrained factor graph optimization.
Figure 8 visual detail: UrbanNav trajectory comparisons under integrity-constrained factor graph optimization.

Summary

Integrity-constrained FGO reweights faulty GNSS measurements with switchable pseudorange and chi-square-test factors while preserving geometry for protection-level calculation.

Highlights

  • The factor graph combines switchable pseudorange, switch prior, switch reliable, and chi-square test factors.
  • UrbanNav experiments connect the method to real medium and harsh urban scenarios, including HPE, HPL, skyplot, and trajectory results.

Figures

The flowchart becomes a factor graph in which switch variables are estimated across epochs instead of removing satellites outright.

Integrity-constrained factor graph with satellite nodes, switch variables, pseudorange factors, switch priors, switch reliable factors, and chi-square test factor.
Figure 2: graph structure of the proposed integrity-constrained factor graph.

The controlled bias test shows how the chi-square-test factor affects horizontal position error and protection level during the fault period.

HPE and HPL curves for FGO, RAIM-FGO, SW-FGO, and SWFDE-FGO during a bias-injection period.
Figure 6: HPE and HPL for the four methods during injected satellite biases.

The skyplot explains the key design choice: faulty satellites are downweighted by switch values, helping preserve useful geometry.

Skyplots comparing FGO, RAIM-FGO, SW-FGO, and SWFDE-FGO switch values at epoch A.
Figure 7: skyplot of switch values for four methods at epoch A.

The real UrbanNav trajectories move the evaluation from controlled bias injection to medium and harsh urban routes.

Bird's-eye-view trajectories for UrbanNav-Medium and UrbanNav-Harsh datasets.
Figure 8: bird’s-eye-view trajectories for the UrbanNav-Medium and UrbanNav-Harsh datasets.

The UrbanNav result curves connect trajectory behavior to the integrity metrics used to compare the methods.

UrbanNav result curves for snapshot test statistic, HPE, and HPL across algorithms.
Figure 9: snapshot test statistic, HPE, and HPL during the UrbanNav experiment.

The pseudorange-error distribution explains how switch values narrow or reshape residuals while retaining geometric information.

Distribution of switchable pseudorange errors for FGO, SW-FGO, and SWFDE-FGO.
Figure 13: switchable pseudorange error distribution for FGO, SW-FGO, and SWFDE-FGO.