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Fault Detection Algorithm for Gaussian Mixture Noises: An Application in Lidar/IMU Integrated Localization Systems

Yan, P., Li, Z., Huang, F., Wen, W., Hsu, L. T.

NAVIGATION: Journal of the Institute of Navigation (2025)

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CARLA simulation route, vehicle scene, and extracted LiDAR/IMU map face used for fault detection validation.
Figure 4 visual detail: CARLA simulation route, vehicle scene, and extracted LiDAR/IMU map face used for fault detection validation.

Summary

This paper derives a chi-squared fault detector for Gaussian-mixture measurement noise and validates it in a lidar/IMU localization system.

Highlights

  • The method transforms EKF residuals under GMM assumptions so they can be tested with a chi-squared statistic.
  • CARLA-based lidar/IMU experiments compare Gaussian and Gaussian-mixture detectors under step and slope failures.

Figures

After deriving the residual transformation, the paper applies it to an EKF-based localization system with lidar range-bearing measurements and IMU propagation.

Architecture of the lidar/IMU localization system and fault-detection process.
Figure 2: fault-detection architecture and sensor platform for the lidar/IMU localization system.

The lidar measurement model defines the residuals that later enter the EKF and the fault-detection statistic.

2D lidar line-segment extraction and plane-based measurement model diagrams.
Figure 3: extracting line segments and constructing the 2D lidar measurement model.

The controlled simulation platform supplies repeatable vehicle motion, map geometry, and configurable GMM-distributed noise for testing.

CARLA simulated route, vehicle view, and extracted building face model.
Figure 4: CARLA simulation platform, designed vehicle track, and extracted environmental faces.

Before introducing faults, the paper shows where localization error grows in the simulated route, especially near large turns with fewer features.

Absolute translation error plot for the fault-free simulated environment.
Figure 6: absolute translation error of positioning results in the fault-free simulated environment.

The step-failure experiment then compares whether the GMM-based statistic detects the shaded failure period more reliably than the Gaussian baseline.

Step-failure detection plots comparing total Gaussian-GMM and Gaussian methods.
Figure 7: step-failure detection results for total Gaussian-GMM and Gaussian methods.

The slope-failure case tests the same detector when the fault magnitude grows over time rather than appearing as a fixed step.

Slope-failure detection plots comparing total Gaussian-GMM and Gaussian methods.
Figure 8: slope-failure detection results for total Gaussian-GMM and Gaussian methods.