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

Abstract

Fault detection is crucial to ensurethe reliability of localization systems. However, conventional fault detection methods usually assume that noises in the system have a Gaussian distribution, limiting their effectiveness in real-world applica­ tions. This study proposes a fault detection algorithm for an extended Kalman filter (EKF)-based localization system by modeling non-Gaussian noises as a Gaussian mixture model (GMM). The relationship between GMM-distributed noises and the measurement residual is rigorously established through error propagation, which is utilized to construct the test statistic for a chi-squared test. The proposed method is applied to an EKF-based two-dimensional light detection and ranging/inertial measurement unit integrated localization sys­ tem. Experimental results in a simulated urban environment show that the pro­ posed method exhibits a 30% improvement in the detection rate and a 17%–23% reduction in the detection delay, compared with the conventional method with Gaussian noise modeling.

Problem Addressed

Conventional fault detection methods for localization systems assume Gaussian noise distributions, which limits their effectiveness in real-world applications where noises are non-Gaussian.

Key Contributions

• Fault detection algorithm for EKF-based localization modeling non-Gaussian noises as a Gaussian mixture model
• Rigorous error propagation establishing the relationship between GMM-distributed noises and the measurement residual
• Chi-squared test statistic built from a residual transformed toward a standard multivariate normal distribution
• Application to a 2D lidar/IMU integrated system with reproducible CARLA-based simulated urban evaluation

Conclusions

Experiments in a simulated urban environment show the proposed method achieves a 30% improvement in detection rate and a 17%-23% reduction in detection delay compared with the conventional method based on Gaussian noise modeling.