Fault Detection Algorithm for Gaussian Mixture Noises:An Application in LiDAR/IMU Integrated Localization System

1) What problem is this paper solving?

Context: Lidar-based localization noise often exhibits heavy-tailed or non-Gaussian behaviors.
Core contribution: Modeling non-Gaussian noise as GMM and deriving a rigorous Chi-squared test.
Achieved goal: Reliable fault detection in EKF-based Lidar/IMU systems.

2) Why is this paper important?

What changed: High-precision sensors like LiDAR have complex, non-Gaussian noise characteristics.
Problem created: Conventional Gaussian assumptions lead to poor fault detection performance.
Why current solutions fail: They lack the statistical framework to handle multimodal or heavy-tailed noise.

3) How does this paper solve it?

Contribution 1: Models noise as GMM and propagates it through EKF to establish residual distribution.
Contribution 2: Transforms the GMM residual to approximate a standard multivariate normal for testing.
Key result: 30% improvement in detection rate and 17-23% reduction in detection delay.

🎯 Takeaway: Rigorous GMM error propagation enables standard Chi-squared tests to work for non-Gaussian systems.

@article{yan2024fdegmm,
  author = {Yan, Penggao and Li, Zikai and Huang, Fan and Wen, Weisong and Hsu, Li-Ta},
  title = {Fault Detection Algorithm for Gaussian Mixture Noises: An Application in LiDAR/IMU Integrated Localization Systems},
  journal = {NAVIGATION: Journal of the Institute of Navigation},
  year = {2024},
  volume = {72},
  number = {1},
  doi = {10.33012/navi.684}
}