Robust Kalman filter for heavy-tailed process and measurement noises
Qianxin Wang1,2, Chenwang Ye1, Guobin Chang3,4
1School of Environment Sciences and Spatial Informatics, China University of Mining and Technology, Xuzhou, 221116, China.
Scientific Reports
|May 7, 2026
Summary
This study introduces a robust Kalman filter designed to handle heavy-tailed noise in both process and measurement data. The new filter maintains the standard Kalman filter structure, improving accuracy in tracking and navigation systems.
Area of Science:
- Signal Processing
- Estimation Theory
- Robust Control
Background:
- Kalman filters assume normal distribution for errors, which can lead to performance degradation with heavy-tailed noise.
- Existing robust Kalman filters often do not specifically address both process and measurement noise distributions.
- Heavy-tailed distributions are common in real-world measurements and dynamic models, deviating from the normality assumption.
Purpose of the Study:
- To develop a robust Kalman filter modification effective against heavy-tailed distributions in both process and measurement noises.
- To propose a filter that is simple, automated, effective, general, and flexible.
- To enhance the performance of estimation and tracking systems operating under non-ideal noise conditions.
Main Methods:
- A novel robust Kalman filter algorithm is proposed, maintaining the standard Kalman filter's structure.
- The filter is designed to be insensitive to heavy-tailed noise distributions.
- Initialization is automated using standard Kalman filtering techniques, allowing for flexibility with prior distributional information.
Main Results:
- Simulations show the robust Kalman filter reduces positioning Root Mean Squared Error (RMSE) by 11.1% compared to the standard Kalman filter in tracking applications, reaching 20.0% with iterations.
- Real-world experiments with integrated Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) demonstrated up to 22% reduction in positioning RMSE.
- Significant improvements in velocimetry performance were observed in the GNSS/INS navigation experiment.
Conclusions:
- The proposed robust Kalman filter effectively mitigates performance degradation caused by heavy-tailed noise in both process and measurement data.
- The filter offers practical advantages in simplicity, automation, and flexibility, making it suitable for various applications.
- The method proves effective in real-world scenarios, enhancing accuracy in navigation and tracking systems.
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