A Robust Extended Kalman Filter Algorithm Based on a Sliding Window Fractional-Order Grey Prediction Model and Its
1School of Geomatics, Liaoning Technical University, Fuxin 123000, China.
Sensors (Basel, Switzerland)
|March 28, 2026
Summary
This study introduces a robust Kalman filter using fractional-order grey prediction to improve navigation accuracy. The new method enhances micro-electro-mechanical inertial navigation systems/global navigation satellite systems (MINS/GNSS) accuracy during GNSS signal faults.
Area of Science:
- Navigation Systems Engineering
- Signal Processing
- Control Theory
Background:
- Integrated navigation systems, combining micro-electro-mechanical inertial navigation systems (MINS) and global navigation satellite systems (GNSS), are crucial for accurate positioning.
- Small-amplitude faults in GNSS measurements can significantly degrade the accuracy and even cause divergence in these integrated systems.
- Existing robust Kalman filter algorithms struggle with subtle GNSS measurement errors.
Purpose of the Study:
- To develop a robust extended Kalman filter (REKF) algorithm that effectively handles small-amplitude faults in GNSS measurements for MINS/GNSS integrated systems.
- To enhance the fault detection and data replacement capabilities within integrated navigation systems.
- To improve the overall filtering accuracy and reliability of navigation solutions.
Main Methods:
- Proposed a novel sliding window fractional-order grey prediction model (SWFGM(1,1)) for predicting GNSS measurements.
- Implemented a weighted index sequential probability ratio test (SPRT) for detecting system faults and identifying faulty GNSS data.
- Integrated the SWFGM(1,1) prediction model with a robust extended Kalman filter (REKF) to replace faulty GNSS data and correct integrated navigation information.
Main Results:
- The proposed SWFGM(1,1)-REKF algorithm demonstrated superior performance compared to traditional chi-square test-based robust extended Kalman filters.
- In simulations and vehicle experiments involving small-amplitude abrupt GNSS faults, the algorithm significantly improved velocity and position filtering accuracy.
- Specifically, velocity accuracy improved by over 50% and position accuracy by over 80% in vehicle experiments with small-amplitude mutation faults.
Conclusions:
- The SWFGM(1,1)-REKF algorithm effectively addresses the challenge of small-amplitude GNSS faults in integrated navigation systems.
- The combination of fractional-order grey prediction and robust estimation provides a significant advancement in navigation system accuracy and reliability.
- This approach offers a promising solution for maintaining high-precision navigation even under challenging GNSS signal conditions.
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