Enhanced GNSS Navigation Using a Centered Error Entropy Extended Kalman Filter in Non-Gaussian Noise Environments

Area of Science:

• Geomatics Engineering
• Signal Processing
• Navigation Systems

Background:

• Global Navigation Satellite Systems (GNSS), including Global Positioning System (GPS), face signal interference from multipath effects, challenging accurate state estimation.
• Traditional extended Kalman filters (EKF) perform poorly in non-Gaussian noise environments due to their reliance on the minimum mean square error (MMSE) criterion.
• Existing alternative criteria like minimum error entropy (MEE) and maximum correntropy criterion (MCC) have limitations in handling bias and achieving optimal convergence.

Purpose of the Study:

• To develop an enhanced extended Kalman filter (EKF) that overcomes the limitations of existing criteria for improved GNSS state estimation.
• To introduce the centered error entropy (CEE) extended Kalman filter (CEE-EKF) by integrating the strengths of MEE and MCC.
• To validate the performance of the CEE-EKF in complex, nonlinear GPS environments with non-Gaussian noise and outliers.

Main Methods:

• Development of the centered error entropy (CEE) criterion by combining minimum error entropy (MEE) and maximum correntropy criterion (MCC) principles.
• Integration of the CEE criterion into the extended Kalman filter framework, resulting in the CEE-EKF.
• Experimental validation using simulated complex nonlinear GPS data with non-Gaussian noise and outlier scenarios.

Main Results:

• The CEE-EKF demonstrated significantly superior performance in noise suppression compared to individual MEE and MCC-based filters.
• The proposed CEE-EKF exhibited enhanced robustness and accuracy, particularly in the presence of outliers in the GPS observables.
• Experimental results confirmed the effectiveness of the CEE-EKF in complex nonlinear GPS environments with non-Gaussian noise.

Conclusions:

• The CEE-EKF offers an effective solution for enhancing the reliability of GPS navigation in challenging real-world conditions.
• The algorithm provides improved state estimation accuracy and robustness against non-Gaussian noise and outliers.
• The CEE-EKF methodology is readily extendable to other Global Navigation Satellite Systems (GNSS) applications requiring robust state estimation.