Robust Nonlinear GNSS Navigation Under Heavy-Tailed Measurement Noise Using a Cauchy-Kernel Correntropy Extended Kalman Filter

Abstract

In urban canyon environments, the performance of global navigation satellite systems (GNSS) is severely degraded by multipath propagation, signal occlusion, and non-Gaussian measurement noise. These effects reduce positioning accuracy and service reliability. Kalman filtering and its nonlinear extensions are widely used for GNSS positioning. However, these filters rely on Gaussian noise assumptions and are formulated using the minimum mean square error (MMSE) criterion. Consequently, their performance degrades in non-Gaussian environments. Recently, filtering methods based on the maximum correntropy criterion (MCC) have been investigated as robust alternatives to MMSE-based approaches. The performance of MCC filters is strongly influenced by the choice of the kernel function. In particular, Gaussian kernel-based MCC algorithms may suffer from numerical instability under large measurement noise and strong sensitivity to kernel bandwidth selection. These limitations compromise estimation robustness and convergence stability. To address these limitations, this study proposes a Cauchy kernel-based maximum correntropy extended Kalman filter (CKMCEKF). The effectiveness of the proposed filter was validated using both simulation and real GNSS datasets. The results confirm the superior accuracy, stability, and reduced sensitivity to kernel bandwidth selection of the proposed method.