Robust Navigation for INS/GNSS/BPNS Integration Using Adaptive Weighted q-Rényi Kernel Mixture Correntropy Filter

Abstract

Robust and reliable state estimation is critical for the performance of integrated navigation systems. However, in complex measurement environments, the deficiencies of the Kalman filter (KF) in handling measurement outliers and non-Gaussian noise pose a significant challenge to accurate navigation. To address this problem, information entropy filters are emerging as an alternative for achieving the robust fusion for inertial navigation/global navigation satellite system/bionic polarization navigation (INS/GNSS/BPNS integration). However, the robustness of existing information entropy filters is limited by the kernel function and the choice of its bandwidth. This article presents a <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-Rényi kernel-based maximum mixture correntropy filter with adaptive weighting (qRK-AWMMCF) to strengthen the robustness of navigation solutions. Based on the framework of mixture correntropy, a maximum mixture correntropy filter is developed by constructing a <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-Rényi kernel to replace the traditional Gaussian kernel to address the problem of singular matrices. Subsequently, an adaptive weighting mechanism is established on the basis of the likelihood probability of each kernel function to automatically regulate the mixture weights for different <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-Rényi kernels. Finally, the convergence analysis of the proposed methodology is derived. Results on simulation and experimentation demonstrate the robustness of the proposed filter against measurement outliers and non-Gaussian noise for INS/GNSS/BPNS integration.