# Student's t Kernel-Based Maximum Correntropy Criterion Extended Kalman Filter for GPS Navigation
## 1 Introduction
Additionally, cubature rules are utilized to compute the second-order statistics of Gaussian random variables undergoing nonlinear transformations. Building on this foundation, the current research investigates an adaptive and robust CKF. The adaptive capability is achieved using the variational Bayesian (VB) method to dynamically estimate the measurement noise covariance [16]. Meanwhile, robustness is established by leveraging MCC to effectively suppress outliers. This method addresses several key challenges in real-world filtering: handling non-Gaussian noise, adapting to variable and unpredictable noise covariances, and ensuring efficient performance under dynamic conditions. A more recent advancement is the robust Student's t-based stochastic cubature filter (RSTSCF), designed for nonlinear state-space models, where the relationship between state variables and observations is complex. By applying cubature integration rules, the RSTSCF efficiently estimates system states. It is particularly well suited for scenarios involving heavy-tailed process and measurement noise. The benefits of kernel adaptive filters,including linearity and convexity in reproducing kernel Hilbert space (RKHS) and the ability to approximate nonlinear functions using universal kernels have attracted significant attention. In the fields of machine learning and nonlinear signal processing, especially under non-Gaussian conditions, correntropy has emerged as a compelling alternative to traditional Mean Square Error (MSE)-based criteria. This trend has motivated the development of a new kernel adaptive filtering method, termed the kernel maximum correntropy (KMC) method [17; 18; 19; 20; 21]. The RSTSCF also introduces a powerful framework for addressing heavy-tailed noise through the use of the Student's t-distribution, known for its robustness against outliers and impulsive disturbances, which is common in navigation and tracking applications [22]. The degrees of freedom in the distribution allow control over tail heaviness, offering flexibility in noise modeling. In this work, a generalized Gaussian model incorporating a Student's t kernel is proposed, as it more effectively captures the characteristics of heavy-tailed non-Gaussian noise compared to traditional Gaussian assumptions. This paper introduces a novel filtering approach, the Student's t kernel Maximum Correntropy Criterion Extended Kalman Filter (STMCCEKF), designed to improve the robustness of the EKF in the presence of impulsive noise. To address the limitations of EKF and Gaussian MCCEKF under heavy-tailed GPS noise, we propose a robust STMCCEKF that employs a Student's t kernel for enhanced outlier suppression. Unlike prior methods, it adapts better to impulsive, non-Gaussian noise through a tailored fixed-point iteration and revised covariance update, offering improved accuracy and robustness in challenging navigation scenarios. Although this work focuses on GPS-based navigation, the proposed STMCCEKF framework applies to general GNSS systems, as the underlying measurement and error models are common across GPS. The remainder of this paper is organized as follows. A brief review of the Maximum Correntropy Criterion EKF is provided in Section 2. In Section 3, the basic description of the STMCCEKF is presented. The STMCCEKF with adaptive kernel bandwidth (STMCCEKF-AKB) is introduced. The proposed STMCCEKF-AKB's performance compared to the EKF, MCCEKF, and STMCCEKF techniques is assessed using illustrative examples based on simulation experiments in Section 4. Finally, conclusions are given in Section 5.