# Student's t Kernel-Based Maximum Correntropy Criterion Extended Kalman Filter for GPS Navigation
## 1 Introduction  
The Global Positioning System (GPS) [1, 2] offers several advantages in modern satellite navigation systems, including global coverage, resistance to weather-related disruptions, and high positioning accuracy. However, real-world environments such as tunnels, dense urban areas with tall buildings, and forests present diverse topographies and atmospheric conditions that can obstruct GPS signals or cause satellite failures. These disruptions may degrade system performance and lead to positioning errors. In such challenging conditions, especially under non-Gaussian noise, ensuring algorithmic robustness becomes essential. When the noise is assumed to follow a Gaussian distribution, estimators based on Mean Square Error (MSE) are commonly employed, such as the Extended Kalman Filter (EKF). To address this, it is logical to design cost functions that directly influence the learning process, transferring the information within data samples into system parameters. Information Theoretic Learning (ITL) provides a framework for such learning without assuming specific data distributions or relying on particular learning architectures, only requiring data availability. This perspective blurs the traditional boundaries between supervised and unsupervised learning and offers significant utility for engineering applications [3; 4; 5]. Recent advances have introduced nonlinear filtering methods based on entropy concepts as alternatives for GPS signal processing. However, ITL methods utilizing entropy measures, such as Minimum Error Entropy (MEE) [6; 7] and Maximum Correntropy Criterion (MCC) [8; 9; 10; 11], have shown strong performance in non-Gaussian settings, particularly by suppressing the effects of impulsive noise via kernel-based approaches. By applying entropy-based criteria like MEE, optimal estimation becomes more feasible. Specifically, the Mean Error Entropy Extended Kalman Filter (MEEEKF) leverages the full randomness of residuals to improve estimation accuracy. This technique has demonstrated effectiveness in multipath parameter estimation and loop tracking in GPS code tracking systems. Correntropy is a statistical measure that captures both second and higher-order statistics, making it particularly effective in non-Gaussian noise environments. [PERSON] et al. [12] proposed the Maximum Correntropy Kalman Filter (MCCKF) as a robust alternative to conventional Kalman filtering. Unlike traditional approaches based on the Minimum Mean Square Error (MMSE) criterion, the MCCKF uses the MCC for optimization, enhancing resilience against impulsive or non-Gaussian noise. The filter estimates state and covariance using standard propagation equations and updates posterior estimates through a fixed-point algorithm, improving robustness where traditional Kalman Filters may fail. It assesses relationships between variables using the probability density function (PDF). Within this framework, MCC serves as a robust cost function in filtering applications, especially in vehicle navigation systems. Subsequently, a robust statistical linearization approach based on the Maximum Correntropy Criterion (MCC) is applied to compute the posterior state and covariance estimates. The MCC, developed through Information Theoretic Learning, has been widely adopted in filter designs involving non-Gaussian noise environments. To further enhance numerical stability, a square root formulation of the Kalman filter has been introduced. The studies in [13; 14] introduce a new filter known as the maximum correntropy unscented filter (MCUF), developed to enhance the robustness of the unscented Kalman filter (UKF) in the presence of impulsive noise. In the MCUF framework, the unscented transformation (UT) is employed to generate prior estimates of both the state and covariance matrices. The robustness and adaptability for GNSS integration have been verified by using the cubature Kalman filter (CKF) [15].