# Student's t Kernel-Based Maximum Correntropy Criterion Extended Kalman Filter for GPS Navigation
## 5 Conclusions  
This study presents a hybrid Student's t-based maximum entropy criterion algorithm for robust GPS positioning in non-Gaussian noise environments. By replacing the conventional Gaussian kernel with a Student's t-distribution, the proposed filter achieves improved estimation accuracy, particularly under heavy-tailed noise and in the presence of outliers. Experiments were conducted in two simulated environments: one focusing on multipath-induced noise, and the other involving time-varying heavy-tailed disturbances. In both cases, the Student's t-based filter consistently outperformed the extended Kalman filter and its maximum correntropy-based variants.  
Furthermore, both robust filters outperformed the extended Kalman filter when significant anomalies were present. Although the experiments were based on simulated data, the Student's t-distribution, derived from Bayesian inference with unknown variance, effectively captures impulsive noise characteristics and abrupt state transitions. The simulation results confirm that STMCCEKF outperforms standard MCCEKF in terms of robustness and estimation precision. While the STMCCEKF filter with fixed kernel bandwidth may suffer from parameter rigidity, the proposed STMCCEKF-AKB demonstrated superior overall robustness and estimation accuracy by combining heavy-tailed modeling with  
Figure 10: Comparison of position errors of EKF, STMCCEKF, and STMCCEKF-AKB for Environment 2: (**a**) east; (**b**) north; (**c**) altitude.  
adaptive kernel tuning. This highlights the advantage of incorporating the degrees of freedom parameter, which plays a key role in controlling the influence of outliers.  
Future work should involve collecting real-world GNSS data or conducting field tests to validate whether the filter retains its effectiveness in practical environments. In addition, future work will also focus on validating the STMCCEKF using real GPS data to assess its performance under practical conditions with multipath and dynamic noise. The STMCCEKF offers robust and accurate state estimation under non-Gaussian noise, making it suitable for GPS-based applications such as autonomous vehicles, UAVs, and mobile robots operating in multipath-affected or dynamic environments. The integration of a generalized stochastic integration rule allows the filter to combine the statistical properties of both Student's t and Gaussian distributions, offering improved performance under complex noise conditions. This hybrid entropy-based framework has the potential to be extended to other filtering architectures, such as the unscented Kalman filter or the cubature Kalman filter. Its flexibility makes it a promising approach for robust state estimation in challenging GNSS environments.  
Conceptualization, D.-J.J.; methodology, D.-J.J. and Y.-H.H.; software, D.-J.J., Y.-H.H., and Y.C.; validation, D.-J.J., Y.-H.H., Y.C., and A.B.; writing--original draft preparation, D.-J.J., Y.-H.H., A.B., and Y.C.; writing--review and editing, D.-J.J.; supervision, D.-J.J. All authors have read and agreed to the published version of the manuscript.  
The authors express their gratitude for the assistance from the grant numbers NSTC 112-2221-E-019-030 and NSTC 113-2221-E-019-059 of the National Science and Technology Council, Taiwan.  
Not applicable.  
The data that support the findings of this study are available upon reasonable request from the authors.  
Author [PERSON] was employed by the company Wistron Corporation. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.