## 5 Conclusions  
This study investigates UWB localization using the adaptive distributed Student's t EKF with Allan variance. The distributed Student's t EKF is designed as follows: First, a local t EKF for the signal distance between the UWB BS and the target object is proposed, which incorporates the t distribution. Then, the main filter fuses the local filter's outputs and computes the final result. Meanwhile, the Allan variance is computed to assist the local filter. Experimental results confirm the superiority of the proposed adaptive distributed Student's t EKF with Allan variance, demonstrating the method's effectiveness. We are currently investigating the effectiveness of the proposed method in enhancing our understanding of processes affected by colored and interrelated noise patterns. The objective of this research is to meticulously analyze and clarify the complexities of these processes, providing deeper insights into their operational dynamics. With a strong commitment to advancing knowledge, we aim to disseminate the comprehensive findings and inferences derived from these studies. Our intention is to publish these results in the near future, contributing to the growing body of academic research in this specialized field.  
Conceptualization, Y.G., Y.X. and M.S.; methodology, Y.G., Y.X. and M.S.; software, M.Y., X.Z., L.D. and M.L.; validation, M.Y., X.Z., L.D. and M.L.; formal analysis, M.S., M.Y., X.Z., L.D. and M.L.; investigation, M.S., M.Y., X.Z., L.D. and M.L.; resources, Y.G., Y.X. and M.S.; data curation, Y.G., Y.X. and M.S.; writing--original draft preparation, Y.G., Y.X. and M.S.; writing--review and editing, Y.X.; visualization, M.Y., X.Z., L.D. and M.L.; supervision, Y.X.; project administration, M.Y., X.Z., L.D. and M.L.; funding acquisition, Y.G., Y.X. and M.S. All authors have read and agreed to the published version of the manuscript.  
This research was financially supported by the Key R&D Program of Linyi City, with the grant identifier 2023004.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All related data are contained in this article.  
**Conflicts of Interest:** Authors [PERSON] and [PERSON] were employed by Shandong Huichuang Information Technology Co., Ltd. Authors [PERSON], [PERSON] and [PERSON] were employed by Jinan Chenhe Information Technology Co., Ltd. The remaining authors declare that the research  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **First Time** & **Second Time** & **Mean** \\ \hline UWB & 0.666 & 0.637 & 0.652 \\ Federal EKF & 0.476 & 0.618 & 0.547 \\ Distributed t EKF & 0.479 & 0.623 & 0.551 \\ Adaptive distributed t EKF with Allan variance & 0.459 & 0.612 & 0.535 \\ \hline \hline \end{tabular}
\end{table}
Table 4: RMSEs measured by the UWB, federal EKF, distributed t EKF, and adaptive distributed t EKF with Allan variance for the robotic dog localization.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **East Position** & **North Position** & **Mean** \\ \hline UWB & 0.661 & 0.613 & 0.637 \\ Federal EKF & 0.624 & 0.611 & 0.618 \\ Distributed t EKF & 0.644 & 0.603 & 0.623 \\ Adaptive distributed t EKF with Allan variance & 0.625 & 0.599 & 0.612 \\ \hline \hline \end{tabular}
\end{table}
Table 3: RMSEs measured by the UWB, federal EKF, distributed t EKF, and adaptive distributed t EKF with Allan variance for the robotic dog localization for the second time.  
was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.