## 1 Introduction
It should be noted that these methods are able to build the map and provide the target object's position; however, the high-precision position information of these methods relies on high-density point cloud information, which results in a relatively high computational load and a long time required for position information calculation. Moreover, if these methods cannot obtain enough feature points, these methods cannot obtain accurate position information. The UWB method can provide position information just by employing several BSs; when compared with visual SLAM and LiDAR SLAM, its cost is cheap. Its localization accuracy is higher than that of similar methods, such as RFID, Wi-Fi, etc. It should be pointed out that all the methods mentioned above are not suitable for all environments. The integration of cutting-edge technologies, particularly in data processing and sensor systems, has significantly improved data fusion filtering techniques, leading to enhanced localization accuracy. By leveraging various data inputs, these advanced methods offer a more detailed understanding of spatial location [13]. Today, the Kalman filter is the most widely used technique, with its improved versions playing a critical role across various sectors [14]. For example, in [15], a dual-rate Kalman filter (DRKF) combined a time-differential GPS carrier phase and GPS pseudorange with INS measurements. A federated Kalman filter was used to analyze the effects of varying weight distribution in multiple GNSS time-transfer measurements [16]. In [17], an adaptive Kalman filter was employed for GNSS/IMU/LiDAR fusion localization. It is important to note that the Kalman filter is well-suited for linear systems, while the EKF is recommended for nonlinear system dynamics. For example, in [18], an adaptive-network fuzzy inference system (ANFIS)-improved EKF method was proposed for the determination of the accurate positions of autonomous underwater vehicles (AUVs) using a single beacon. In [19], the integration of the nonlinear autoregressive exogenous model (NARX) with an EKF was used to enhance UAV swarm localization. However, the Kalman filters mentioned above primarily assume Gaussian noise, meaning that their performance depends heavily on model accuracy and noise characteristics. In practical applications, noise is often non-Gaussian, making Kalman filters less effective in harsh localization environments. To address this, this study proposes an adaptive distributed Student's t EKF using Allan variance for UWB localization. The adaptive distributed filter employs a federation structure. The local filter uses a t EKF to estimate the signal distance between the UWB base station (BS) and the target, modeling the noise with a t distribution. The main filter then fuses the local filter's outputs to compute the final result, while Allan variance assists the local filter. Experimental results show that the proposed method significantly improves navigation accuracy compared to the distributed EKF. The structure of this paper is shown in Figure 1. The results of our research are summarized as follows:  
* We design a distributed UWB localization strategy for mobile objects, utilizing a distributed filter structure. The system employs multiple local filters to estimate the target's position by fusing distance measurements. The main filter then combines these outputs to compute the final position. * An adaptive Allan variance computation method was derived, where Allan variance is calculated based on noise estimation from the previous moment. * Building on the distributed UWB localization scheme and Allan variance method, we propose the adaptive distributed Student's t EKF. This method uses a t distribution to model the noise, and the main filter fuses the local filter outputs to compute the final result, with Allan variance assisting the local filter. * Experimental results, supported by rigorous statistical analyses, demonstrate the superior efficiency and effectiveness of the proposed algorithms, which significantly outperform traditional methods.