## 2 Related Work  
To date, to enhance the UWB-based positioning accuracy, various scholars combined UWB with different sensors (such as inertial measurement unit (IMU), laser radar, R-GBD camera, and so on) to improve the positioning accuracy by multi-sensor combination. [PERSON] et al. proposed an adaptive complementary Kalman filter to filter the UWB and IMU data and track the errors of variables such as position, velocity, and direction, which not only eliminated the multipath effect caused by the UWB signal being shielded, but also corrected the velocity and acceleration bias caused by the IMU drift [7]. [PERSON] et al. used an IMU/UWB loose combination precise positioning system to calculate the accurate position, speed, and attitude information of a robot, in which the positioning coordinates from the UWB base station (EKF) corrected the UWB error in real time [8]. [PERSON] et al. proposed a novel algorithm for motion estimation that could reduce the drift in IMU sensors. This algorithm employed a Kalman filter to estimate and fuse the UWB measurements, and the drift-free position obtained by the UWB localization Kalman filter was used to fuse the position calculated by IMU [9].  
The most commonly used fusion algorithms include the Kalman filter (KF), extended Kalman filter (EKF), complementary Kalman filter (CKF), and Monte Carlo filter.  
1. Kalman filter (KF). [PERSON] [10] proposed a new method for linear filtering and prediction problems, which used the linear system state equation to observe system input and output data in order to best estimate the state of the system. Benefiting from the advantages of strong real-time performance, high speed, and high efficiency, the KF has been widely used in anti-interference [11].
2. Extended Kalman filter (EKF). Although linear systems often exist in theory, more nonlinear systems exist in practical engineering applications. Therefore, a linear time-varying system was used to approximate the nonlinear system within each sampling interval by linearization methods, such as Taylor series expansion [12]. Therefore, linear time-varying systems can still use KF.
3. Complementary Kalman filter (CKF). [PERSON] [13] put forward a new method for nonlinear problems with better performances than the EKF, mainly based on a third-order spherical radial displacement criterion known as the CKF. Using a group of volume points to approximate the state mean and covariance of nonlinear systems with additional Gaussian noise, CKF is the closest approximation algorithm to Bayesian filtering. It is also a powerful tool to solve the state estimation of nonlinear systems [14].
4. Monte Carlo filter (MCL). MCL is a fast and scalable unsupervised clustering algorithm based on the random Walk and Markov chain [15]. It has been mainly applied in the field of robot positioning, and the posterior probability density function of mobile robot state is approximated to the real state through MCL random sampling [16].  
Based on the related work analysis above, most conventional UWB/IMU fusion methods still lack error convergence analysis. Therefore, this study proposes a two-loop accumulated error dynamics model based on EKF. The proposed model analyzes the cumulative error of the IMU quadratic integral and EKF-positive feedback accumulated error, guarantees error convergence and controllability of the whole UWB/IMU positioning system, and further improves the positioning accuracy of the fusion positioning system.