As a fundamental method for integrated indoor positioning, UWB/IMU offers more stable performance compared to separate UWB sensor and IMU sensor positioning and uses the least squares (LS) method for positioning processing, however, the performance of conventional LS will be seriously affected when the contamination rate of measurement noise is high. To address this problem, this paper proposes a Robust Extended Kalman Filter (REKF) based algorithm for robot-integrated indoor positioning, which combines Ultra Wideband (UWB) and Inertial Measurement Unit (IMU) positioning methods to obtain a more robust system performance and optimal positioning accuracy. In this paper, a vehicle equipped with UWB/IMU sensors and four anchor points is set up to perform straight, circular, and arbitrary motions in an experimental environment with visible obstacles. In this paper, a vehicle equipped with a UWB/IMU sensor and four anchor points is set up to perform linear, circular, and trajectory motions in an experimental environment with visible obstacles. The experimental results show that compared with EKF, REKF improves the localization precision and accuracy in the three motions by 20.98%, 35.51%, and 47.06%, respectively, which effectively improves the accuracy and robustness of the robot's indoor positioning, and provides an improved and practical method for integrating indoor positioning algorithms to make indoor positioning more accurate and reliable..