Autonomous mobile robots (AMRs) play a crucial role in smart factories and Internet of Things (IoT) applications. This paper presents a high-accuracy localization system called the global UWB system (GUS) for the AMR based on ultra-wideband (UWB) distance measurements. By using two UWB modules (tags) on AMR, it is possible to estimate both position and heading angle simultaneously, which can solve the problem of error accumulation over time in internal sensors. A new tightly coupled algorithm called baseline constraint extended Kalman filter (BC-EKF) is proposed. The baseline is the actual distance between the two tags that is used as a constraint for the measurement process. The relationship between the baseline and the heading angle error is also discussed to ensure reasonable deployment of the tags. The proposed localization method is persistent as value of the geometric dilution of precision (GDOP) increases. This helps to secure the performance of the localization method even in tight workspaces where the number of fixed UWBs (anchors) is limited. The simulation and experiment results demonstrate the localization performance of the proposed method.