Future sub-THz cellular deployments may be utilized to complement the coverage of the global positioning system (GPS) and provide centimeter-level accuracy. In this work, we use measurement data at 142 GHz to test a map-based position location algorithm in an outdoor urban microcell (UMi) environment. We utilize an extended Kalman filter (EKF) to track the position of the user equipment (UE) along a rectangular track, with the transmitter-receiver separation distances varying from 24.3 m to 52.8 m. The position and velocity of the UE are tracked by the EKF, with measurements of the angle of arrival and time of flight information obtained along an outdoor track, to provide a mean accuracy of 24.8 cm at 142 GHz, over 34 UE locations, using a single base station in line-of-sight and non-line-of-sight.