A Closed-Form Algorithm for Integrated TOF-PDR Positioning Using a Single Anchor

In this letter, we propose a hybrid indoor positioning method that integrates propagation distance estimation using a single ultra-wideband (UWB) anchor and pedestrian dead reckoning (PDR) on commercial smartphones. The proposed method estimates the smartphone's coordinates by comparing two distances: one derived from time-of-flight information provided by the UWB system, and the other obtained through smartphone-based PDR. Since the terminal position is obtained directly in a closed form, the computational complexity is reduced, facilitating integration with PDR on portable devices. Experiments were conducted in an indoor environment using a single UWB anchor capable of both transmission and reception, along with a commercial smartphone. The effectiveness of the proposed method was validated by comparing its positioning accuracy and computational complexity with brute-force search. The proposed approach achieved an average positioning error of 1.7 m and reduced the computational complexity to approximately 1/1000 of that required by the brute-force search, thereby validating its effectiveness.