Positioning and Tracking of High-speed Trains with Non-linear State Model for 5G and Beyond Systems

High-speed trains (HSTs) with fifth generation (5G) communications services, including both high rate data links and high reliability mission-critical services, are considered as one of the new industry verticals facilitated by the 5G connectivity. In this paper, we study positioning of HSTs in 5G new radio (NR) networks based on time difference of arrival (TDoA) and angle-of-arrival (AoA) measurements, obtained with specific 5G NR reference signals at the millimeter wave (mmWave) frequency. Moreover, the HST is tracked with an extended Kalman filter, where, instead of conventional linear state-transition model, we propose and derive a non-linear state-transition model, including the train position, absolute train velocity, and train heading. Furthermore, by introducing a state-dependent process variance for the angular velocity of the train, we show that the positioning performance of the HST can be significantly improved compared to the conventional linear state-transition modeling. Based on realistic simulations on a real-life high-speed track, we show that the proposed positioning engine can reach 95% percentile estimation accuracies of 2.3 m, 0.47 m/s, and 1.6 deg, for the train position, train velocity, and train heading, respectively, thus fulfilling the requirements specified by the 3GPP for machine control and transportation services.