A High-Order Extended Kalman Filtering-Enabled Nonlinear State Estimation Method for High-Speed Trains Considering Multiple Operating Phases

Rail transportation has undergone a prolonged evolutionary trajectory and remains pivotal in contemporary society. Technological advancements have shifted considerable attention toward methodologies such as virtual coupling, which promise enhanced transport efficiency without the need for additional railway infrastructure. However, virtual coupling requires precise state estimation for each train to ensure optimal safety margins. Currently, the use of Kalman filtering (KF) for state estimation has matured significantly. Nevertheless, existing KF methodologies for nonlinear systems, primarily based on extended KF (EKF) and unscented KF (UKF), often fall short of the required precision standards in high-speed train (HST) environments. To address this challenge, this article first delineates various motion scenarios for HSTs based on dynamic modeling. Following this, a high-order extended Kalman filter (HEKF) based on the unscented least-squares (ULS) approach is proposed, specifically tailored for the modeled train systems. These methodologies excel at extracting comprehensive information from the nonlinear components of HST systems, thereby significantly enhancing estimation accuracy. Furthermore, to validate the estimation capabilities of the HEKF in real-world settings, performance comparisons are made against traditional nonlinear estimation algorithms across diverse simulation scenarios and during actual train operations on the Zhengzhou-Xi’an line. The findings demonstrate that the proposed algorithm markedly improves both precision and stability.