A High-Precision Deep Kalman Filter Design for Nonlinear Train Operation State Estimation

In the actual operating environment of trains, the state model often exhibits nonlinear characteristics, and the Kalman filter and its related theories are commonly used for accurate estimation of position and velocity. However, in the filtering process of nonlinear systems, the performance of the Extended Kalman Filter (EKF) is severely affected by the influence of linearization rounding errors, which can lead to performance degradation and even divergence as the rounding errors increase. This paper primarily proposes a category of high-precision Kalman filtering methods to enhance the estimation accuracy of train operation states. Firstly, we establish identification methods for discarding residual terms in the state and measurement models, and design a new type of Extended Kalman Filter, referred to as the Residual-based Extended Kalman Filter (REKF), which incorporates the statistical characteristics of the residual terms in the Kalman filter framework. Furthermore, a REKF-embedded deep neural network (DREKF) is developed to further augment the REKF's capability in nonlinear systems. Numerical simulations show that the REKF improves the estimation accuracy by more than 5$\%$ on average compared to the EKF, and the DREKF estimation accuracy is better than the REKF with higher stability.