Trajectory prediction of the train ahead is vital for deciding the minimum safe distance for train separation. An important research challenge, in this regard, is how to effectively and accurately estimate the trajectory of the train ahead using spatiotemporal approaches with train operating data. In this paper, we present a novel hybrid model for predicting train trajectories by integrating Long Short-Term Memory (LSTM) and Kalman Filter (KF). In the proposed hybrid LSTM-KF model, the LSTM model is used to analyze time series data and discover the long-term dependencies of train trajectory data, which can be assumed as observation data for the KF model. The KF model can combine train dynamics mechanism to extract local features of train operation data, so as to smooth the train trajectory predicted by LSTM model. A novel on-the-fly algorithm is devised for efficient realization of the proposed LSTM-KF model. Experiments are carried out using the train data collected from Chengdu Metro Line 8. The results indicate that our hybrid LSTM-KF model has greatly improved the accuracy of long-term train trajectory prediction.

The accurate trajectory of the train ahead with more dynamic behaviour, such as train position, speed, acceleration, etc., is the critical issue of virtual coupling for future railways, which can drastically reduce their headways and increase line capacity. This paper presents an integrated convolutional neural network (CNN) and long short-term memory (LSTM) hybrid model for the task of trajectory prediction. A CNN–LSTM hybrid algorithm has been proposed. The model employs CNN and LSTM to extract the spatial dimension feature of the trajectory and the long-term dependencies of train trajectory data, respectively. The proposed CNN–LSTM model has superiority in achieving collaborative data mining on spatiotemporal measurement data to simultaneously learn spatial and temporal features from phasor measurement unit data. Therefore, the high-precision prediction of the train trajectory prediction is achieved based on the sufficient fusion of the above features. We use real automatic train operation (ATO) collected data for experiments and compare the proposed method with recurrent neural networks (RNN), recurrent neural networks (GRU), LSTM, and stateful-LSTM models on the same data sets. Experimental results show that the prediction performance of long-term trajectories is satisfyingly accurate. The root mean square error (RMSE) error can be reduced to less than 0.21 m, and the hit rate achieves 93% when the time horizon increases to 4S, respectively.

Rail transit plays a significant role in the operation of an efficient and effective urban public transportation system. Safety and capacity are some of the most crucial objectives in railway operations. The communication-based train control (CBTC) system is a continuous and automatic train control system that realizes constant and high-capacity train ground two-way communication. In this study, a dynamic headway model of the ‘softwall’ moving-block approach is proposed for CBTC to increase the track capacity and improve dispatching efficiency based on the train trajectory prediction. For this precise trajectory prediction task, we introduce a hybrid trajectory prediction model to combine Long Short-term memory (LSTM) and Kalman Filter (KF) to extract the train’s local data features and learn the long-term dependencies, respectively. Then we present a dynamic headway model to maximize the train headway and reduce the track distance. The leading trains’ information is used to construct the iterative learning control strategy, and the predicted trajectory is input into the algorithm of the headway model. We use a simulation model of the rail network in Chengdu to demonstrate the effectiveness of our proposed approach. The results show the Mean Absolute Error (MAE) of the predicted trajectory retreated to 93.97 cm and reductions in operation headway of at least 64.33% under the dynamic headway model versus the traditional moving-block model.