Position calculation models by neural computing and online learning methods for high-speed train

For high-speed trains, high precision of train positioning is important to guarantee train safety and operational efficiency. By analyzing the operational data of Beijing---Shanghai high-speed railway, we find that the currently used average speed model (ASM) is not good enough as the relative error is about 2.5 %. To reduce the positioning error, we respectively establish three models for calculating train positions by advanced neural computing methods, including back-propagation (BP), radial basis function (RBF) and adaptive network-based fuzzy inference system (ANFIS). Furthermore, six indices are defined to evaluate the performance of the three established models. Compared with ASM, the positioning error can be reduced by about 50 % by neural computing models. Then, to increase the robustness of neural computing models and real-time response, online learning methods are developed to update the parameters in the last layer of neural computing models by the gradient descent method. With the online learning methods, the positioning error of neural computing models can be further reduced by about 10 %. Among the three models, the ANFIS model is the best in both training and testing. The BP model is better than the RBF model in training, but worse in testing. In a word, the three models can reduce the half number of transponders to save the cost under the same positioning error or reduce the positioning error about 50 % in the case of the same number of transponders.