For a high-speed train (HST), quick and accurate localization of its position is crucial to safe and effective operation of the HST. In this paper, we develop a mathematical localization model by analyzing the location report created by the HST. Then, we apply two sparse optimization algorithms, i.e., iterative pruning error minimization (IPEM) and L-norm minimization algorithms, to improve the sparsity of both least squares support vector machine (LSSVM) and weighted LSSVM models. Furthermore, in order to enhance the adaptability and real-time performance of established localization model, four online sparse learning algorithms LSSVM-online, IPEM-online, L-norm-online, and hybrid-online are developed to sparsify the training data set and update parameters of the LSSVM model online. Finally, the field data of the Beijing-Shanghai high-speed railway (BS-HSR) is used to test the performance of the established localization models. The proposed method overcomes the problem of memory constraints and high computational costs resulting in highly sparse reductions to the LSSVM models. Experiments on real-world data sets from the BS-HSR illustrate that these methods achieve sparse models and increase the real-time performance in online updating process on the premise of reducing the location error. For the rapid convergence of proposed online sparse algorithms, the localization model can be updated when the HST passes through the balise every time.