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-0-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-0-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　highspeed　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.