For　high-speed　train　(HST),　high-precision　of　train　positioning　is　important　to　guarantee　train　safety　and　operational　efficiency.　For　improving　train　positioning　accuracy,　we　develop　a　mathematical　positioning　model　by　analyzing　the　wireless　position　report　created　by　HST.　To　begin　with,　k-means　algorithm　is　integrated　with　the　least　square　support　vector　machine　(LSSVM)　to　differentiate　the　position　data　and　establish　the　corresponding　prediction　model　for　each　position　data　class.　Then,　the　ant　colony　optimization　(ACO)　algorithm　is　introduced　to　adaptively　optimize　the　clustering　number　of　position　data　and　solve　the　over-fitting　problem　of　the　single　k-means　algorithm.　So,　a　better　classification　of　position　data　can　be　obtained　by　ACO-k-means　than　the　single　k-means　algorithm.　Furthermore,　the　online　learning　algorithms　are　designed　for　improving　the　adaptability　and　real-time　performance　of　established　positioning　model.　Finally,　the　field　data　of　Beijing-Shanghai　high-speed　railway　(BS_HSR)　is　used　to　test　the　performance　of　the　established　positioning　models.　Experiments　on　real-world　positioning　data　sets　from　BS_HSR　illustrate　that　the　proposed　methods　can　enhance　the　real-time　performance　in　online　updating　process　on　the　premise　of　reducing　the　positioning　error.　IEEE