Since　energy　storage　system　(ESS)　usually　works　under　complex　environments　that　are　susceptible　to　noise　or　other　random　fluctuations,　it　is　crucial　to　develop　robust　state　of　charge　(SOC)　estimation　methods　in　battery　management　system　for　effectively　management　of　the　ESS.　The　mean　square　error　(MSE)　criterion　based　original　extreme　learning　machine　(ELM)　model　can　only　perform　well　under　Gaussian　measurement　noise.　To　enhance　the　estimation　accuracy　of　ELM　under　non-Gaussian　measurement　noise,　a　new　robust　ELM　is　utilized　to　achieve　accurate　estimation　of　SOC　in　this　paper,　in　which　the　kernel　mean　p-power　error　(KMPE)　loss　with　wider　performance　surface　and　flexibility　is　used　to　replace　the　MSE　in　conventional　ELM.　Some　experiments　are　conducted　to　test　the　effectiveness　of　the　proposed　approach　for　SOC　estimation　under　various　work　conditions　with　complex　non-Gaussian　measurement　noises.　©　2022　IEEE.