In　the　surface　profile　analysis,　there　are　often　a　few　observations　that　contain　outliers.　Due　to　the　existence　of　outliers,　the　application　of　non-robust　reconstruction　algorithms　for　measurement　data　will　become　a　huge　problem　because　these　methods　are　often　sensitive　to　outliers　and　the　approximation　effectiveness　will　be　greatly　aggravated.　In　view　of　this,　this　paper　presents　a　novel　angle-based　moving　total　least　squares　reconstruction　method,　to　the　best　of　our　knowledge,　that　applies　two-step　pre-treatment　to　handle　outliers.　The　first　step　is　an　abnormal　point　detection　process　that　characterizes　the　geometric　features　of　discrete　points　in　the　support　domain　through　a　new　angle-based　parameter　constructed　by　total　least　square.　Then,　the　point　with　the　largest　anomaly　degree　is　removed,　and　a　relevant　weight　function　is　defined　to　adjust　the　weights　of　the　remaining　points.　After　pretreatment,　the　final　estimates　are　calculated　by　weighted　total　least　squares　(WTLS)　based　on　the　compact　weight　function.　The　detection　and　removal　of　outliers　are　automatic,　and　there　is　no　need　to　set　a　threshold　value　artificially,　which　effectively　avoids　the　adverse　impacts　of　human　operation.　Numerical　simulations　and　experiments　verify　the　applicability　of　the　proposed　algorithm　as　well　as　its　accuracy　and　robustness.　(C)　2022　Optica　Publishing　Group