Structural　health　monitoring　(SHM)　is　vital　for　ensuring　the　service　safety　of　aging　bridges.　As　one　of　the　most　advanced　sensing　techniques,　Global　Navigation　Satellite　Systems　(GNSS)　could　capture　massive　spatiotemporal　information　for　effective　bridge　structural　health　monitoring　(BSHM).　Unfortunately,　GNSS　measurements　often　contain　outliers　due　to　various　factors　(e.g.,　severe　weather　conditions,　multipath　effects,　etc.).　All　such　outliers　could　jeopardize　the　accuracy　and　reliability　of　BSHM　significantly.　Previous　studies　have　examined　the　feasibility　of　integrating　the　conventional　multi-rate　Kalman　filter　(MKF)　with　an　adaptive　algorithm　in　the　data　processing　processes　to　ensure　BSHM　accuracy.　However,　frequent　parameter　adjustments　are　still　needed　in　tedious　data　processing　processes.　This　study　proposed　an　outlier　detection　method　using　a　Nelder-Mead　simplex　robust　multi-rate　Kalman　filter　(RMKF)　for　supporting　trustworthy　BSHM　using　GNSS　and　accelerometer.　In　the　end,　the　authors　have　validated　the　proposed　method　using　the　monitoring　data　collected　at　the　Wilford　Bridge　in　the　UK.　Results　showed　that　the　accuracy　of　the　total　dynamic　vibration　displacement　time　series　has　been　improved　by　21%　compared　with　the　results　using　the　conventional　MKF　approach.　The　authors　envision　that　the　proposed　method　will　shed　light　on　reliable　and　explainable　data　processing　policy　and　trustworthy　BSHM.