Accurate　acquisition　of　interactive　information　is　crucial　for　the　effective　execution　of　rehabilitation　training.　However,　due　to　model　and　sensor　errors,　it　is　difficult　to　obtain　interactive　information　accurately　and　quickly.　To　overcome　these　challenges,　a　novel　accurate　and　fast　estimation　method　for　the　human-robot　interaction　torques　(HRITs)　is　proposed　in　this　article.　First,　the　HRIT　model　with　order　adaptive　adjustment　ability　(HMOAA)　is　constructed.　The　polynomial　order　of　HMOAA　can　be　adaptively　adjusted　based　on　the　partial　state　estimation,　which　is　more　consistent　with　the　dynamic　time-varying　characteristics　of　HRIT.　Second,　the　Sage-Husa　adaptive　strong　tracking　Kalman　filter　(SHASTKF)　is　designed　based　on　the　modified　Sage-Husa　adaptive　Kalman　filter　(SHAKF)　and　strong　tracking　Kalman　filter　(STKF).　The　SHASTKF　can　quickly　track　the　abrupt　HRIT　changes　when　the　subject　suddenly　exerts　active　torques　in　rehabilitation　training.　Moreover,　it　also　has　the　ability　to　recursively　estimate　the　noise　characteristics,　and　can　stably　complete　the　HRIT　estimation　task　when　the　noise　characteristics　are　unknown.　Finally,　simulations　and　experiments　are　conducted　to　validate　the　proposed　method,　and　the　comparison　results　demonstrate　that　the　proposed　method　has　good　torque　estimation　precision　and　fast　tracking　ability　of　abrupt　changes　in　HRITs.