To　improve　the　safety　and　stability　of　maglcv　train　Suspension　Operation,　the　train　Suspension　control　System　was　sclcctcd　as　the　rcscarch　objcct,　the　rcal-timc　adaptive　adjustment　of　tracking　differentiator　(TD)　Parameters　based　on　the　BP　neural　network　(BP-NN)　was　analyzed.　To　avoid　nonlincar　complex　Operations　in　the　TD　algorithm,　a　fastest　control　synthesis　funetion　with　linear　characteristics　was　construeted　using　the　second-order　fastest　time　System　and　the　State　backstepping　method,　and　a　discrete　form　of　fastest　TD　(FST-TD)　was　proposed.　Frcquency　domain　and　convergence　analysis　was　rigorously　condueted　on　the　proposed　algorithm.　For　the　issue　of　delayed　parameter　adjustment　when　FST-TD　encountered　irregulär　input　signals,　the　self-learning　capability　of　BP-NN　and　the　dynamic　characteristics　of　the　adaptive　uncertain　System　were　integrated　to　propose　a　FST-TD　based　on　BP-NN　(BP-FST-TD)　algorithm.　In　this　algorithm,　BP-NN　parameter　adaptive　adjustment　was　achieved　through　online　updated　weights　by　the　backpropagation　algorithm.　FST-TD　performed　real-time　tracking　and　filtering　of　complex,　multi-condition　input　signals　based　on　the　adaptive　parameters.　To　validatc　the　algorithm＇s　effectiveness　and　practicality,　the　real-time　tracking　and　filtering　Performance　of　BP-FST-TD　was　examincd　using　gap　signals　with　random　noisc　in　the　maglcv　train　Suspension　control　System.　Research　results　show　that　FST-TD　has　decent　filtering　and　differentiation　capabilities.　The　convergence　analysis　reveals　that　it　exhibits　no　oscillation　or　overshoot.　Furthermore,　this　FST-TD　strueture,　without　complex　nonlincar　Operation,　is　relatively　straightforward　in　design.　The　FST-TD　maintains　ideal　smoothness　and　phase　integrity　during　the　tracking　of　various　input　signals.　Undcr　working　conditions　1　and　2,　the　BP-FST-TD　reduces　the　mean　absolute　error　(MAE)　of　the　gap　signals　by　32.　6%　and　61.　8%　respectively　compared　to　traditional　TD　algorithms.　Bcsidcs,　the　intcgrals　of　timc-weighted　absolute　error　reduec　by　51.　8%　and　70.　2%,　respectively.　These　findings　substantiate　the　effective　tracking　and　filtering　Performance　of　BP-FST-TD,　and　the　algorithm　effectively　suppresses　random　noise　from　the　gap　sensors　under　various　operational　conditions　of　the　maglev　train.　Thus,　it　can　be　concluded　that　the　Suspension　control　System　based　on　BP-FST-TD　effectively　ensures　the　stable　Suspension　Operation　of　the　train.　The　research　results　offer　novel　approaches　and　methods　for　TD　control　parameter　optimization　in　other　engineering　domains.　©　2025　Chang＇an　University.　All　rights　reserved.