This　paper　proposes　a　fast　speech　enhancement　algorithm　for　the　removal　of　noise　from　single-channel　speech　signal,　based　on　a　novel　noise　constrained　least-squares　(NCLS)　method.　Parameters　of　speech　signal　modeled　as　autoregressive　process　are　well　estimated　by　the　NCLS　method　and　thus　the　speech　signal　can　be　recovered　from　Kalman　filtering.　Simulation　results　show　that　the　proposed　NCLS　estimation-based　algorithm　has　a　much　faster　speed　than　the　generalized　least　absolute　deviation　estimation-based　algorithm　and　possesses　good　speech　enhancement　performance　than　the　Kalman　filtering　algorithms　based　on　the　conventional　second-order　estimation　and　the　high-order　estimation.　©　2012　IEEE.