The　frequency　modulated　continuous　wave　(FMCW)　radar　has　been　used　to　determine　the　position　and　movements　of　a　target.　In　this　paper,　we　design　a　liner　FMCW　radar-based　indoor　position　system　for　better　target　localization　and　trajectory　detection.　First,　with　the　received　radar　signals,　we　construct　a　two-dimensional　range-Doppler　map.　Using　the　map,　We　extend　the　one-dimensional　constant-false-alarm　rate　(CFAR)　technique　into　the　two-dimensional　one　and　develop　a　two-dimensional　cell-averaging　CFAR　detector;　it　effectively　eliminates　the　outliers　of　the　original　CFAR　results　and　hence　reduces　localization　error　significantly.　Finally,　we　adopt　the　Kalman　filter　to　optimize　the　target　trajectory.　The　experimental　results　are　provided　and　they　show　that　the　accuracy　of　the　estimated　range　is　improved　by　about　38%　and　11%　in　stationary　and　moving　target　localization,　respectively,　as　compared　with　the　current　detectors.　©　2020　IEEE.