The　research　on　connected　and　automated　vehicles　attracts　much　attention　recently.　In　connected　vehicle　systems,　connected　cruise　control　(CCC)　is　a　wildly　concerned　technique　to　improve　traffic　safety　and　mitigate　congestion.　In　this　article,　an　optimal　state-estimation-based　(SE-based)　control　algorithm　is　proposed　in　a　backward　recursion　manner　to　regulate　CCC　vehicle＇s　longitudinal　motion　under　stochastic　communication　delays,　state　noises,　and　channel　interferences.　Based　on　the　analysis　of　error　dynamics　of　vehicles　and　optimal　state　estimation　strategy,　the　SE-based　system　dynamics　is　first　formulated　by　using　the　Kalman　filtering　method.　Then,　a　two-step　SE-based　control　algorithm　aiming　at　minimizing　the　quadratic　system　cost　is　proposed　to　enhance　the　vehicular　platoon　stability.　In　particular,　the　optimal　control　strategy　can　be　generated　online　as　a　linear　function　of　the　estimated　state　information　and　previous　control　signals,　and　the　corresponding　coefficient　can　be　iteratively　calculated　in　an　offline　step.　Finally,　the　results　are　successfully　extended　to　the　case　of　arbitrary　communication　delays,　and　the　condition　for　the　asymptotically　mean　square　stability　of　the　proposed　optimal　SE-based　CCC　algorithm　is　derived.　Simulation　results　indicate　that　the　proposed　SE-based　control　algorithm　has　better　system　performance　and　control　stability　compared　with　existing　works.