Therandomstepmaneuverwithuniformlydistributedstartingtimeshasthedisadvantagethatitcannotfocusthestartingtimeonthemoreefficiencytime.Itdecreasesthepenetrationprobability.Toresolvethisproblem,arandomsteppenetrationalgorithmwithnormaldistributionstartingtimeisproposed.Usingtheshapingfiltersandadjointsystemmethod,themissdistancewithdifferentstartingtimescanbeacquired.Accordingtothepenetrationstandard,thetimewindowensuringsuccessfulpenetrationcanbecalculatedanditisusedasthe3σboundofthenormallydistributedrandommaneuver.Simulationresultsindicatethatthenormallydistributedrandommaneuverhashigherpenetrationprobabilitythantheuniformlydistributedrandommaneuver.
