WhyGPSandHowItWorks?WhatsGPS?Navigationandpositioningarecrucialtosomanyactivitiesandyettheprocesshasalwaysbeenquitecumbersome.Overtheyearsallkindsoftechnologieshavetriedtosimplifythetask,buteveryonehashadsomedisadvantage.Finally,theU.S.DepartmentofDefense(DoD)decidedthatthemilitaryhadtohaveasuperpreciseformofworldwidepositioning.Andfortunatelytheyhadthekindofmoney.Ittooktobuildsomethingreallygood.TheresultistheGlobalPositioningSystem,asystemthatschangednavigationforever.TheGlobalPositioningSystem(GPS)isaworldwideradio-navigationsystemformedfromaconstellationof24satellitesandtheirgroundstation.GPSusesthese“man-madestars”asreferencepointstocalculatepositionsaccuratetoamatterofmeters.Infact,withadvancedformsofGPSyoucanmakemeasurementstobetterthanacentimeter.Inasenseitslikegivingeverysquaremeterontheplanetauniqueaddress.GPSreceivershavebeenminiaturizedtojustafewintegratedcircuitsandsoarebecomingveryeconomical.Andthatmakesthetechnologyaccessibletovirtuallyeveryone.ThesedaysGPSisfindinguswayintocars,boats,planes,constructionequipment,moviemakinggear,farmmachinery,evenlaptopcomputers.SoonGPSwillbecomealmostasbasicasthetelephone.Indeeditjustmaybecomeauniversalutility.WorkinginFiveLogicalStepsInprinciple,GPSoperatesinfivelogicalsteps:Step1:TriangulatingfromsatellitesImprobableasitmayseem,thewholeideabehindGPSistousesatellitesinspaceasreferencepointsforlocationshereonearth.Thatsabigideageometrically,asbyvery,veryaccuratelymeasuringourdistancefromthreesatelliteswecan“triangulate”ourpositionanywhereonearth.Supposewemeasureourdistancefromasatelliteandfindittobe11,000miles.Knowingthatwere11,000milesfromaparticularsatellitenarrowsdownallthepossiblelocationswecouldbeinthewholeuniversetothesurfaceofaspherethatiscenteredonthissatelliteandhasaradiusof11,000miles.Next,saywemeasureourdistancetoasecondsatelliteandfindoutthatits12,000milesaway.Thattellsusthatwerenotonlyonthefirstspherebutwerealsoonaspherethats12,000milesfromthesecondsatellite.Orinotherwords,weresomewhereonthecirclewherethesetwospheresintersect.Ifwethenmakeameasurementfromathirdsatelliteandfindthatwere13,000milesfromthatone,thatnarrowsourpositiondownevenfarther,tothetwopointswherethe13,000milespherecutsthroughthecirclethatstheintersectionofthefirsttwospheres.Sobyrangingfromthreesatelliteswecannarrowourpositiontojusttwopointsinspace.Todecidewhichoneisourtruelocationwecouldmakeafourthmeasurement.Butusuallyoneofthetwopointsisaridiculousanswer(eithertoofarfromEarthoranimpossiblevelocity)andcanberejectedwithoutameasurement.Step2:MeasuringdistancefromasatelliteWesawinthelastsectionthatapositioniscalculatedfromdistancemeasurementstoatleastthreesatellites.Buthowcanyoumeasurethedistancetosomethingthatsfloatingaroundinspace?Wedoitbytiminghowlongittakesforasignalsentfromthesatellitetoarriveatourreceiver.Inasense,thewholethingboilsdowntothose“velocitytimestraveltime”mathproblemswedidinhighschool.InthecaseofGPSweremeasuringaradiosignalsothevelocityisgoingtobethespeedoflightorroughly186,000milespersecond.Theproblemismeasuringthetraveltime.Butassumingwehavepreciseclocks,howdowemeasuretraveltime?Toexplainitletsuseagoofyanalogy:Supposetherewasawaytogetboththesatelliteandthereceivertostartplaying“TheStar-SpangledBanner”atprecisely12Noon.Ifsoundcouldreachusfromspace(which,ofcourse,isridiculous),thenstandingatthereceiverwedheartwoversionsof“TheStar-SpangledBanner,”onefromourreceiverandonefromthesatellite.Thesetwoversionswouldbeoutofsync.Theversioncomingfromthesatellitewouldbealittledelayedbecauseithadtotravelover11,000miles.Ifwewantedtoseejusthowdelayedthesatellitesversionwas,wecouldstartdelayingthereceiversversionuntiltheyfellintoperfectsync.Theamountwehavetoshiftbackthereceiversversionisequaltothetraveltimeofthesatellitesversion.SowejustmultiplythattimetimesthespeedoflightandBLNGO.Wevegotourdistancetothesatellite.ThatsbasicallyhowGPSworks.Onlyinsteadof“TheStar-SpangledBanner”thesatellitesandreceiversusesomethingcalleda“PseudoRandomCode”-whichisprobablyeasiertosingthan“TheStar-SpangledBanner”.ThePseudoRandomCode(PRC)isafundamentalpartofGPS.Physicallyitsjustaverycomplicateddigitalcode,orinotherwords,acomplicatedsequenceof“on”and“off”pulses.Thesignalissocomplicatedthatitalmostlookslikerandomelectricalnoise.Hencethename“Pseudo-Random.”Step3:GettingperfecttimingIfmeasuringthetraveltimeofaradiosignalisthekeytoGPSthenourstopwatcheshadbetterbeverygood,becauseiftheirtimingisoffbyjustathousandthofasecond,atthespeedoflight,thattranslatesintoalmost200milestoerror!Onthesatelliteside,timingisalmostperfectbecausetheyhaveincrediblypreciseatomicclocksonboard.Butwhataboutourreceivershereontheground?Rememberthatboththesatelliteandthereceiverneedtobeabletopreciselysynchronizetheirpseudo-randomcodestomakethesystemwork.Ifourreceiversneededatomicclocks(whichcostupwardsof$50Kto$100K)GPSwouldbealameducktechnology.Nobodycouldaffordit.LuckilythedesignersofGPScameupwithabrilliantlittletrickthatletsusgetbywithmuchlessaccurateclocksinourreceivers.T