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HowGPSWorksHowGPSWorksOutlineWhatisGPSHowGPSworksHowGPScodesworkWhyIuseGPSformyresearchOutlineWhatisGPSHowdoyouusethesesatellitestocalculateyourposition?TheGlobalPositioningSystemisaconstellationof31satellitesthatisusedtocalculateyourposition.HowdoyouusethesesatelliteInsteadofsatellites,letsusetransmittersontheground.Insteadofsatellites,letsusGrandJunctionsendsasignaltoRadon’sGPS.Whatkindofsignal?GrandJunctionTransmitterRadoninBoulderitputsthetimeonthesignal.

Forthistowork,we’llneedforboththetransmitterandRadontohaveclocks.GPSGrandJunctionsendsasignalWhenRadon’sGPSreceivergetsthesignal,hecomparesthetimeonthesignalwiththetimeonhisclock.So,aGPSsignaltellsyouhowfaryouarefromthetransmitter.TimeDifference(inseconds)*2.99792458108meters/second=Distance(inmeters)WhenRadon’sGPSreceivergetsIfthedistancefromtheGPStransmitteris250miles,thatmeansyouaresomewhereonacircleofradius250miles.IfthedistancefromtheGPStNowadda2ndtransmitterinFt.Collins.Nowadda2ndtransmitterinFAndathirdtransmitterinPuebloRadonisattheintersectionofthe3circlesAndathirdtransmitterinPueThisonlyworksif:Youknowwherethetransmittersare.GPSsignalsalsotransmitthesatellitelocations.Everyonehasgoodclocks.TheGPSsatelliteshaveverygoodclocks.AGPSusercanusea4thsignaltopiggy-backontotheGPSsatelliteclocks.Andyoucantellthetransmittersapart.Thesignalsaremadeinawaysothatyoucantellwhichtransmittersentthem.Forrealproblems,weusetheintersectionofthreespheres,notthreecircles.Thisonlyworksif:YouknowwhIntersectingSpheresButonly1pointisontheEarthIntersectingSpheresButonly1WhenGPSreceivesasignalItcomparesthatsignalwithalltheknowncodes(therearecurrently37).Thereceiverdetermineswhichsatelliteitis.Itdecodesthetiminginformation,multipliesbythespeedoflighttofindtheradiusofthesphere.Onceithasdonethatfor3satellites,itcandeterminethelocation.WhenGPSreceivesasignalItcHowdoGPSsignalssendallthisinformation?Theyusecodes!Binarycodes.Eachsatellitehasadifferentcode.HowdoGPSsignalssendallth000010001010011100001110010010001000010001010110001111011100101011011001111010110010110010100110011111101100111100100110011010001110001001000101100010110111000000110110010001000101101000101001000000011111000110001011111011111100110111001011011110001111110101001010000101010011100001101001110110001111011111000011111111110100100100100110011101010111110000100010110100111111000010011011110011100011011010110110101000010110100101000101001000111001110001010010111010111010101000001011011100110110011010000000000011101110110001101101010101101100011100011001100111110101111100111010101000001111110010010100000011101000111101101001011011000001001001001100001101100001111011101110001101110110100111001000110101010000110110100101110010111111111011000111000000110111000110000001000000001000001101010001010111101100011101101000110010101111100111101000000011011110011001110101111000001111011001000100101011100000000100001010101001111101100111011011111100101111000100110101Forexample,herearethefirst1000numbersofthecodeforsatellite1100111101110100010011011111111101111001011011110110011011111010101000111110110001100010011001101000010000010111111100001000011010110101110101101001100000110100001100010101011001000100100000110000011110000111010000011100100111011000000010110011110001001010101111101010011110010111110110010100010111000010011100001111101110101110101101100111100100110101110010001101101111101100110101110000111010111000110001111000001000111011011100010000011010011001001110000100010111000100100011011111000111010101001100000000110011110011101010000100100011100101010100111001011011111001111111001101001110110011101100101001010011001010111011100111000110111100110000010100011110011011110110011110100110111010011100110101010110100000101110001110001110101100011110001001010011101010110000110001000110010101110011000011111000001111100010010001101000101000101001001000110000110010000011000110001010000110110010110100110011000101101110011110010001010010100011110011101100001111101100101Thisisthecodeforsatellite6000010001010011100001110010010StrategyFirstweneedtolearnhowGPScreatesthesecodesThenweneedtocomeupwithawaytoquicklytellthecodesapart.StrategyFirstweneedtolearnHowdoyoucreatecodes?Youusebinaryadditionrules.0+0=01+0=10+1=11+1=10(butonlyusethelastbit,0)GPSuses“shiftregisters.”Themoreshiftregistersyouhave,themorecomplicatedyoucanmakeyourcode.Howdoyoucreatecodes?YouusRegister1Register2Register3Code111-Startwithall1’sinyourshiftregisters

AddRegister1andRegister3Theanswer0goesintoRegister1andeverythingshiftstotheright.Hereisanexamplewith3shiftregistersForthisexample,1+1=10==>0Register1Register2Register3CodResultinginRegister1Register2Register3Code111-0111ResultinginRegister1Register2Next0+1=1Register1Register2Register3Code111-01111011Next0+1=1Register1Register2ReAfter2N-1steps(Nisthenumberofregisters),thecoderepeatsRegister1Register2Register3Code111-0111101101010010100111001110For3shiftregisters,thecoderepeatsafter7steps.After2N-1steps(NisthenuRealGPSUses10shiftregisters.Theyadddifferentregisterstoproducethecodesfordifferentsatellites.Satellite1uses2and6.Satellite2uses3and7,andsoon.A10-shiftregistercoderepeatsafter210-1,or1023.RealGPSUses10shiftregisterHowdoyoucomparecodes?100111101110100010011011111111101000010001010011100001110010010001Everytimethenumbersagree,add1.Everytimethenumbersdisagree,subtract1.Howdoyoucomparecodes?10011Thisexample:2differentsatellites10011110111010001001101111111111100001000101001110000111001001000114agree11disagreeTotalscore:3Perfectagreementwouldbe35Thisexample:2differentsate0110001010101100100010010000011000001111000011000101010110010001001000001100000111100001

0110001010101100100010010000011000001111000011000101010110010001001000001100000111100001

AgreementisperfectButifyourecognizetheyareshiftedby1:Thisexample:samesatellitecodes,butshiftedNotsogood-scoreof-3.011000101010110010001001000001It’susefultohaveacomputertodothesecomparisons,especiallysinceyouhavetotestalotofdifferentshifts.Thenyoucanplothowgoodtheagreementisasafunctionofshift.It’susefultohaveacomputerSatellite9comparedtoSatellite10codeSatellite9comparedtoSatellSatellite10comparedtoSatellite10codeVerygoodagreementhere.Satellite10comparedtoSatelSatellite10comparedtoSatellite10codethathasbeenshiftedby200.Satellite10comparedtoSatelWhytwopeaks?Orisblackshiftedby823?Startwith2codesIsredshiftedby200?Whytwopeaks?OrisblackshifWhyarethecodesshifted?TheshiftgivestheGPSreceiverthetimedifference.TimeDifference(inseconds)*2.99792458108meters/second=Distance(inmeters)WhatisatypicalTimeDifference?GPSsatellitesare~20,000,000metersabovetheEarth.20,000,000/300,000,000~70millisecondsWhyarethecodesshifted?ThePlatetectonicsTheEarthisasphericaljigsawpuzzle.Differenttectonicplatesmoveindifferentdirectionsatdifferentspeeds.PlatetectonicsTheEarthisaImostlyuseGPStostudyhowtheEarthchanges.Istudyplatetectonics,volcanoes,and

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