6/29/2015 ExaminingGPSData(GPSandGIS)Part1

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ExaminingGPSData(GPSandGIS)Part1

INWHICHwecontinueourdiscussionofthetheoreticalframeworkofGPSpositionfinding,andyoupracticeusingPCsoftwaretoinvestigatefilescollectedbyGPSreceivers.

OVERVIEW

SomeQuestionsAnswered

Asyoureadthelasttwotopicssomequestionsmayhaveoccurredtoyou.Andtheanswerstothesequestionsmaygenerateotherquestions.Herearesomethatcomeupfrequently:

Question#1:"ThecaptainoftheshipofFigure21hadamapshowingthelocationsofthesoundhouses.ButhowdoestheGPSreceiverknowwherethesatellitesare?"

AmapisatwodimensionalscalemodelofthesurfaceoftheEarth.Butmodelscantakemanyforms,includingmathematical.Duetothenatureofnature,aselucidatedbyIsaacNewtonandJohannesKepler,thepositionofasatelliteatanytimemaybepredictedwithahighdegreeofaccuracybyafewmathematicalequations.Asatelliteorbitingtheearthmaybemodeledbyformulascontainedinthememoryofthemicrocomputerinthereceiver.WhentheformulasareappliedtobodiesatthehighaltitudesoftheGPSsatellites,wheretheyarefreefromatmosphericdrag,theformulasarerelativelysimpleandcanpredictthepositionofthesatellitequiteaccurately.

Almostallformulashaveageneralform,intowhichspecificnumbersare"loaded."Forexample,inanequationoftheform

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AandBareparameterswhichrepresentconstantnumbersthatmaybeinsertedintheequation.WhenAandBarereplacedbyactualnumbers,thentheequationisonlytrueforcertainvaluesofx,y,andz.Thereceivercarriesthegeneralformoftheformulasthatgivethepositionofeachsatellite.Beforetherangereadingsaretakenbythereceiver,thesatelliteswillhavebroadcastthevaluesoftheirparticularparameterssothereceivercancompleteitsequations.Then,byknowingthecurrenttimeatagivenmoment(themomentatwhichthedistancereadingistaken),thereceivercanknowwherethesatellitesare.

Actually,thesatellitemessagecomingtothereceiverantennaisinmanyparts.Twoofthesemightbecalledthealmanacandtheephemerisdata.Almanacinformationisbroadcasttoprovideclose,butnotprecise,satellitepositioninformation.Thealmanacforallsatellitesisbroadcastfromeachsatellite.Furthermore,eachsatellitebroadcastsephemerisinformation(whichappliestothatsatelliteonly),thatprovidesuptotheminutecorrections.Thesatellitesarenotcompletelypredictableintheirorbitsbecauseofsuchforcesasgravitationalpullfromthesunandmoon,thesolarwind,andvariousothersmallfactors.ThereforethesatellitesarecarefullymonitoredbygroundstationsandtoldtheirpositionseachsatellitethenrebroadcaststhisinformationtoGPSreceivers.

Question#2:"Thecaptainneededtoknowexactlywhattimeitwasinordertodeterminehisdistancefromthesoundhouse.HowistheclockinthereceiverkeptaccuratelyonGPStime?"1

TheshortansweristhatthereceiverclockisresettoGPStimebythesatelliteseachtimeapositionisfound.Suchresettingisnecessarybecause,whilethereceiverclockisveryconsistentovershortperiodsoftime,ittendstodriftoverlongerperiods.(Eachofthefouratomicclocksineachsatellitecostsabout$50,000thesingleclockinthereceiverobviouslycostsawholelotless,soyoucantexpectthesamesortofaccuracy.Ifyoudontusethereceiverforaweekortwo,youmaynoticeadifferenceofseveralsecondsbetweenthetimethereceiverdisplaysandtruetime.)Theclocksinthesatelliteskeeptimetoaboutatenthofabillionthofasecond(atenthofananosecond).

Ifyouconsider"time"2asthe4thdimensionandacceptthatittakesonesatellitetofixeachdimension,thenitisclearthatfoursatellites,workinginconcert,cansettheclockandprovidea3Dspatialposition.

RecallingourdiscussionofthetheoryofGPSandfromthegeometryofthediagramsyouexamined,youmightpresumethatonlythreesatellitesarerequiredfora3Dfix.Butgiventhatthereceiverhasonlyanapproximateideaofwhattimeitis,whatmustbecalculatedisa4Dfix.Sofoursatellitesarerequired.Itisnotcorrecttosaythatthreesatellitesareusedforthe3Dfixandthefourthsetsthereceiverclock.Rather,allofthe

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satellitesoperateinconcerttofindthetrue"position"ofareceiverantennathatmaymoveinspace(relativetotheearth)anddoesmoveintime.

GPS,aspreviouslymentioned,hashadarevolutionizingeffectonthebusinessofkeepingextremelyaccuratetimetobetterthanabillionthofasecond.WhilemostofthosewhouseGPSareconcernedwithfindingpositions,thesystemalsosuppliesextremelyaccuratetimesignalstoreceiverswhosepositionsareknownwithhighprecision.GPShasmadeitpossibletosynchronizeclocksaroundtheworld.Thishasmadeitpossible,amongotherthings,togainknowledgeaboutthemakeupoftheearthscenter.Sinceseismologiststhroughouttheworldknowtheexacttime,theycantracktheshockwavesfromearthquakesastheypassthroughtheearth.AnotheruseoftheabilityofGPStosynchronizeclocksaroundtheworldisinroutingInternet(worldwideweb)traffic.ItwouldnothavebeenunreasonabletohavecalledGPSbytheacronymGPTS:theGlobalPositioningandTimingSystem.)

Question#3:"Thesoundhousesentasignaleveryminute.Howoftendoesasatellitesendasignal?Whatisthesignallike?"

Actually,eachsatellitesendsasignalcontinuously,ratherlikearadiostationbroadcasts24hoursperday.Theradiostationsignalcanbeconsideredtoconsistoftwoparts:acarrier,whichisonallthetime,and"modulation"ofthatcarrier,whichisthevoiceormusicthatyouhearwhenyoulistentothestation.(Youprobablyhavedetectedthepresenceofthecarrierwhenthepeopleatthestationneglecttosayorplayanything.3Thecarrierproducessilence,whereasifyourradioistunedtoafrequencyonwhichnonearbystationisbroadcastingyouwillhearstatic.)

Eachsatelliteactuallybroadcastsontwofrequencies.Onlyoneoftheseisforcivilianuse.(ThemilitaryGPSunitsreceiveboth.)Theciviliancarrierfrequencyis1575.42megaHertz(1,575.42millioncyclespersecond).Incontrast,FMradiosignalsareontheorderofabout100megaHertz.SotheGPSradiowavescycleabout15timesasoften,andare,therefore,onefifteenthaslong:about20centimetersfromwavetoptowavetop.Asthisgoestopressthereisseriousdiscussionaboutaddingoneortwonewciviliansignals.Havingtwosignalsatdifferentfrequenciesavailableallowsareceivertocomputeamoreaccuratepositionthandoesasinglesignal.

ThemodulationoftheGPSwaveisprettydull,evenwhencomparedto"goldenoldies"radiostations.Thesatellitesbroadcastonly"bits"ofinformation:zerosandones.Formostcivilianuse,thistransmission,andtheabilitytomakemeaningoutofit,iscalledthe"C/Acode"standingforCoarse/Acquisitioncode.Theword"Coarse"isincontrasttoanothercodeusedbythesatellites:the"P"or"Precise"code.Theterm"Acquisition"refersthecapabilitythatallowsbothcivilianandmilitaryreceiverstoacquiretheapproximatepositionofthereceiverantenna.TheC/Acodeisasequenceof1,023bitswhichisrepeatedeveryonethousandthofasecond.

AcopyoftheC/Acodeforagivensatellitemightlooklikethis:

10001101001011110110001

andonandonforatotalof1,023bits.Thenthesequencestartsagain.Thesequenceaboveprobablylooksrandomtoyouasthoughyoubeganflippingacoin,recordinga"1"eachtimeitcameupheadsanda"0"fortails.Itis,infact,calledapseudorandomnoisecodetheterm"noise"comingfromtheideathatanauralversionofitwouldgreatlyresemblestaticonemighthearonaradio.TheacronymisPRN.

Question#4:"Howdoesthereceiverusethe0sand1stodeterminetherangefromthesatellitetothereceiver?"

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ThePRNcodeisanythingbutrandom.Agivensatelliteusesacomputerprogramtogenerateitsparticularcode.TheGPSreceiveressentiallyusesacopyofthesamecomputerprogramtogeneratetheidenticalcode.Further,thesatelliteandthereceiverbeginthegenerationofthecodeatexactlythesamemomentintime.

ThereceivercanthereforedetermineitsrangefromthesatellitebycomparingthetwoPRNsequences(theoneitreceivesandtheoneitgenerates).Thereceiverfirstdetermineshowmuchthesatellitesignalisdelayedintime,andthen,sinceitknowsthespeedofradiowaves,itcancalculatehowfarapartthetwoantennasareinspace.

Asanexample(usinglettersratherthanbitssowecanhaveamoreobvioussequence,andcookingthenumberstoavoidexplainingsomeunimportantcomplications),supposethesatelliteandthereceivereachbegan,at4:00P.M.,togenerateonehundredletterspersecond:

GJKETYUOWVWTDHK

Thereceiverwouldthenlookatitsowncopyofthissequenceandtheoneitreceivedfromthesatellite.Obviouslyitsowncopywouldstartat4:00,butthecopyfromthesatellitewouldcomealongafterthat,becauseofthetimeittookthesignaltocoverthedistancebetweentheantennas.Belowisagraphicillustrationofwhatthetwosignalsmightlookliketothecomputerinthereceiver:

Thereceiverwouldattempttomatchthesignals.Youcanseethatthesignalfromthereceiverbegantoarrivesevenletterslaterthan4:00thereceiversmicrocomputercouldthereforedeterminethatittook7/100ofasecondforthesignalfromthesatellitetoreachthereceiverantenna.Sincetheradiowavetravelsatabout300,000kilometerspersecond,thetimedifferencewouldimplythatthesatellitewas21,000(thatis,7/100*300,000)kilometersfromtheantenna.

Question#5:"Thereceivermustfindrangesfromatleastfoursatellitestodetermineitsposition.Howdoesthereceiver"listento"severalsatellitesatonce?Sinceallsatellitesbroadcastonthesamefrequency,howdoesthe

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receiveridentifythesatellites?"

ThefirstthingtoknowisthateachsatellitehasitsowndistinctivePRNcode.Infact,thesatellitenumbersyouwerelogginginthefirstassignmentwerethePRNnumberswhichistheprincipalwaysatellitesareidentified.Asatellitemayalsohaveanumberpaintedonitsside,butitisthePRNnumberthatcounts.Whenanoldersatelliteisretired,itsreplacementcantakeonitsPRNnumber.

Mostreceivershaveseveralelectroniccomponents,called"channels,"thataretunedtoreceivethecivilianGPSfrequency.Althoughallchannelsaretunedtothesamefrequency,asinglechannelcantrackaGPSsatellitebylockingontoitsPRNcode.Inmoreexpensivereceiverswithseveralormanychannels,eachchannelisassignedfulltimetotrackingasinglesatellite.Otherreceivers"timeshare"achannelflippingitbetweensatellites,asyoumightflipbetweenchannelsonaTV,tryingtokeeptrackoftwoprogramsatonce.

Question#6:"IveheardthattheaccuracyofGPSreceiverswasgreatlyincreasedrecentlywhenselectiveavailabilitywasturnedoff.Whatwasselectiveavailability?Whydiditexist?"

SelectiveAvailability,orSA,wastheerrordeliberatelyintroducedbytheGPSmanagersintheC/AcodebroadcasttodiminishtheaccuracyofGPSreceivers.Sometimesthesatellitesliedabouttheirpositions.Sometimestheyliedaboutwhentheysentthecode.

WhatwastheextentoftheerrorcausedbySA?Thegovernmentguaranteedthat95%ofthetimeafixwouldbewithin100metersofthetrueposition.TounderstandwhySAexistedyouhavetorealizethattheNAVSTARsystemstartedasamilitaryprojecttoprovidenavigationforunitsofthearmedforces.Inthebroadsense,GPSwasdesignedasaweaponssupportsystem.Onedoesntwantonesweaponstofallintoenemyhands.Sostepsweretakentodenyuseofthesystemtoallbutauthorizedreceivers.Infact,theveryexistenceoftheGPSsystem,whosefirstsatellitewaslaunchedin1978,remainedsecretforseveralyears.

Itwasneverplannedthatyoucouldbuya$200receiverforyourfishingboat.Themilitaryfearedsuchusesasaterroristwithamortarknowingexactlywherehewas,andhencebeingabletomoreaccuratelytargethisfire.Orthecomputerinamissilebeingabletomonitoritspositionandcorrectitspathduringitsflight.

Ifsufficientwarningweregiven,ofcourse,theentireciviliansideofNAVSTARcouldbeshutdowntodenyitsusetohostileforces.(Theconsequenceswouldbedisastrous,butnotasmuchsoasanuclearwar.)But,inanyevent,themilitarywasstilluncomfortablewithallowingthebestGPSaccuracyinthehandsofeverybody.SowhywasSAturnedoff?Asitturnsout,verygoodaccuracymaybeobtainedbyusingtwoGPSreceiversinconcertandfortheverybestaccuracyyouneedtworeceivers,SAorno.SoSAbecamemoreofanuisancethatofferednorealprotection.Infact,theArmyCorpsofEngineersbeganbroadcastingcorrectionstopositionsobtainedbycivilianreceivers.UnderpressurefromthecivilianGPSusers,andothercountriesJapanandEuropeanwhobegancontemplatingtheirownversionofGPS,usingthemoregeneraltermGlobalNavigationSatelliteSystem(GNSS)4theU.S.governmentabruptlyclickedtheSAswitchoff.Thisoccurredon2May2000,justaftermidnightEasternTime.ItwasanimportantenoughdecisionthatthePresidentmadetheannouncementhimself.TheslimprotectionSAprovidedmightbereplacedandenhancedbyjammingtheGPSsignalsinselectedgeographicalareas,ifnecessary.IfyouareinterestedinSA,andothermattersrelatedtoGPSpolicy,youcangotothewebsiteoftheInteragencyGPSExecutiveBoard(www.igeb.gov)andfindoutconsiderablymorethanthereisspaceforhere.YoucanalsoviewthePresidentsdeclarationof1May2000.

Question#7:"Howisitthatasatellite,cuttingEarthsmeridiansat55andmovingat8600mph,generatesatrackthatisalmostduenorthsouthinthevicinityoftheequator,asseeninFigure11?"

Whilethesatelliteismovingveryfast,itisalsofaroutinspace.ThereforethemotionofthecorrespondingpointontheEarthssurfacealongthesatellitestrack(picturewherealinefromthecenteroftheearthtothesatellitewouldintersectthesurfaceoftheEarth)isconsiderablyslowerabout2100mph.ThesatellitestrackalongthesurfaceoftheEarthmovesatthisspeedtowardthenortheastontheupswingandsoutheastonthedownswing,sotheeastwardpartofitsmotionisinthesamedirectionastherotationoftheEarth.AnygivenpointonEarthssurfaceattheequatormovesabout1050milesperhoureastwardduetoEarthsrotationabout

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itsaxis.Thenorthorsouthcomponentofthesatellitesvelocityisabout1700mph,whiletheeastcomponentisonlyabout1200mph.Soanobserverattheequatorwouldseeonlyaslowdrifting(about150milesperhour)ofthesatellitetotheeastovertheperiodofanhourortwo.

Question#8:"Iftheorbitalperiodis12hours,whydoeseachsatelliteriseandsetaboutfourminutesearliereachday?CouldtheNAVSTARsystemdesignersarrangetohavethesamesatellitesinviewatthesametimeeachdayinagivenlocation?"

Theshortanswertothefirstquestion,ifyouknowabitofastronomy,isthatthesatellitesorbittheearthtwiceduringasidereal(pronouncedsideareul,meaning"starbased")day,ratherthanasolar(sunbased)day.Alongerexplanation:SupposeyoulookupatthestarsonmidnightofthefirstofAprilandnotetheirpositions.ToseethesamepictureonMayfirstyouhavetolookupat10:00P.M.Inthe30daysthestars"moved"120minutesfourminutesaday.Ofcoursethestarsdidntmovetheearthrotated.Bymidnightitwouldhaveturnednotonlythe10,800degrees(thatis,360perdaytimes30days)fromitsdailyrotation,but30degreesfurther(360degreesmultipliedbyonetwelfth)fromitsyearlyrotationinitsorbitaroundthesun.The10,800degreesworksouttozerobasically(youarebackwhereyoustartedfrom)butthe30degreesissignificant.

Orthinkofitthisway:WhileeachindividualsatelliteisinorbitabouttheEarth,makingitscircuitexactlytwiceaday,thesetofsatellitesareindependentlyinorbitaboutthesun.Theyorbitthesunasapackagetheringsoftheirorbitmakingupsortofasphericalbirdcage.ThecageiscenteredontheEarthandcontainsit.TheEarthisabodythatrotatesindependentlywithinthiscage.Thecagedoesnotrotateatallonitsownaxis,butorbitsthesun.

Tounderstandwhat"notrotatingonitsaxis"means,realizethatthemoonrotatesonitsownaxisonceduringeachtriparoundtheearth,sothatitalwaysshowsthesamefacetoEarth.Ifthemoondidnotrotate,wewouldseedifferentsidesofitasitmadeitswayaroundtheEarth.Incontrasttothemoonearthsituation,considerthecagesunsituation:thecagedoesnotrotateonitsaxisandthereforedoespresentdifferentsidesofitselftothesunoverthecourseofayear.

Soatanygiventime(saynoon,whenthesunisdirectlyoveragivenmeridian),apersononEarthwillsee(thatis,"lookthrough,"towardthesun)onesideofthecageonthesolsticeinJanuary.ButfromthesamepointonearththatpersonwouldbelookingthroughtheoppositesideofthecageinJuly.Ineffect,then,thecagewillbeseenfromEarthtohavemadehalfacompleterotationaroundtheEarthonceeachhalfyear.ToapersonontheEarth,then,thecageapparentlymovesabout1/365thofarotationperday.Thatamountstoaboutfourminutesadaycalculatedas1440minutesinadaydividedbythenumberofdaysinayear.

InanswertothesecondpartofQuestion#8,ifthesatellitesorbitswereboostedanother50kilometersorsofurtherouttheywouldappearintheskyatthesameplaceatthesametimeeachday.Thefurtherasatelliteisfromtheearththelongeritsperiodbothbecauseitmovesmoreslowlyandbecauseithasfurthertogo.

Question#9:"Inearliertextitwassuggestedthatitwassomewhatmoreimportantthattherebeagoodviewoftheskytothesouthforgoodreception.Why?"

Thestatementaboutreceptionbeingbettertowardthesouthappliesonlytothemiddleandupperlatitudesinthenorthernhemisphere.Asyouknow,thesatellitesareinobliqueorbits.Theirtracksgivethenorthandsouthpolesawideberth.InFigure31youarelookingdirectlydownonthenorthpoleatsatellitetracksgeneratedoverasixhourperiod.Thedashedcircleisaparallelat45,soyoucanseethatthereisadearthofsatellitesoverheadifyougoveryfarnorthofthat.ThereisstillgoodGPScoverageallthewaytotheNorthPole.

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Figure31.GPSsatellitetracksseenfromspacelookingtowardtheNorthPole.

STEPBYSTEP

Recallthestoryofthetwo"logicallychallenged"peoplewhorentedaboatandwentfishing.Theywerehighlysuccessfulcatchingalotoffish.Said"A"to"B,""Besuretomarkthisspotsowecancomebacktoit."Asthedayendedandtheywereapproachingthedock,"A"asked"B":"Didyoumarkthatfishingspot?",towhich"B"replied:"SureIdid,justlikeyouaskedmerighthereonthesideoftheboat"Therewasapauseastheabsurdityofthispenetrated"As"brain.Youidiot!Whatifnexttimewedontgetthesameboat?"

Butnow,aswemoveintoanewcentury,youhaveawayofmarkingwhereyouwere.Infact,youhavedoneso.Byuseoftheprogramyoucandeterminewhereyouaretowithin5to15meters.Ourgoalnowistolookatthoseuploadedfiles,andsomeothers,bothgraphicallyandstatistically.Youwillalsoacquireanunderstandingofthequalityofyourdata.

Nextpost:ExaminingGPSData(GPSandGIS)Part2

Previouspost:AutomatedDataCollection(GPSandGIS)Part3

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