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Understanding Satellite Navigation Rajat Acharya AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO AcademicPressisanimprintofElsevier AcademicPressisanimprintofElsevier 32JamestownRoad,LondonNW17BY,UK 225WymanStreet,Waltham,MA02451,USA 525BStreet,Suite1800,SanDiego,CA92101-4495,USA TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK Copyright(cid:1)2014ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans, electronicormechanical,includingphotocopying,recording,oranyinformationstorageand retrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseek permission,furtherinformationaboutthePublisher’spermissionspoliciesandour arrangementswithorganizationssuchastheCopyrightClearanceCenterandtheCopyright LicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythe Publisher(otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchand experiencebroadenourunderstanding,changesinresearchmethods,professionalpractices, ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribedherein. Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyandthe safetyofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors, assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterof productsliability,negligenceorotherwise,orfromanyuseoroperationofanymethods, products,instructions,orideascontainedinthematerialherein. ISBN:978-0-12-799949-4 BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress ForinformationonallAcademicPresspublications visitourwebsiteathttp://store.elsevier.com/ TypesetbyTNQBooksandJournals www.tnq.co.in PrintedandboundintheUnitedStatesofAmerica Dedicated to the loving memory of Chiku, Charki and Gunda Preface IwasverymuchmotivatedtowriteabookonSatelliteNavigationPrincipleswhen mybookletpublishedinternallyinISROonthissubjectfortheSatelliteNavigation Course by the Centre for Space Science and Technology Education-Asia Pacific (CSSTE-AP) was much appreciated by my students. From the feedback I received from people from a wide spectrum of professions and countries and represent both commercialandstrategicusers,aswellasresearchers,itwasclearthatabook was neededwhichwasacceptableequallyintermsofeaseofunderstandingandpertinent. Itwasobviousthatagoodintroductorybookwithaselectiveassortmentofsubjects and explanations simple enough for new learners was necessary. So, this book has been written with the aim of introducing the subject to beginners, coming from different backgrounds, in a very congenial form, so that the subject can be learned fromscratch. Oneofthemainfeaturesofthisbookisthatitexplainsthebasicworkingprin- ciples right from a foundation level with just the necessary mathematics and no complex-looking equations. This book is written keeping in mind the undergradu- ates and all those readers who are being introduced to the subject for the first time. It is expected that the simplistic approach developed from the first principle yetincorporatingalltechnicalities,willnotonlyservethemwellbutalsobeasource of enjoyable learning. Thisbookwillcoverthebasicworkingprinciplesofthegenericsatellitenaviga- tion system, instead of concentrating on any particular existing system. It will emphasize the build up of fundamental ideas for each involved process based on elementary physics added to rational common sense. Every basic principle is fol- lowed by mathematical substantiation, but using only as much mathematics as is deemed necessary for target readers. In addition, this book employs MATLAB as a visualisation tool, for every important new concept that is introduced. This will allow readers to corroborate all that they have learned through simulation, which we believemakesthis book unique. Finally, it is worth mentioning that all the relevant topics on the subject have beenencompassedinacomprehensivemanner.Howevertheviewsandtheopinions presentedherearethoseoftheauthoranddonotnecessarilyreflecttheviewsofhis employer, northe Government ofIndia. RajatAcharya XIII Acknowledgment IwishtoextendmysinceregratitudetotheUniversityofCalcuttaandespeciallyto personalities like Prof. Asish Dasgupta, Prof. Apurba Datta and Prof. Bijoy Banerjee, who have always been my inspiration. I am also grateful to the, Space Applications Centre (SAC-ISRO) for the supportit has providedme. Thecourtesy extended by Dr Bijoy Roy, Dr Chandrashekhar, Mr Suman Aich, and Mr Ananya RoyofSACbyagreeingtoreviewandcommentontheearlyversionsofthemanu- script are also very much appreciated. Thanks are due to Dr Suman Ganguly of CFRSI for his kind cooperation. I also acknowledge the generous gestures of Dr M R Sivaraman, Dr Kalyan Bandyopadhyay, Mr Vilas Palsule and the whole team of the CSSTE-AP. I would also like to thank the entire Elsevier team and the peer reviewers of this book. Last but not the least, I sincerely thank my wife Chandrani,mysonAnubrata,andmyparents,fortheirinspirationandfortherelent- lesssacrificestheymadeduringthewritingofthisbookinordertomakethiseffort a success. XV CHAPTER 1 Introduction to Navigation CHAPTER OUTLINE 1.1 Introduction.........................................................................................................1 1.1.1 Organizationofthisbook.....................................................................2 1.2 Navigation...........................................................................................................4 1.2.1 Historyofnavigation...........................................................................4 1.2.2 Typesofnavigation.............................................................................8 1.2.2.1 Guidance.....................................................................................8 1.2.2.2 Deadreckoning............................................................................8 1.2.2.3 Piloting.........................................................................................9 1.3 Referencingaposition..........................................................................................9 1.3.1 Referenceframe...............................................................................11 1.3.1.1 Heliocentricreferenceframe.......................................................12 1.3.1.2 Geocentricreferenceframes.......................................................12 1.3.1.3 Localreferenceframes...............................................................17 1.3.1.4 Conversionsbetweencoordinatesystems....................................17 1.4 Radionavigationsystem.....................................................................................21 1.4.1 Pilotingsystem................................................................................22 1.4.2 Guidancesystem..............................................................................23 1.4.3 Deadreckoningsystem.....................................................................24 Conceptualquestions................................................................................................25 References...............................................................................................................25 1.1 Introduction Navigationisabasicneedforanyonewhowantstomovewithapurpose.Navigation istheartofmovinginasuitabledirectioninordertoarriveatadesiredlocation.Thus, eveninprehistorictimes,whenthemostprimitiveformofanimalsstartedmovingon earth,theartofnavigationexistedinitsmostancientform.Eventoday,whenhumans, the most evolved species on earth, move by flying in the most technologically advanced aircraft or by driving a car, or by riding a bicycle or simply walking, withadesiretoreachsomewhere,weperformsomesortofnavigation. You may have noticed that when we move without the aid of instruments and the route to our destination is known to us, we generally use some sort of mental 1 UnderstandingSatelliteNavigation.http://dx.doi.org/10.1016/B978-0-12-799949-4.00001-4 Copyright©2014ElsevierInc.Allrightsreserved. 2 CHAPTER 1 Introduction to Navigation map, which is mostly pictorial in the form of landmarks and connected paths. On this map, we identify our positions and apply our previous experience to guide us anddecidethecourseofourmovement.However,thismethoddoesnotworkfora new destination or for places where such landmarks are not present, which is the reasonwhypeoplegetlostindesertsorontheoceans.Insuchsituations,wepaper ordigitalmaps,whichgivesimilarinformation.However,whetherpaperordigital, orasmentalpicturesincludingothergeographicalinformation,thesemapsareaids to navigation that enable us to locate and relate our positions with respect to our destinations and show different possible ways to reach there. The decisions we make in choosing the course of our movement by comparing our position with the available information on these maps is called navigation. Thus,itisapparentthatwefirstneedtoknowourpositiontoidentifycorrectly where we are, and then to make an appropriate decision about where to move. Satellite navigation is a method that provides us with the correct position on or off the earth for this purpose. Here, signals transmitted from navigation satellites are used to derivethe required set of position parameters by a navigation receiver. In turn and in conjunction with the additional information, these parameters are used to further decide the course ofmovement. However, positions are not sought only for movement. Sometimes our exact positionisalsorequiredtobecorrelatedwithotherfactsortoderiveancillaryinfor- mation.Forexample,ifweknowourpositionontheearth’ssurface,wecaneasily figure out the kind of climate we must expect. Knowing precise positions of a network of points on the earth will also let one obtain the exact shape of the earth oritsderivatives,suchastectonicorothercrustalmovements.Therearemanyother interestingapplicationsofnavigation, which wewilldiscussinChapter10. There, weshallcometoknowhowthisknowledgeaboutpositionanditsderivativescanbe used for manyexcitingapplications. Thegeneralrequirementoftheestimationofpositionisglobal;forthat,weneed to represent positions uniquely. Positions are hence represented in terms of global standardssuchthatpositionsofallthepointsonandneartheearthcanbeexpressed by a certain unique coordinate based on a common reference. It is like the unique identity of that position. Thus, finding the position of a person is simply a matter ofdeterminingtheuniqueidentityoftheplacewhereheorsheiscurrentlylocated. Thesecoordinatesarehencechosentospecifythepositionsinaconvenientmanner. Inlater subsections ofthischapter, wewill learn about reference frames andcoor- dinate systems, which forms the basis for representing the positions. Nevertheless, the definition of these coordinates assumes the existence of certain geodetic parameters. 1.1.1 Organization of this book ThephilosopherSocratessaid“Knowthyself.”Attheoutsetoflearningnavigation, wecanupdatethistosay,“Know(thepositionof)thyself.”Thus,ourentireendeavor throughout thisbookwillbetounderstand thefundamentals ofhowmodern space 1.1 Introduction 3 technologyisusedtofixourownposition,aidedbyadvancedtechniquesandeffec- tiveresources.Detailsaboutexistingsystemscurrentlybeingusedforthispurpose will be discussed post hoc. However, it is also important to know how the information is organized in this book.Themorelogicallythingsaredevelopedhere,themoreeasyitwillbetoun- derstandthem.Thus,itisagoodideatofirsthaveaholisticviewofhowthedifferent aspects of a satellite navigation system are gradually introduced in the chapters in this book. We therefore suggest that readers continue to pursue this section describingtheoverallorganizationofthisbook,aboutwhichmanyofushaveagen- eral apathy and atendency towant toskip this explanatorymaterial. Thefirstchapterofthisbookisinformative.Wewillstartbyintroducingtheterm ‘navigation’ and getting a feel for the real development of a navigation system through a chronological description from their inception up to the current state of theart.Wewillfirstlearnaboutthehistoricaldevelopmentofthenavigationsystem. WhilsttosomehistorymaysoundboringaccordingtoSirFrancisBacon“Histories makemenwise”.Wewillthereforetakealookatthehistoryofsatellitenavigation before we gear up to understand the technological aspects of the subject. Then, before we move on to the topics of satellite-based navigation, a brief introduction to its predecessors, including other forms of navigation, should prove helpful. All ofthesewillbecoveredinthischapter,andreadingit,wehope,willbeasinteresting asthetechnologyinsubsequentchapters.Chapter2isalsoinformation based,pri- marilyregardingtheoverallarchitecturalsegmentsofthewholesatellitenavigation system.Althoughwewillonlylearnindetailaboutthecontrolsegmentinthischap- ter, other elements will be discussed in the following chapters. Enjoyment of this bookwillintensifyinChapter3,wherewedescribethespacesegmentofthearchi- tecture. From this chapter onward, there will be frequent Matlab activities illus- trating the current topic. We suggest that readers attempt these activities as they comeacrossthem,ratherthanleavingthemtotheend.Chapter4detailsthesatellite signals used for navigation purposes and transmitted by satellites. Their character- isticswillbedescribedandtherationalefortheiruseexplained.Chapter5describes the user segment and will provide the working principles of a navigation receiver and the different aspects of it. We will explain how signals are used in receivers toderivetheparametersrequiredtofixaposition.Chapter6explainsthealgorithms for the derivation of the navigation parameters i.e. position, velocity, and time, by usingthemeasurementsandestimationsperformedinthereceivers.Receivererrors insuchestimationswiththeirsourcesandeffectsarediscussedindetailinChapter7. Chapter8containsthetopicofdifferentialnavigationsystem.Itisavastsubjectthat could easily fill a book the same size as this or even bigger. However, we have accommodated it here into a single concise chapter of only few pages. Chapter 9 looksatspecial topics suchastheKalmanfilterandtheionosphere,bothofwhich have large implications for navigation systems. Readers may skip reading this particular chapter if they wish, without loss of continuity. However, that would be at the cost of some very interesting material. Finally, Chapter 10 provides details of some important applications ofsatellite navigation. 4 CHAPTER 1 Introduction to Navigation 1.2 Navigation Navigationisrelatedtotheartofgettingfromoneplacetoanother,safelyandeffi- ciently.Although,theword‘navigation’stemsfromtheLatinwordNavigare,which means ‘to sail or drive a ship,’ its contemporary meaning is the art of providing position and/ordirection toanyoneon land orsea or inspace (Elliot et al. 2001). 1.2.1 History of navigation Theartofnavigationpredatedtheadventofmankind.Prehistoricanimalsmovedin search of food using their innate navigation skills. Figure 1.1, however, is only indicative. Humanshavebeenusingdifferenttechniquesofnavigationfromtheearlyages of civilization. Primitive people living in caves had to hunt deep in the forest in search of food when geographical movement was not easy and finding their way back was difficult. Thus, they made special marks on trees or erected stone pillars tocreatelandmarksinordertofindtheirwaybackhome.Theuseofsoundorsmoke signalswereanothercommonmeansoffindingtheirwayback.Wewilllookmoreat theformalclassificationslater,butitisworthmentioningherethatthesemostprim- itivemethods ofnavigation were oftheguidance type. Navigationdevelopedatsea,withmostdevelopmentsinthemodernnavigation systemoccurringintheprocessofguidingseavehicles.Inancienttimes,seafaring explorers started traveling across the oceans in search of new lands, in order to increase trade and colonize. Development in the field became necessary in order to cater to the needs of voyages and the constant effort to improve them. FIGURE1.1 Primitivenavigation. 1.2 Navigation 5 Asmentionedbefore,mappingtheseaalongsideitsadjacentlandsisnotnavigation, butderivingonesownpositionfromitandthusdecidingthedirectionofmovement toward a certain destination is. However, both systems were developed simulta- neously and are sometimes treated as the same thing. In this section, we restrict our discussion tonavigation only. Thefirstkindofseanavigatingwasprobablydonebyskirtingaroundthecoast, andthusbystayinginsightofland.Pictorialmapswerecreatedduringthistimeby sailorswhowoulddrawwhattheycouldseealongthecoast.Usingthese,theycould return or retrace their course on subsequent journeys. The first known coastal and river maps were from China in around 2000 B.C. and indicated sailing directions (Wellenhof et al. 2003). However, whenvoyages ventured further out into the sea, the only means of navigating was by observing the position of the sun and stars. This kind of navigation is termed celestial navigation. Some experienced sailors could also navigate by understanding the winds or determining the depth of the seabed,fromwhichtheycouldestimatetheirdistancefromtheland.Thiswasprob- ably the earliest form ofbathymetric navigation. WrittenrecordsofcelestialnavigationdatebacktothethirdcenturyB.C.Some oftheseaccountsareavailableinHomer’sepic,TheOdyssey(HistoryofNavigation, 2007).Theastrolabe,whichmeasurestheelevationofthesunandthestars,asshown inFigure1.2(a)becamethemaininstrumentforpositioningandwasapparentlyused evenbefore600BC(Kayton,1989).HeronandVitruviousgaveadetaileddescrip- tion of the odometer, an instrument to measure distance (Wellenhof et al. 2003). During thistime, Greek andEgyptian sailors started using the polarstars andcon- stellationstonavigatebecausetheydidnotdisappearbelowthehorizonthroughout thenight.However,movementusingpolestarsneededtobecorrectedwithtimeas the stars change their positions because of the wobbling of the earth on its axis. Measurementsoftheinstrumentswere aidedbynauticalcharts.Ptolemyproduced the first world map, which remained in use for many years during sea voyages. Textual descriptions for sailing directions have been in use in one form or another since then. Themiddleagesinnavigationweremarkedbythediscoveryoflodestone.With this,navigationbecameeasierforsailors,whostartedtouseitforitsmagneticprop- erties. Comparing it with detailed maps of the period, they could find their way easily evenwith unfavorable skyconditions allowing sailors tonavigate evenwith limited visibility. The first true mariner’s compass was invented in Europe toward the beginning of the thirteenth century A.D. Thus, when Christopher Columbus set out on his transatlantic voyage in 1492, he had only a compass, a few dated measuringinstruments,amethodtocorrectforthealtitudeofPolaris,andsomerudi- mentarynautical charts astools for navigation. Fromthemiddleofthesixteenthcentury,navigationsawarapiddevelopmentin relatedtechnologywhenanumberofinstrumentsandmethodswereinvented.This was when the Europeans started to settle colonies in different countries, and they used sea routes to navigate to these new lands. The improvement of navigational techniques became mandatory and the mathematical approach toward navigation

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This book explains the basic principles of satellite navigation technology with the bare minimum of mathematics and without complex equations. It helps you to conceptualize the underlying theory from first principles, building up your knowledge gradually using practical demonstrations and worked exa
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