《航海学》课程参考文献（地文资料）CHAPTER 11 SATELLITE NAVIGATION

CHAPTER 11SATELLITE NAVIGATIONINTRODUCTION1100.EarlyDevelopmentsInSatelliteNavigationbetween the satellite and the navigator.Knowing the satel-lite orbit precisely,the navigator's absolute position can beaccuratelydeterminedfromthetimerate ofchange ofrangeThe idea that led to development of the satellite navi-to the satellite.gationsystemsdatesbackto1957andthefirst launchofanartificial satellite into orbit,Russia's Sputnik I.Dr.WilliamThe Johns Hopkins University Applied Physics Labora-H.GuierandDr.GeorgeC.WieffenbachattheAppliedtory developed NAVSAT for the U. S.Navy.The operationPhysics Laboratory of the Johns Hopkins University wereofthesystem isunderthecontroloftheU.S.NavyAstronau-monitoringthefamous“beeps"transmittedbythepassingtics Group with headquarters at Point Mugu, California.satellite. They plotted the received signals at precise inter-vals,and noticed that a characteristic Dopplercurve1102. System Configuration, Operation, Andemerged. Since celestial bodies followed fixed orbits, theyTerminationreasoned that this curve could be used to describe the satel-lite orbit. Later, they demonstrated that they couldTheNAVSAT consists of 10 orbiting satellites and3determineall oftheorbital parametersforapassingsatelliteorbiting spares;anetwork oftrackingstations continuouslyby doppler observation of a single pass from a single fixedmonitoring the satellites and updating the information theystation. The doppler shift apparent while receiving a trans-transmit; and the receivers and computers for processingmission from a passing satellite proved to be an effectivesignals.measuringdeviceforestablishingthesatelliteorbit.Eachsatelliteis inanominallycircularpolarorbitatanDr.Frank T.McClure,also of theApplied Physicsapproximatealtitudeof600nauticalmiles.Thereareusual-Laboratory,reasoned that if the satellite orbit wasknown,ly five satellites operating in the system.Five satellites indoppler shiftmeasurementscouldbeusedtodetermineorbitprovideredundancy;theminimum constellationforone's position on earth.His studies in support of this hy-system operation is four.This redundancy allows for an un-pothesis earned him the first National Aeronautics andexpected failure ofa satellite and the relatively longperiodSpace Administration award for important contributions tooftime requiredto schedule,prepare,andlaunch areplacespacedevelopment.ment satellite.This redundancy also provides for turningIn1958, the Applied Physics Laboratory proposed ex-offa satellitewhen (onrareoccasions)its orbital planepre-ploringthepossibilityof anoperational satellitedopplercesses near another satellite's plane, or when the timingnavigation system.TheChief of Naval Operations then set(phasing)of several satellites in theirorbits aretemporarilyforth requirements for such a system.The first successfulsuch thatmany satellitespass nearly simultaneouslynearlaunching of a prototype system satellite in April 1960one of the poles.demonstratedthedopplersystem'soperationalfeasibilityEach satellite contains: (1)receiver equipment to ac-cept injection data and operational commandsfromthe1101.NAVSAT,TheFirst SatelliteNavigationSystemground, (2)a decoder for digitizing the data, (3)switchinglogic and memorybanks for sorting and storing the digitalThe Navy Navigation Satellite System (NAVSATdata, (4) control circuits to cause the data to be read out atalsoknownasTRANSIT)wasthefirstoperational satellitespecifictimesintheproperformat,(5)anencodertotrans-navigation system.The system's accuracywas better thanlate the digital data to phasemodulation,(6)ultra stable50.1 nautical mile anywhere in the world.It was used prima-MHz oscillators,and (7)1.5-watt transmitters tobroadcastrilyforthenavigationofsurfaceshipsandsubmarines:butthe 150-and 400-MHz oscillator-regulated frequencies thatit also had some applications in air navigation. It was alsocarry thedatato earth.used in hydrographic surveying and geodetic positionThe transit launch program ended in 1988. Accordingdetermination.to the Federal Radionavigation Plan, the Navy will ceaseNAVSATusesthedopplershiftofradiosignalstrans-operationofNAVSATbythe end of1996,as thenewGlo-bal Positioning System (GPS)comes into operation.mitted from a satellite to measure the relative velocity179

179 CHAPTER 11 SATELLITE NAVIGATION INTRODUCTION 1100. Early Developments In Satellite Navigation The idea that led to development of the satellite navi￾gation systems dates back to 1957 and the first launch of an artificial satellite into orbit, Russia’s Sputnik I. Dr. William H. Guier and Dr. George C. Wieffenbach at the Applied Physics Laboratory of the Johns Hopkins University were monitoring the famous “beeps” transmitted by the passing satellite. They plotted the received signals at precise inter￾vals, and noticed that a characteristic Doppler curve emerged. Since celestial bodies followed fixed orbits, they reasoned that this curve could be used to describe the satel￾lite orbit. Later, they demonstrated that they could determine all of the orbital parameters for a passing satellite by doppler observation of a single pass from a single fixed station. The doppler shift apparent while receiving a trans￾mission from a passing satellite proved to be an effective measuring device for establishing the satellite orbit. Dr. Frank T. McClure, also of the Applied Physics Laboratory, reasoned that if the satellite orbit was known, doppler shift measurements could be used to determine one’s position on earth. His studies in support of this hy￾pothesis earned him the first National Aeronautics and Space Administration award for important contributions to space development. In 1958, the Applied Physics Laboratory proposed ex￾ploring the possibility of an operational satellite doppler navigation system. The Chief of Naval Operations then set forth requirements for such a system. The first successful launching of a prototype system satellite in April 1960 demonstrated the doppler system’s operational feasibility. 1101. NAVSAT, The First Satellite Navigation System The Navy Navigation Satellite System (NAVSAT, also known as TRANSIT) was the first operational satellite navigation system. The system’s accuracy was better than 0.1 nautical mile anywhere in the world. It was used prima￾rily for the navigation of surface ships and submarines; but it also had some applications in air navigation. It was also used in hydrographic surveying and geodetic position determination. NAVSAT uses the doppler shift of radio signals trans￾mitted from a satellite to measure the relative velocity between the satellite and the navigator. Knowing the satel￾lite orbit precisely, the navigator’s absolute position can be accurately determined from the time rate of change of range to the satellite. The Johns Hopkins University Applied Physics Labora￾tory developed NAVSAT for the U. S. Navy. The operation of the system is under the control of the U. S. Navy Astronau￾tics Group with headquarters at Point Mugu, California. 1102. System Configuration, Operation, And Termination The NAVSAT consists of 10 orbiting satellites and 3 orbiting spares; a network of tracking stations continuously monitoring the satellites and updating the information they transmit; and the receivers and computers for processing signals. Each satellite is in a nominally circular polar orbit at an approximate altitude of 600 nautical miles. There are usual￾ly five satellites operating in the system. Five satellites in orbit provide redundancy; the minimum constellation for system operation is four. This redundancy allows for an un￾expected failure of a satellite and the relatively long period of time required to schedule, prepare, and launch a replace￾ment satellite. This redundancy also provides for turning off a satellite when (on rare occasions) its orbital plane pre￾cesses near another satellite’s plane, or when the timing (phasing) of several satellites in their orbits are temporarily such that many satellites pass nearly simultaneously near one of the poles. Each satellite contains: (1) receiver equipment to ac￾cept injection data and operational commands from the ground, (2) a decoder for digitizing the data, (3) switching logic and memory banks for sorting and storing the digital data, (4) control circuits to cause the data to be read out at specific times in the proper format, (5) an encoder to trans￾late the digital data to phase modulation, (6) ultra stable 5 MHz oscillators, and (7) 1.5-watt transmitters to broadcast the 150- and 400-MHz oscillator-regulated frequencies that carry the data to earth. The transit launch program ended in 1988. According to the Federal Radionavigation Plan, the Navy will cease operation of NAVSAT by the end of 1996, as the new Glo￾bal Positioning System (GPS) comes into operation

180SATELLITENAVIGATIONTHEGLOBALPOSITIONINGSYSTEM1103.BasicSystemDescriptioncated in Hawai, Colorado Springs,Kwajalein,DiegoGarcia, and Ascension Island, passively track the satel-TheFederalRadionavigationPlanhasdesignatedlites,accumulating ranging data from the satellitesthe Navigation System using Timing and Rangingsignals andrelaying themtotheMCS.TheMCSprocess-(NAVSTAR)GlobalPositioningSystem(GPS)asthees thisinformationtodeterminesatelliteposition andsignal data accuracy,updates the navigation message ofprimarynavigation systemoftheU.S.government.GPSeach satellite and relays this information to theground an-is a spaced-based radio positioning system which pro-tennas.Thegroundantennasthen transmitthisvides suitably equipped users with highly accurateposition,velocity,and time data.It consists of three ma-information tothesatellites.Thegroundantennas,locatedjor segments: a space segment, a control segment, andat Ascension Island, Diego Garcia, and Kwajalein, arealso usedfortransmitting and receiving satellite controla user segment.information.The space segment contains 24 satellites. PreciseThe user segment is designed for different require-spacing of the satellites in orbit is arranged such that aments of various users. These receivers can be used inminimum of four satellites are in view to a user at anytime on a worldwide basis.Each satellite transmits sig-high,medium, and lowdynamic applications.An exam-ple of a low dynamic application would be a fixednalsontworadiofrequencies,superimposedonwhichantenna or slowly drifting marine craft.An example ofaarenavigationand svstemdata.Included inthisdata ismediumdynamicapplicationwouldbeamarineorlandpredicted satelliteephemeris,atmosphericpropagationcorrection data,satellite clock error information,and sat-vehicletravelingat a constant controlled speed.Finally,ellite health data. This segment consists of 21an example of a high dynamic application would beahigh performance aircraft or a spacecraft. The useroperational satellites with three satellites orbiting as ac-tive spares. The satellites orbit in six separate orbitalequipment is designed to receive and process signalsfromfourormoreorbitingsatelliteseithersimultaneous-planes.The orbital planes have an inclination relative tothe equator of 55and an orbital height of 20,200 km.ly or sequentially.The processor in the receiverthenThesatellites complete an orbitapproximatelyonce ev-converts these signals to three-dimensional navigationinformationbased ontheWorldGeodeticSystem1984ery12hours.GPS satellitestransmitpseudorandom noise(PRN)reference ellipsoid. The user segment can consist ofstand-alone receivers or equipment that is integrated intosequence-modulated radio frequencies, designated L1another navigation system.Since GPS is used in a wide(1575.42MHz)andL2(1227.60MHz).Thesatellitetrans-mits botha Coarse Acquisition Code (C/A code)and avarietyofapplicationsfrommarinenavigationtolandsurveying, these receivers can vary greatly in functionPrecision Code (P code).Both the P and C/A codes areand design.transmittedontheL1carrier,onlythePcodeistransmittedontheL2carrier.Superimposed onboththeC/AandP1104. System Capabilitiescodes is the Navigation message.This message containssatellite ephemeris data, atmospheric propagation correc-tiondataandsatelliteclockbiasGPS provides multiple users withaccurate,continu-GPSassigns a unique C/Acode anda uniquePcodetoous,worldwide,all-weather,common-grid,three-dimensional positioningand navigation information.each satellite.Thispractice,knownas codedivision multi-ple access (CDMA), allows all satellites the use of aToobtainanavigation solution of position(latitudecommon carrier frequencywhile still allowing the receiverlongitude,and altitude)and time (fourunknowns),fourto determine which satellite is transmitting.CDMAalso al-satellitesmustbe selected.TheGPS usermeasures pseu-lows for easy user identification of eachGPS satellite.dorangeandpseudorangeratebysynchronizingandSince each satellite broadcasts using its own unique C/Atracking the navigation signal from each of the four se-andPcodecombination,it canbeassigned a uniquePRNlected satellites. Pseudorange is the true distancesequencenumber.Thisnumberishowasatelliteisidenti-between the satellite and the userplus an offset dueto thefiedwhentheGPScontrolsystemcommunicateswithusersuser'sclockbias.Pseudorangerateisthetrueslantrangeabout aparticularGPSsatellite.rateplusanoffset due tothefrequency errorof the user'sThe control segment includes a master control sta-clock.By decoding the ephemeris data and system tim-tion (MCS), a number of monitor stations, and grounding information on each satellite's signal, the user'santennaslocated throughout theworld.Themastercontrolreceiver/processorcan convertthe pseudorangeandstation.locatedinColoradoSprings,Colorado.consistsofpseudorange rate to three-dimensional position and ve-equipmentand facilities requiredfor satellitemonitoring.locity.Fourmeasurementsarenecessarytosolveforthetelemetry,tracking,commanding,control,uploading,andthreeunknowncomponentsofposition(orvelocity)andnavigation message generation.The monitor stations, lo-the unknown user time (or frequency)bias

180 SATELLITE NAVIGATION THE GLOBAL POSITIONING SYSTEM 1103. Basic System Description The Federal Radionavigation Plan has designated the Navigation System using Timing and Ranging (NAVSTAR) Global Positioning System (GPS) as the primary navigation system of the U.S. government. GPS is a spaced-based radio positioning system which pro￾vides suitably equipped users with highly accurate position, velocity, and time data. It consists of three ma￾jor segments: a space segment, a control segment, and a user segment. The space segment contains 24 satellites. Precise spacing of the satellites in orbit is arranged such that a minimum of four satellites are in view to a user at any time on a worldwide basis. Each satellite transmits sig￾nals on two radio frequencies, superimposed on which are navigation and system data. Included in this data is predicted satellite ephemeris, atmospheric propagation correction data, satellite clock error information, and sat￾ellite health data. This segment consists of 21 operational satellites with three satellites orbiting as ac￾tive spares. The satellites orbit in six separate orbital planes. The orbital planes have an inclination relative to the equator of 55° and an orbital height of 20,200 km. The satellites complete an orbit approximately once ev￾ery 12 hours. GPS satellites transmit pseudorandom noise (PRN) sequence-modulated radio frequencies, designated L1 (1575.42 MHz) and L2 (1227.60 MHz). The satellite trans￾mits both a Coarse Acquisition Code (C/A code) and a Precision Code (P code). Both the P and C/A codes are transmitted on the L1 carrier; only the P code is transmitted on the L2 carrier. Superimposed on both the C/A and P codes is the Navigation message. This message contains satellite ephemeris data, atmospheric propagation correc￾tion data, and satellite clock bias. GPS assigns a unique C/A code and a unique P code to each satellite. This practice, known as code division multi￾ple access (CDMA), allows all satellites the use of a common carrier frequency while still allowing the receiver to determine which satellite is transmitting. CDMA also al￾lows for easy user identification of each GPS satellite. Since each satellite broadcasts using its own unique C/A and P code combination, it can be assigned a unique PRN sequence number. This number is how a satellite is identi￾fied when the GPS control system communicates with users about a particular GPS satellite. The control segment includes a master control sta￾tion (MCS), a number of monitor stations, and ground antennas located throughout the world. The master control station, located in Colorado Springs, Colorado, consists of equipment and facilities required for satellite monitoring, telemetry, tracking, commanding, control, uploading, and navigation message generation. The monitor stations, lo￾cated in Hawaii, Colorado Springs, Kwajalein, Diego Garcia, and Ascension Island, passively track the satel￾lites, accumulating ranging data from the satellites’ signals and relaying them to the MCS. The MCS process￾es this information to determine satellite position and signal data accuracy, updates the navigation message of each satellite and relays this information to the ground an￾tennas. The ground antennas then transmit this information to the satellites. The ground antennas, located at Ascension Island, Diego Garcia, and Kwajalein, are also used for transmitting and receiving satellite control information. The user segment is designed for different require￾ments of various users. These receivers can be used in high, medium, and low dynamic applications. An exam￾ple of a low dynamic application would be a fixed antenna or slowly drifting marine craft. An example of a medium dynamic application would be a marine or land vehicle traveling at a constant controlled speed. Finally, an example of a high dynamic application would be a high performance aircraft or a spacecraft. The user equipment is designed to receive and process signals from four or more orbiting satellites either simultaneous￾ly or sequentially. The processor in the receiver then converts these signals to three-dimensional navigation information based on the World Geodetic System 1984 reference ellipsoid. The user segment can consist of stand-alone receivers or equipment that is integrated into another navigation system. Since GPS is used in a wide variety of applications, from marine navigation to land surveying, these receivers can vary greatly in function and design. 1104. System Capabilities GPS provides multiple users with accurate, continu￾ous, worldwide, all-weather, common-grid, three￾dimensional positioning and navigation information. To obtain a navigation solution of position (latitude, longitude, and altitude) and time (four unknowns), four satellites must be selected. The GPS user measures pseu￾dorange and pseudorange rate by synchronizing and tracking the navigation signal from each of the four se￾lected satellites. Pseudorange is the true distance between the satellite and the user plus an offset due to the user’s clock bias. Pseudorange rate is the true slant range rate plus an offset due to the frequency error of the user’s clock. By decoding the ephemeris data and system tim￾ing information on each satellite’s signal, the user’s receiver/processor can convert the pseudorange and pseudorange rate to three-dimensional position and ve￾locity. Four measurements are necessary to solve for the three unknown components of position (or velocity) and the unknown user time (or frequency) bias

SATELLITENAVIGATION181The navigation accuracy that can be achieved by any(as it would were there no transmission error present);rath-user dependsprimarilyon thevariability of theerrors iner,it will plot as a triangle.Thenavigator can then applyaconstantbearing correction to eachLOPuntilthecorrectionmakingpseudorangemeasurements,theinstantaneousge-ometry of the satellites as seen fromthe user's location onapplied equals the bearing transmission error.When theEarth,and the presence of Selective Avaliability (SA).Se-correction applied equals the original transmission errorlectiveAvailability is discussedfurtherbelow.theresultant fix should plotas a pinpoint.The situation withGPS receiver timing inaccuracies is analogous; time mea-surement error simply replaces bearing measurement error1105.Global Positioning System Basic Conceptsin the analysis. Assuming that the satellite clocks are per-fectly synchronized and the receiver clock's error isAs discussed above,GPS measures distancesbetweenconstant.thesubtractionofthatconstanterrorfromtheresatellites in orbit and a receiver on or abovethe earth andsulting distancedeterminations will reduce thefix errorcomputes spheres of position from those distances.The in-until a“pinpoint"position is obtained. It is important totersections of those spheres of position then determine thenoteherethatthenumberoflinesofpositionreguiredtoreceiver'sposition.employthistechniqueis a functionof thenumberof linesThe distance measurements described above are done byof position required to obtain a fix.In the two dimensionalcomparingtiming signals generated simultaneouslybythesat-visual plotting scenario described above,only two LOP'sellitesand receiver's internal clocks.These signals,were required to constitute a fix.The bearing error intro-characterized by a special waveform known as the pseudo-duced another unknown into theprocess, resulting in threerandom code,aregenerated in phasewith eachother.Thesigtotalunknowns(thexcoordinateofposition.theycoordinal from the satellitearrives at the receiver following a timenate ofposition,and the bearing error).Becauseofthe threedelayproportional to itsdistancetraveled.This timedelay isunknowns, three LOP's were required to employ this cor-detected by the phase shift between the received pseudo-ran-rection technique. GPS determines position in threedom codeand the code generated bythe receiver.Knowing thedimensions; thepresenceofreceiverclock erroradds an ad-time required for the signal to reach the receiver from the sat-ditional unknown.Therefore, four timing measurementsellite allows the receiver to calculatethe distance from thearerequired to solve for the resulting four unknowns.satellite.The receiver,therefore,must be located on a spherecentered at thesatellite witharadius equal to thisdistance mea-1106.GPSSignalCodingsurement.The intersection of three spheres of position yieldstwo possiblepoints ofreceiverposition.Oneof thesepointsTwo separate carrier frequencies carry the signal trans-can be disregarded since it is hundreds of miles from the sur-face of the earth. Theoretically,then, only three timemitted by a GPS satellite. The first carrier frequency (LI)measurements arerequired to obtain a fixfromGPStransmitson1575.42MHz,thesecond(L2)transmitson1227.60MHz.TheGPSsignalconsistsofthreeseparateIn practice,however,afourthmeasurement is requiredmessages:theP-code,transmitted on bothL1 and L2;theC/to obtain an accurate position from GPS. This is due to re-Acode.transmittedonLlonlv,andanavigationdatamesceiver clock error.Timing signals travel from the satellitesage.The P code and C/A code messages are divided intotothereceiveratthespeed oflight:evenextremelyslighindividualbitsknownaschips.Thefrequencyatwhichbitstiming errors between the clocks on the satellite and in theare sent for each typeof signal is known as thechippingreceiver will lead to tremendous range errors.The satel-rate. The chipping rate for the P-code is 10.23 MHz (10.23lite's atomic clock is accurate to 10-9 seconds; installing ax 106 bits per second); for the C/A code, 1.023 MHz (1.023clock that accurate on a receiver would make the receiverx106bitspersecond),andforthedatamessage,50Hz(50prohibitively expensive.Therefore,receiverclock accuracybitsper second).ThePand C/A codes phasemodulatetheis sacrificed, and an additional satellite timing measure-carriers,the C/A code is transmitted at a phase angle of 900ment is made.The fix eror caused by the inaccuracies infrom thePcode.Theperiods ofrepetitionfortheC/AandPthe receiver clock is reduced by simultaneously subtractingcodes differ.The C/A code repeats once every millisecond;a constanttiming errorfrom four satellite timing measure-the P-code sequence repeats every seven days.ments until apinpointfixisreached.Thisprocess isanalogousto thenavigator's plottingof a visual fix whenAsstatedabovetheGPScarrierfrequenciesarephasemodulated. This is simply another way of saying that thebearing transmission error is present in his bearing repeatersystem.With that bearing error present, twovisual LOP'sdigital"1's"and"O's"contained in the P and C/A codes arewill not intersect at a vessel's true position, there will be anindicated along the carrier by a shift in the carrierphase.This is analogous to sending the same data along a carriererror introduced due to the fixed, constant error in thebear-ingtransmissionprocess.Therearetwowaystoovercomeby varying its amplitude (amplitude modulation, or AM) orsuch an error.The navigator can buy extremely accurateitsfrequency(frequencymodulation, orFM).See Figure(andexpensive)bearingtransmissionanddisplayequip-1i106a. Inphase modulation, thefrequency and the ampli-tude of the carrier are unchanged by the “informationment, or he can simply take a bearing to a third visualnavigation aid.Theresulting fix will not plot as a pinpointsignal,"and the digital information is transmitted by shiff-

SATELLITE NAVIGATION 181 The navigation accuracy that can be achieved by any user depends primarily on the variability of the errors in making pseudorange measurements, the instantaneous ge￾ometry of the satellites as seen from the user’s location on Earth, and the presence of Selective Avaliability (SA). Se￾lective Availability is discussed further below. 1105. Global Positioning System Basic Concepts As discussed above, GPS measures distances between satellites in orbit and a receiver on or above the earth and computes spheres of position from those distances. The in￾tersections of those spheres of position then determine the receiver’s position. The distance measurements described above are done by comparing timing signals generated simultaneously by the sat￾ellites’ and receiver’s internal clocks. These signals, characterized by a special wave form known as the pseudo￾random code, are generated in phase with each other. The sig￾nal from the satellite arrives at the receiver following a time delay proportional to its distance traveled. This time delay is detected by the phase shift between the received pseudo-ran￾dom code and the code generated by the receiver. Knowing the time required for the signal to reach the receiver from the sat￾ellite allows the receiver to calculate the distance from the satellite. The receiver, therefore, must be located on a sphere centered at the satellite with a radius equal to this distance mea￾surement. The intersection of three spheres of position yields two possible points of receiver position. One of these points can be disregarded since it is hundreds of miles from the sur￾face of the earth. Theoretically, then, only three time measurements are required to obtain a fix from GPS. In practice, however, a fourth measurement is required to obtain an accurate position from GPS. This is due to re￾ceiver clock error. Timing signals travel from the satellite to the receiver at the speed of light; even extremely slight timing errors between the clocks on the satellite and in the receiver will lead to tremendous range errors. The satel￾lite’s atomic clock is accurate to 10-9 seconds; installing a clock that accurate on a receiver would make the receiver prohibitively expensive. Therefore, receiver clock accuracy is sacrificed, and an additional satellite timing measure￾ment is made. The fix error caused by the inaccuracies in the receiver clock is reduced by simultaneously subtracting a constant timing error from four satellite timing measure￾ments until a pinpoint fix is reached. This process is analogous to the navigator’s plotting of a visual fix when bearing transmission error is present in his bearing repeater system. With that bearing error present, two visual LOP’s will not intersect at a vessel’s true position; there will be an error introduced due to the fixed, constant error in the bear￾ing transmission process. There are two ways to overcome such an error. The navigator can buy extremely accurate (and expensive) bearing transmission and display equip￾ment, or he can simply take a bearing to a third visual navigation aid. The resulting fix will not plot as a pinpoint (as it would were there no transmission error present); rath￾er, it will plot as a triangle. The navigator can then apply a constant bearing correction to each LOP until the correction applied equals the bearing transmission error. When the correction applied equals the original transmission error, the resultant fix should plot as a pinpoint. The situation with GPS receiver timing inaccuracies is analogous; time mea￾surement error simply replaces bearing measurement error in the analysis. Assuming that the satellite clocks are per￾fectly synchronized and the receiver clock’s error is constant, the subtraction of that constant error from the re￾sulting distance determinations will reduce the fix error until a “pinpoint” position is obtained. It is important to note here that the number of lines of position required to employ this technique is a function of the number of lines of position required to obtain a fix. In the two dimensional visual plotting scenario described above, only two LOP’s were required to constitute a fix. The bearing error intro￾duced another unknown into the process, resulting in three total unknowns (the x coordinate of position, the y coordi￾nate of position, and the bearing error). Because of the three unknowns, three LOP’s were required to employ this cor￾rection technique. GPS determines position in three dimensions; the presence of receiver clock error adds an ad￾ditional unknown. Therefore, four timing measurements are required to solve for the resulting four unknowns. 1106. GPS Signal Coding Two separate carrier frequencies carry the signal trans￾mitted by a GPS satellite. The first carrier frequency (L1) transmits on 1575.42 MHz; the second (L2) transmits on 1227.60 MHz. The GPS signal consists of three separate messages: the P-code, transmitted on both L1 and L2; the C/ A code, transmitted on L1 only; and a navigation data mes￾sage. The P code and C/A code messages are divided into individual bits known as chips. The frequency at which bits are sent for each type of signal is known as the chipping rate. The chipping rate for the P-code is 10.23 MHz (10.23 × 106 bits per second); for the C/A code, 1.023 MHz (1.023 × 106 bits per second); and for the data message, 50 Hz (50 bits per second). The P and C/A codes phase modulate the carriers; the C/A code is transmitted at a phase angle of 90° from the P code. The periods of repetition for the C/A and P codes differ. The C/A code repeats once every millisecond; the P-code sequence repeats every seven days. As stated above the GPS carrier frequencies are phase modulated. This is simply another way of saying that the digital “1’s” and “0’s” contained in the P and C/A codes are indicated along the carrier by a shift in the carrier phase. This is analogous to sending the same data along a carrier by varying its amplitude (amplitude modulation, or AM) or its frequency (frequency modulation, or FM). See Figure 1106a. In phase modulation, the frequency and the ampli￾tude of the carrier are unchanged by the “information signal,” and the digital information is transmitted by shift-

182SATELLITENAVIGATIONSTRINGOFONESANDZEROSTOBETRANSMITTED:sAMPLITUDEMODULATION(AM)FREQUENCYMODULATION (FM)smsPHASEMODULATION (PM)Figure1106a.Digital datatransmissionwithamplitude,frequencyandphasemodulationTHEL1SIGNALTHEL2SIGNALP(dBW)P(dBW)2.046 MHzC/A-CODE160-CODEP-CODE-163-1569F(Hz)DF(Hz)1227.6MHz1227.6MHz20.46Ml20.46MHzFigure1106b.Modulation of theLI and L2carrier frequencies with theC/Aand Pcode signals.POWERMSGNASVARRIERSPREADNOISEFigure1106c.GPSsignal spreadingandrecoveryfromsatellitetoreceiver

182 SATELLITE NAVIGATION Figure 1106a. Digital data transmission with amplitude, frequency and phase modulation. Figure 1106b. Modulation of the L1 and L2 carrier frequencies with the C/A and P code signals. Figure 1106c. GPS signal spreading and recovery from satellite to receiver

183SATELLITENAVIGATIONingthecarrier'sphase.Thephasemodulationemployed bysignal with the square wave function generated by the re-GPS isknown as bi-phase shiftkeying (BPSK)ceiver.The computer logic of the receiver recognizes thesquare wave signals as either a +1 or a 0 depending onDue to this BPSK, the carrier frequency is “spread”"whether the signal is “"on" or “"off" The signals are pro-aboutitscenterfrequencybyanamountequal totwicethecessed and matched byusing an autocorrelationfunction."chipping rate"of the modulating signal. In the case of theP code, this spreading is equal to (2 × 10.23 MHz)=20.46This process defines the necessity for a "pseudo-ran-dom code."The code must be repeatable (i.e., non-random)MHz.For the C/Acode,the spreading is equal to (2×1.023MHz)=2.046MHz.SeeFigure1106b.NotethattheL1because it is in comparing the two signals that the receivercarrier signal, modulated with both theP code and C/Amakes its distance calculations.At the same time,the codecode, is shaped differently from the L2 carrier, modulatedmust be random for the correlation process to work; the ran-with only the P code.This spreading of the carrier signaldomness of the signals must be such that the matchinglowers thetotal signal strength below the thermal noiseprocess excludes all possiblecombinations except the com-threshold present at thereceiver.This effect is demonstrat-bination that occurs when the generated signal is shifted aed inFigure 1106c.When the satellite signal is multiplieddistance proportional to the received signal's time delaywith the C/Aand Pcodesgenerated bythereceiver,thesat-These simultaneous requirements to be both repeatableellite signal will be collapsed into the original carrier(non-random)and random giveriseto thedescription offrequencyband.The signal power is then raised abovethe"pseudo-random";the signal has enough repeatability tothermalnoiselevelenable the receiver to make the required measurementwhile simultaneously retaining enough randomness to en-Thenavigation message is superimposed on both thePsure incorrect calculations are excluded.codeand C/Acodewithadatarateof50bitspersecond (50Hz.) The navigation message consists of 25 data frames,eachframeconsistingof1500bits.Eachframeisdivided1108.Precise Positioning Service And Standardintofive subframes of300bits each.It will,therefore,takePositioning Service30seconds toreceiveonedataframeand12.5minutestoreceive all 25 frames.The navigation message containsTwo levels of navigational accuracy areprovided byGPS system time of transmission;a hand over wordthe GPS:the Precise Positioning Service (PPS)and the(HOW),allowingthetransitionbetweentrackingtheC/AStandard Positioning Service (SPS).GPS was designed,codeto the P code;ephemeris and clock data for the satel-first and foremost, by the U.S.Department of Defense as alitebeingtracked,andalmanacdataforthesatellitesinUnited States military asset, its extremely accurate posi-orbit.It also contains coefficients for ionospheric delaytioning capability is an asset access to which the U.s.models used by C/Areceivers and coefficients used to cal-militarywould like to limit during time of war.Therefore,culateUniversal CoordinatedTime(UTC)thePPs is available only to authorized users, mainly theU.S.militaryand authorized allies.SPS, onthe other hand,1107.TheCorrelationProcessis available worldwidetoanyone possessingaGPS receiv-er.PPS,therefore,providesamoreaccuratepositionthandoes SPSThecorrelation process compares the signal receivedwith the signal generated internal to the receiver. It doesTwo cryptographicmethods areemployed todenythePPS accuracy to civilian users: selective availability (SA)this by comparingthe square wave function of the receivedSA/A-S ConfigurationSIS Interface ConditionsPPS UsersSPs UsersSA Set to ZeroFull accuracy,Full accuracy,*P-Code, no errorsA-S OffC/A-Code, no errorsspoofablespoofableSA at Non-Zero ValueP-Code, errorsFullaccuracy,Limited accuracy,A-S offC/A-Code, errorsspoofablespoofableSA Setto ZeroY-Code, no errorsFull accuracyFull accuracy,***Not spoofable**A-S OnC/A-Code, no errorsspoofableSA at Non-Zero ValueY-Code, errorsFull accuracyLimited accuracy,Not spoofable**A-S OnC/A-Code,errorsspoofable*Full accuracy" defined as equivelent to a PPS-capable UE operated in a similar manner.*Certain PPS-capable UE do not have P-or Y-code tracking abilities and remain spoofabledespite A-S protectionbeing applied***Assuming negligable accuracy degradation due to C/A-code operation (but moresusceptibletojamming)Figure 1108. Effect of SA and A-S on GPS accuracy

SATELLITE NAVIGATION 183 ing the carrier’s phase. The phase modulation employed by GPS is known as bi-phase shift keying (BPSK). Due to this BPSK, the carrier frequency is “spread” about its center frequency by an amount equal to twice the “chipping rate” of the modulating signal. In the case of the P code, this spreading is equal to (2 × 10.23 MHz) = 20.46 MHz. For the C/A code, the spreading is equal to (2 × 1.023 MHz) = 2.046 MHz. See Figure 1106b. Note that the L1 carrier signal, modulated with both the P code and C/A code, is shaped differently from the L2 carrier, modulated with only the P code. This spreading of the carrier signal lowers the total signal strength below the thermal noise threshold present at the receiver. This effect is demonstrat￾ed in Figure 1106c. When the satellite signal is multiplied with the C/A and P codes generated by the receiver, the sat￾ellite signal will be collapsed into the original carrier frequency band. The signal power is then raised above the thermal noise level. The navigation message is superimposed on both the P code and C/A code with a data rate of 50 bits per second (50 Hz.) The navigation message consists of 25 data frames, each frame consisting of 1500 bits. Each frame is divided into five subframes of 300 bits each. It will, therefore, take 30 seconds to receive one data frame and 12.5 minutes to receive all 25 frames. The navigation message contains GPS system time of transmission; a hand over word (HOW), allowing the transition between tracking the C/A code to the P code; ephemeris and clock data for the satel￾lite being tracked; and almanac data for the satellites in orbit. It also contains coefficients for ionospheric delay models used by C/A receivers and coefficients used to cal￾culate Universal Coordinated Time (UTC). 1107. The Correlation Process The correlation process compares the signal received with the signal generated internal to the receiver. It does this by comparing the square wave function of the received signal with the square wave function generated by the re￾ceiver. The computer logic of the receiver recognizes the square wave signals as either a +1 or a 0 depending on whether the signal is “on” or “off.” The signals are pro￾cessed and matched by using an autocorrelation function. This process defines the necessity for a “pseudo-ran￾dom code.” The code must be repeatable (i.e., non-random) because it is in comparing the two signals that the receiver makes its distance calculations. At the same time, the code must be random for the correlation process to work; the ran￾domness of the signals must be such that the matching process excludes all possible combinations except the com￾bination that occurs when the generated signal is shifted a distance proportional to the received signal’s time delay. These simultaneous requirements to be both repeatable (non-random) and random give rise to the description of “pseudo-random”; the signal has enough repeatability to enable the receiver to make the required measurement while simultaneously retaining enough randomness to en￾sure incorrect calculations are excluded. 1108. Precise Positioning Service And Standard Positioning Service Two levels of navigational accuracy are provided by the GPS: the Precise Positioning Service (PPS) and the Standard Positioning Service (SPS). GPS was designed, first and foremost, by the U.S. Department of Defense as a United States military asset; its extremely accurate posi￾tioning capability is an asset access to which the U.S. military would like to limit during time of war. Therefore, the PPS is available only to authorized users, mainly the U.S. military and authorized allies. SPS, on the other hand, is available worldwide to anyone possessing a GPS receiv￾er. PPS, therefore, provides a more accurate position than does SPS. Two cryptographic methods are employed to deny the PPS accuracy to civilian users: selective availability (SA) SA/A-S Configuration SIS Interface Conditions PPS Users SPS Users SA Set to Zero A-S Off P-Code, no errors C/A-Code, no errors Full accuracy, spoofable Full accuracy,* spoofable SA at Non-Zero Value A-S Off P-Code, errors C/A-Code, errors Full accuracy, spoofable Limited accuracy, spoofable SA Set to Zero A-S On Y-Code, no errors C/A-Code, no errors Full accuracy, Not spoofable** Full accuracy,*** spoofable SA at Non-Zero Value A-S On Y-Code, errors C/A-Code, errors Full accuracy, Not spoofable** Limited accuracy, spoofable * ** *** “Full accuracy” defined as equivelent to a PPS-capable UE operated in a similar manner. Certain PPS-capable UE do not have P- or Y-code tracking abilities and remain spoofable despite A-S protection being applied Assuming negligable accuracy degradation due to C/A-code operation (but more susceptible to jamming). Figure 1108. Effect of SA and A-S on GPS accuracy

184SATELLITENAVIGATIONand anti-spoofing (A-S).SAoperates by introducing con-satellite signals,makepseudorange measurements,andcol-trolled errors intoboth the C/A and P code signals.SA canlectnavigationdata.be programmed to degrade the signalsaccuracy even fur-Atypical satellitetracking sequence begins with the re-ther during time of war, denying a potential adversary theceiver determiningwhich satellites are availablefor it toabilitytouseGPStonominal SPSaccuracy.SA introducestrack.Satellitevisibility is determined by user-entered pre-two errors into the satellite signal: (1)The epsilon error: andictions of position, velocity,and time, and by almanacerror in satellite ephemeris data in the navigation message;information stored internal to the receiver.If no stored al-and(2)clockdither:errorintroducedinthesatelliteatomicmanac information exists,then the receivermust attempttoclocks'timing.The presence of SA is the largest source oflocate and lock ontothe signal from any satellite inviewerrorpresentinanSPSGPSpositionmeasurementWhen the receiver is locked onto a satellite,it can demodu-Anti-spoofing is designed to negate any hostile imita-late thenavigation messageand read the almanactionofGPSsignals.ThetechniquealtersthePcodeintoinformation about all the other satellites in the constella-anothercode.designatedtheYcode.TheC/Acoderemainstion. A carrier tracking loop tracks the carrier frequencyunaffected.The U.S.employs this technique to the satellitewhile acodetracking looptracks theC/A and P codesigsignalsatrandomtimesandwithoutwarning:therefore.ci-nals.Thetwo tracking loops operate together in an iterativevilian users are unawarewhen this P code transformationprocess to acquire and track satellite signalstakes place.Since anti-spoofing is applied only to the PThereceiver's carriertracking loop will locallygener-code,theC/A code is not protected and can be spoofedateanLl carrierfrequencywhichdiffers from the satelliteOnly users employing the proper cryptographic devic-produced L1 frequency due to a doppler shift in the re-es can defeat both SA and anti-spoofing. Without theseceivedfrequency.This doppler offset is proportional tothedevices, the user will be subject to the accuracy degradationrelativevelocityalongthe line ofsightbetweenthe satelliteof SA and will be unableto track theYcode.and the receiver, subject to a receiver frequency bias.TheGPSPPSreceiverscanuseeitherthePcodeortheC/carrier tracking loop adjusts the frequency of the receiver-Acode,orboth,indeterminingposition.Maximumaccura-generatedfrequency until itmatches the incoming frequen-cy is obtained by using the P code on both L1 and L2.Thecy. This determines the relative velocity between thesatellite and the receiver.The GPS receiver uses this rela-difference in propagation delayis then used to calculatetive velocity to calculate the velocity of the receiver. Thisionosphericcorrections.TheC/Acodeisnormallyusedtoacquirethe satellite signal anddetermine the approximatePvelocity is then used to aid the codetracking loopcodephase.Then, the receiver locks on theP codeforpre-The codetracking loop is used to makepseudorangecise positioning (subject to SA if not cryptographicallymeasurements betweentheGPSreceiver and thesatellitesequipped).SomePpreceiverspossessaclockaccurateThereceiver'strackingloopwillgenerateareplicaoftheenough to track and lock on the P code signal without ini-targeted satellite's C/A code with estimated ranging delaytiallytrackingtheC/Acode.SomePPSreceiverscantrackIn order to match the received signal with the internallyonlytheC/AcodeanddisregardthePcodeentirelv.Sincegenerated replica, two things must be done:1)The centerthe C/A code is transmitted on only onefrequency,the dualfrequencyofthereplicamust beadjusted tobethesameasfrequency ionosphere correction methodology is unavail-thecenterfrequency ofthe received signal;and 2)thephaseableandaionosphericmodelingprocedureisrequiredtoof thereplicacodemustbelinedup withthephaseof thecalculate the required corrections.received code.The centerfrequency of the replica is set byusing the doppler-estimated output of the carrier trackingSPS receivers,asmentioned above,providepositionsloop.Thereceiverwill thenslewthecodeloopgeneratedC/with a degraded accuracy.The A-S feature denies SPS usersA codethoughamillisecond searchwindowto correlateaccesstothePcodewhentransformedtotheYcode.There-fore, the SPS user cannot rely on access to the P code towith the received C/A code and obtain C/A tracking.measurepropagationdelaysbetweenL1andL2and computeOnce the carrier tracking loop and the code trackingionosphericdelaycorrections.Consequently,thetypical SPsloophavelocked ontothereceived signal and the C/Acodereceiver uses only the C/A codebecause it is unaffected byhas been stripped from the carrier, the navigation messageA-S.SinceC/AistransmittedonlyonLl,thedualfrequencyis demodulated and read.This gives the receiver other in-methodof calculating ionosphericcorrections is unavailable;formation crucial to a pseudorange measurement.Thean ionospheric modeling technique must be used. This is lessnavigation message also gives the receiver the handoveraccurate than the dual frequency method,this degradation inword,the codethat allowsa GPSreceivertoshiftfromC/accuracyisaccountedfor in the100meteraccuracycalcula-AcodetrackingtoPcodetrackingtion.Figure 1108 presents the effect on SA and A-S onThe handover word is required dueto the long phase (sev-different types of GPS measurements.en days)of theP codesignal.The C/A coderepeats everymillisecond, allowingfora relatively small search window1109.GPSReceiverOperationsThe seven day repeat period of the P code requires that the re-ceiverbegiven the approximatePcode phaseto narrow itsInorderfortheGPSreceivertonavigate,ithas totracksearchwindowtoa manageabletime.Thehandoverword pro-

184 SATELLITE NAVIGATION and anti-spoofing (A-S). SA operates by introducing con￾trolled errors into both the C/A and P code signals. SA can be programmed to degrade the signals’ accuracy even fur￾ther during time of war, denying a potential adversary the ability to use GPS to nominal SPS accuracy. SA introduces two errors into the satellite signal: (1) The epsilon error: an error in satellite ephemeris data in the navigation message; and (2) clock dither: error introduced in the satellite atomic clocks’ timing. The presence of SA is the largest source of error present in an SPS GPS position measurement. Anti-spoofing is designed to negate any hostile imita￾tion of GPS signals. The technique alters the P code into another code, designated the Y code. The C/A code remains unaffected. The U.S. employs this technique to the satellite signals at random times and without warning; therefore, ci￾vilian users are unaware when this P code transformation takes place. Since anti-spoofing is applied only to the P code, the C/A code is not protected and can be spoofed. Only users employing the proper cryptographic devic￾es can defeat both SA and anti-spoofing. Without these devices, the user will be subject to the accuracy degradation of SA and will be unable to track the Y code. GPS PPS receivers can use either the P code or the C/ A code, or both, in determining position. Maximum accura￾cy is obtained by using the P code on both L1 and L2. The difference in propagation delay is then used to calculate ionospheric corrections. The C/A code is normally used to acquire the satellite signal and determine the approximate P code phase. Then, the receiver locks on the P code for pre￾cise positioning (subject to SA if not cryptographically equipped). Some PPS receivers possess a clock accurate enough to track and lock on the P code signal without ini￾tially tracking the C/A code. Some PPS receivers can track only the C/A code and disregard the P code entirely. Since the C/A code is transmitted on only one frequency, the dual frequency ionosphere correction methodology is unavail￾able and a ionospheric modeling procedure is required to calculate the required corrections. SPS receivers, as mentioned above, provide positions with a degraded accuracy. The A-S feature denies SPS users access to the P code when transformed to the Y code. There￾fore, the SPS user cannot rely on access to the P code to measure propagation delays between L1 and L2 and compute ionospheric delay corrections. Consequently, the typical SPS receiver uses only the C/A code because it is unaffected by A-S. Since C/A is transmitted only on L1, the dual frequency method of calculating ionospheric corrections is unavailable; an ionospheric modeling technique must be used. This is less accurate than the dual frequency method; this degradation in accuracy is accounted for in the 100 meter accuracy calcula￾tion. Figure 1108 presents the effect on SA and A-S on different types of GPS measurements. 1109. GPS Receiver Operations In order for the GPS receiver to navigate, it has to track satellite signals, make pseudorange measurements, and col￾lect navigation data. A typical satellite tracking sequence begins with the re￾ceiver determining which satellites are available for it to track. Satellite visibility is determined by user-entered pre￾dictions of position, velocity, and time, and by almanac information stored internal to the receiver. If no stored al￾manac information exists, then the receiver must attempt to locate and lock onto the signal from any satellite in view. When the receiver is locked onto a satellite, it can demodu￾late the navigation message and read the almanac information about all the other satellites in the constella￾tion. A carrier tracking loop tracks the carrier frequency while a code tracking loop tracks the C/A and P code sig￾nals. The two tracking loops operate together in an iterative process to acquire and track satellite signals. The receiver’s carrier tracking loop will locally gener￾ate an L1 carrier frequency which differs from the satellite produced L1 frequency due to a doppler shift in the re￾ceived frequency. This doppler offset is proportional to the relative velocity along the line of sight between the satellite and the receiver, subject to a receiver frequency bias. The carrier tracking loop adjusts the frequency of the receiver￾generated frequency until it matches the incoming frequen￾cy. This determines the relative velocity between the satellite and the receiver. The GPS receiver uses this rela￾tive velocity to calculate the velocity of the receiver. This velocity is then used to aid the code tracking loop. The code tracking loop is used to make pseudorange measurements between the GPS receiver and the satellites. The receiver’s tracking loop will generate a replica of the targeted satellite’s C/A code with estimated ranging delay. In order to match the received signal with the internally generated replica, two things must be done: 1) The center frequency of the replica must be adjusted to be the same as the center frequency of the received signal; and 2) the phase of the replica code must be lined up with the phase of the received code. The center frequency of the replica is set by using the doppler-estimated output of the carrier tracking loop. The receiver will then slew the code loop generated C/ A code though a millisecond search window to correlate with the received C/A code and obtain C/A tracking. Once the carrier tracking loop and the code tracking loop have locked onto the received signal and the C/A code has been stripped from the carrier, the navigation message is demodulated and read. This gives the receiver other in￾formation crucial to a pseudorange measurement. The navigation message also gives the receiver the handover word, the code that allows a GPS receiver to shift from C/ A code tracking to P code tracking. The handover word is required due to the long phase (sev￾en days) of the P code signal. The C/A code repeats every millisecond, allowing for a relatively small search window. The seven day repeat period of the P code requires that the re￾ceiver be given the approximate P code phase to narrow its search window to a manageable time. The handover word pro-

185SATELLITENAVIGATIONfor GPS:videsthisPcodephaseinformation.Thehandoverwordisrepeatedeverysubframeina30bitlongblockofdatainthenavigationmessage.It isrepeatedinthesecond 30 second data1)ThePPS spherical positionaccuracy shall be 16block of each subframe.For somereceivers,thishandovermeters SEP(spherical errorprobable)orbetter.word is unnecessary,they can acquirethePcode directly.This2) The SPS user two dimensional position accuracynormallyrequires thereceiverto have a clock whose accuracyshall be 100meters 2 drms or better.approaches that ofan atomic clock. Since this greatly increasesthecostofthereceiver,most receiversfor non-militarymarineAssumethata universal setof GPSpseudorangemea-use do not have this capability.surements results in a set of GPS position measurements.Once thereceiver has acquired the satellite signalsfromThe accuracy ofthese measurements will conform to a nor-four GPS satellites, achieved carrier and code tracking,andmal (i.e. values symmetrically distributed around a mean ofhas read the navigation message, the receiver is ready to be-zero)probabilityfunctionbecausethetwomostimportantginmakingpseudorange measurements.Recall thatthesefactors affecting accuracy,the geometric dilution of pre-measurements are termed pseudorange because a receivercision (GDOP) and the user equivalent range errorclock offsetmakes them inaccurate, that is, they do not rep-(UERE),are continuouslyvariableresent the true range from the satellite, only a range biasedThe UERE is theerror inthemeasurement of thepseu-byareceiverclockerror.Thisclockbias introducesafourthdoranges from each satellite to the user. The UERE is theunknown into the system ofequations for which the GPS re-product of several factors, including the clock stability,theceiver must solve(the other threebeing the x coordinate,ypredictabilityof the satellite's orbit, errors in the50Hz nav-coordinate,and zcoordinateofthe receiver position).Recalligation message, the precision of the receiver's correlationfrom the discussion in section 1103 that the receiver solvesprocess,errorsduetoatmosphericdistortion andthecalcula-this clock bias problem by making a fourth pseudorangetions to compensate for it, and the quality of the satellite'smeasurement, resulting in a fourth equation to allow solvingsignal. The UERE, therefore, is a random error which is theforthefourthunknown.Once thefour equations are solved,function oferrors in both thesatellites and theuser'sreceiver.the receiver has an estimate of the receiver's position inThe GDOPdepends on the geometryofthe satellites in re-three dimensions and of GPS time.The receiver then con-lation to the user's receiver.It is independent ofthe quality oftheverts this position into coordinates referenced to an earthbroadcast signals and the user's receiver. Generally speaking,model based on theWorld Geodetic System (1984)theGDOPmeasures the“"spread"ofthesatellites aroundthe re-ceiver.The optimum case would be to have one satellite directly1110. User Range Errors And Geometric Dilution Ofoverhead and the other threespaced 120°around thereceiveronPrecisionthehorizonTheworst GDOPwould occur ifthe satelliteswerespaced closely together or in a line overhead.There are two formal position accuracy requirementsThereare special types of DOP'sfor each of theposi-GDOP-GEOMETRICOLUTION OFPRECISIONUEREWUSERFOUTIOLENTRANGEERRORBCOMBNATIONOF:POBITIONDELUTIONOFPRECISION(POOP)ACYIONESIOMA)FTOEDILUTIONOF PRECISION/TDODRODUCTOFMANYFACTORFOOP-CORIBIUATNION OF::SATELITE NONLSE-SRNCE STABLITYMORZONTALDILUTION CFPRECSION PIDOPTERMINISTICCORRECTIONACCURAC:VERTICALDLUTKON GEPRECION INDO)+ETCMULTIPLYTOGETHER*TORESULTINTHREE-DIMENSIONALUSERNAVIGATIONERROR(UNE)*UNE=UEREXPDOPTWO-DIMENSIONALUSERHORIZONTALNAVIGATIONERROR(UHNEY"UHNE=UEREXHDOPFigure1110.Position and time errorcomputations

SATELLITE NAVIGATION 185 vides this P code phase information. The handover word is repeated every subframe in a 30 bit long block of data in the navigation message. It is repeated in the second 30 second data block of each subframe. For some receivers, this handover word is unnecessary; they can acquire the P code directly. This normally requires the receiver to have a clock whose accuracy approaches that of an atomic clock. Since this greatly increases the cost of the receiver, most receivers for non-military marine use do not have this capability. Once the receiver has acquired the satellite signals from four GPS satellites, achieved carrier and code tracking, and has read the navigation message, the receiver is ready to be￾gin making pseudorange measurements. Recall that these measurements are termed pseudorange because a receiver clock offset makes them inaccurate; that is, they do not rep￾resent the true range from the satellite, only a range biased by a receiver clock error. This clock bias introduces a fourth unknown into the system of equations for which the GPS re￾ceiver must solve (the other three being the x coordinate, y coordinate, and z coordinate of the receiver position). Recall from the discussion in section 1103 that the receiver solves this clock bias problem by making a fourth pseudorange measurement, resulting in a fourth equation to allow solving for the fourth unknown. Once the four equations are solved, the receiver has an estimate of the receiver’s position in three dimensions and of GPS time. The receiver then con￾verts this position into coordinates referenced to an earth model based on the World Geodetic System (1984). 1110. User Range Errors And Geometric Dilution Of Precision There are two formal position accuracy requirements for GPS: 1) The PPS spherical position accuracy shall be 16 meters SEP (spherical error probable) or better. 2) The SPS user two dimensional position accuracy shall be 100 meters 2 drms or better. Assume that a universal set of GPS pseudorange mea￾surements results in a set of GPS position measurements. The accuracy of these measurements will conform to a nor￾mal (i.e. values symmetrically distributed around a mean of zero) probability function because the two most important factors affecting accuracy, the geometric dilution of pre￾cision (GDOP) and the user equivalent range error (UERE), are continuously variable. The UERE is the error in the measurement of the pseu￾doranges from each satellite to the user. The UERE is the product of several factors, including the clock stability, the predictability of the satellite’s orbit, errors in the 50 Hz nav￾igation message, the precision of the receiver’s correlation process, errors due to atmospheric distortion and the calcula￾tions to compensate for it, and the quality of the satellite’s signal. The UERE, therefore, is a random error which is the function of errors in both the satellites and the user’s receiver. The GDOP depends on the geometry of the satellites in re￾lation to the user’s receiver. It is independent of the quality of the broadcast signals and the user’s receiver. Generally speaking, the GDOP measures the “spread” of the satellites around the re￾ceiver. The optimum case would be to have one satellite directly overhead and the other three spaced 120° around the receiver on the horizon. The worst GDOP would occur if the satellites were spaced closely together or in a line overhead. There are special types of DOP’s for each of the posi￾Figure 1110. Position and time error computations

186SATELLITENAVIGATIONtion and time solution dimensions; these particular DOP's(K × TEC)combineto determinetheGDOP.For thevertical dimen-△tfsion, the vertical dilution of precision (VDOP)describesthe effect of satellitegeometry on altitude calculations.Thehorizontal dilution of precision(HDOP)describes satel-wherelitegeometry's effect on position (latitude and longitude)errors.ThesetwoDOP's combinetodeterminethepositionAt=grouptime delaydilution ofprecision (PDOP).ThePDOPcombined withifK=operatingfrequencythe time dilution of precision (TDOP)results in the=constantGDOP. See Figure 1110.Since the sun's U-V radiation ionizes the molecules in11l1.lonosphericDelayErrorsthe upper atmosphere, it stands to reason that the time delayvalue will be highest when the sun is shining and lowest atSection 1107covered errors in GPSpositions due to er-night.Experimental evidence has borne this out, showingrors inherent inthe satellite signal (UERE)and thegeometrythat thevalueforTEC is highest around 1500 local time andof the satelliteconstellation(GDOP).Anothermajor causelowestaround0500local time.Therefore,themagnitudeofofaccuracydegradation istheeffectofthe ionosphereon thethe accuracy degradation caused by this effect will be high-radio frequency signals that comprise the GPS signal.est during daylight operations.In addition to thesedailyA discussion of a model of the earth's atmosphere willvariations,the magnitudeofthis timedelay error also varieswith the seasons, it is highest at the vernal equinox.Finallybe useful in understanding this concept.Consider the earthas surrounded bythree layers ofatmosphere.Thefirst layer,thiseffectshowsasolarcvcledependence.Thegreaterthenumber ofsunspots, the higher the TEC value and thegreatextendingfromthesurfaceoftheearthtoanaltitudeofap-erthe group time delay effect.The solar cycletypicallyproximately 10 km,is known as the troposphere.Above thetroposphereand extendingtoan altitudeof approximatelyfollowsanelevenyearpattern.Solarcycle22began in198650km is the stratosphere.Finally,abovethe stratospherepeaked in 1991,and is now in decline.It should reacha min-and extendingto an altitude that varies as a function of theimum in 1997, at which time the effect on thegroup timedelayfrom thisphenomenon will also reachaminimum.time of day is the ionosphere. Though radio signals aresubjected to effects which degrade its accuracy in all threeGiven that this ionospheric delay introduces a seriouslayers of this atmospheric model,the effects of the iono-accuracydegradation into the system,howdoesGPSacsphere are the most significant, therefore, they will becount for it?There are two methods used:(1)the dualdiscussed here.frequencytechnique,and(2)the ionosphericdelaymethodThe ionosphere, as the name implies, is that region ofthe atmosphere which contains a large number of ionized1112.Dual Frequency Correction Techniquemolecules and a correspondingly high number of free elec-trons.These charged molecules are those which have lostAs the term implies, the dual frequency technique re-oneormoreelectrons.Noatomwill looseanelectron with-quires the ability to acquire and track both the LI and L2out an input ofenergy,the energyinput thatcauses the ionsfrequency signals.Recall fromthe discussion in sectionto be formed in the ionosphere comes from theultraviolet1105that theC/AandPcodes aretransmittedoncarrierfre-(U-V) radiation of the sun,Therefore, the more intense thequencyL1,butonlythePcode istransmitted on L2.Recallsun'srays,thelargerthenumber offreeelectronswhichalsofromsection1105thatonlyauthorizedoperatorswithwill exist in this region of the atmosphere.access to DOD cryptographic material are able to copy theThe largest effect that this ionospheric effect has onP code. It follows,then, that onlythose authorized users areGPS accuracy is a phenomenon known as group time de-abletocopytheL2carrierfrequency.Therefore,onlythoselay.As the name implies, group time delay results in aauthorized users are able to use the dual frequency correc-delay in the time a signal takes to travel through a given dis-tion method The dual frequency method measures thetance.Obviously,since GPS relies on extremely accuratedistancebetween the satelliteand the user based on boththetiming measurementof these signals between satellites andLI and L2 carrier signal.Theserangeswill bedifferent be-ground receivers, this group time delay can have a notice-causethegrouptimedelayforeach signal will bedifferentableeffectonthemagnitudeof GPSpositionerror.This is because ofthe frequency dependence of thetime de-The group time delay is a function of several elements. It islay error.The rangefrom the satellite to the userwill be theinversely proportional to the square of the frequency attrue range combined withtherange error caused by the timewhichthesatellitetransmits,and it isdirectlyproportionaltodelay,as shown bythefollowing equation:the atmosphere's total electron content (TEC),a measureof the degree of the atmosphere's ionization.The generalR(f) - Ractual + er termform of the equation describing the delay effect is:

186 SATELLITE NAVIGATION tion and time solution dimensions; these particular DOP’s combine to determine the GDOP. For the vertical dimen￾sion, the vertical dilution of precision (VDOP) describes the effect of satellite geometry on altitude calculations. The horizontal dilution of precision (HDOP) describes satel￾lite geometry’s effect on position (latitude and longitude) errors. These two DOP’s combine to determine the position dilution of precision (PDOP). The PDOP combined with the time dilution of precision (TDOP) results in the GDOP. See Figure 1110. 1111. Ionospheric Delay Errors Section 1107 covered errors in GPS positions due to er￾rors inherent in the satellite signal (UERE) and the geometry of the satellite constellation (GDOP). Another major cause of accuracy degradation is the effect of the ionosphere on the radio frequency signals that comprise the GPS signal. A discussion of a model of the earth’s atmosphere will be useful in understanding this concept. Consider the earth as surrounded by three layers of atmosphere. The first layer, extending from the surface of the earth to an altitude of ap￾proximately 10 km, is known as the troposphere. Above the troposphere and extending to an altitude of approximately 50 km is the stratosphere. Finally, above the stratosphere and extending to an altitude that varies as a function of the time of day is the ionosphere. Though radio signals are subjected to effects which degrade its accuracy in all three layers of this atmospheric model, the effects of the iono￾sphere are the most significant; therefore, they will be discussed here. The ionosphere, as the name implies, is that region of the atmosphere which contains a large number of ionized molecules and a correspondingly high number of free elec￾trons. These charged molecules are those which have lost one or more electrons. No atom will loose an electron with￾out an input of energy; the energy input that causes the ions to be formed in the ionosphere comes from the ultraviolet (U-V) radiation of the sun. Therefore, the more intense the sun’s rays, the larger the number of free electrons which will exist in this region of the atmosphere. The largest effect that this ionospheric effect has on GPS accuracy is a phenomenon known as group time de￾lay. As the name implies, group time delay results in a delay in the time a signal takes to travel through a given dis￾tance. Obviously, since GPS relies on extremely accurate timing measurement of these signals between satellites and ground receivers, this group time delay can have a notice￾able effect on the magnitude of GPS position error. The group time delay is a function of several elements. It is inversely proportional to the square of the frequency at which the satellite transmits, and it is directly proportional to the atmosphere’s total electron content (TEC), a measure of the degree of the atmosphere’s ionization. The general form of the equation describing the delay effect is: where Since the sun’s U-V radiation ionizes the molecules in the upper atmosphere, it stands to reason that the time delay value will be highest when the sun is shining and lowest at night. Experimental evidence has borne this out, showing that the value for TEC is highest around 1500 local time and lowest around 0500 local time. Therefore, the magnitude of the accuracy degradation caused by this effect will be high￾est during daylight operations. In addition to these daily variations, the magnitude of this time delay error also varies with the seasons; it is highest at the vernal equinox. Finally, this effect shows a solar cycle dependence. The greater the number of sunspots, the higher the TEC value and the great￾er the group time delay effect. The solar cycle typically follows an eleven year pattern. Solar cycle 22 began in 1986, peaked in 1991, and is now in decline. It should reach a min￾imum in 1997, at which time the effect on the group time delay from this phenomenon will also reach a minimum. Given that this ionospheric delay introduces a serious accuracy degradation into the system, how does GPS ac￾count for it? There are two methods used: (1) the dual frequency technique, and (2) the ionospheric delay method. 1112. Dual Frequency Correction Technique As the term implies, the dual frequency technique re￾quires the ability to acquire and track both the L1 and L2 frequency signals. Recall from the discussion in section 1105 that the C/A and P codes are transmitted on carrier fre￾quency L1, but only the P code is transmitted on L2. Recall also from section 1105 that only authorized operators with access to DOD cryptographic material are able to copy the P code. It follows, then, that only those authorized users are able to copy the L2 carrier frequency. Therefore, only those authorized users are able to use the dual frequency correc￾tion method. The dual frequency method measures the distance between the satellite and the user based on both the L1 and L2 carrier signal. These ranges will be different be￾cause the group time delay for each signal will be different. This is because of the frequency dependence of the time de￾lay error. The range from the satellite to the user will be the true range combined with the range error caused by the time delay, as shown by the following equation: ∆t = group time delay f = operating frequency K = constant ∆t (K × ) TEC f 2 = - R f() Ractual = + error term

187SATELLITENAVIGATIONwhere R(f) is the range which differs from the actual rangeis obviously a reasonable design consideration because it isas a function of the carrier frequency.The dual frequencyatthetimeofdaywhen themaximum diurnal timedelayoc-correctionmethodtakes two suchrangemeasurements,curs that the largest magnitude of error appears.TheR(LI)and R(L2).Recall that theerror term is afunction ofcoefficients for use in this delay model aretransmittedto thea constantdivided bythe square of thefrequency.By com-receiverinthenavigationdatamessage.Asstatedinsection1112,thismethod ofcorrection is notas accurateasthedualbining the two range equations derived from the twofrequency measurements,the constant term can beelimi-frequencymethod; however,for the non-militaryuser, it isnated and one is left with an equation in which the truetheonlymethodofcorrectionavailable.rangeissimplvafunctionofthetwocarrierfrequenciesand1114.MultipathReflectionErrorsthe measured ranges R(L1)and R(L2).This method has twomajor advantages overthe ionospheric model method.(1)Itcalculates corrections from real-time measured data,there-Multipathreflection errors occurwhenthe receiverde-fore.itismoreaccurate.(2)Italleviatestheneedtoincludetects parts of the same signal at twodifferent times.Theionospheric data on the navigation message.A significantfirst reception isthe directpathreception, the signal that isportion of thedatamessage is devoted to ionospheric cor-received directlyfrom the satellite.The second reception isrection data.Ifthe receiver isdual frequency capable, thenfrom areflection ofthat same signal from the ground or anyit doesnotneed any ofthis data.other reflective surface.The direct path signal arrives first,Thevastmajorityof maritimeusers cannot copydualthe reflected signal, having had to travel a longer distancefrequency signals. For them, the ionospheric delay modelto thereceiver,arrives later.TheGPS signal is designedtoprovidesthecorrectionforthegrouptimedelayminimize this multipath error.The L1 and L2 frequenciesused demonstratea diffuse reflectionpattern, loweringthe1113.ThelonosphericDelayModelsignal strength or any reflection that arrives at the receiverIn addition, the receiver's antenna can be designed to rejectThe ionospheric delaymodel mathematicallymodelsa signal that it recognizes as a reflection. In addition to thethe diurnal ionospheric variation. The value for this time de-properties ofthe carrier frequencies, the high data frequen-cy of both the P and C/A codes and their resulting goodlayisdeterminedfromacosinusoidalfunction intowhichcoefficients representingthe maximumvalue ofthetime de-correlation properties minimize the effect of multipathlay (i.e.,the amplitude of the cosine wave representing thepropagation.delay function);thetime of day,the period of the variation,The design features mentioned above combine to re-andaminimumvalueofdelayareintroduced.Thismodelisducethe maximumerrorexpectedfrom multipathdesigned to be most accurate at the diurnal maximum.Thispropagation to less than 20feet.DIFFERENTIALGPS1115.Differential GPS ConceptHowever,100 meter accuracy is not sufficient to ensureship's safety in most piloting situations.In this situationThediscussions abovemakeit clear that theGlobal Po-the marinerneeds P code accuracy.The problem then be-sitioning System provides themost accurate positionscomes howto obtain the accuracy of the Precise Positioningavailableto navigators today.Theyshould alsomakeclearService withdue regard to the legitimate security concernsof the U.S.military.The answer to this seeming dilemmathat the most accurate positioning information is availableto only a small fraction ofthe using population:U.S.and al-lies in the concept of DifferentialGPS (DGPS)Differential GPS is a system in which a receiver at anliedmilitary.Formostopen oceannavigationapplicationsthe degraded accuracy inherent in selective availability andaccurately surveyed position utilizes GPS signals to calcu-the inabilityto copythe precision codepresents no seriouslate timing errors and then broadcasts acorrection signal tohazardtonavigation.Amarinerseldomifeverneedsgreat-accountforthese errors.This is anextremelypowerful con-erthan100meteraccuracyinthemiddleoftheocean.cept.The errors which contribute to GPS accuracyItis a different situationas the mariner approachesdegradation,ionospheric time delay and selective availabil-shore. Typically for harbor approaches and piloting, theity,are experienced simultaneouslyby both the DGPSmariner will shiftto visual pilotingThe increase in accura-receiverandarelativelycloseuser'sreceiver.Theextremelyhigh altitudeof the GPS satellites means that, aslong ascy provided by this navigational method is required toensureshipssafety.The100meteraccuracyofGPSinthistheDGPS receiver is within100-200km of the user's re-situation is not sufficient.Anymariner who has groped hisceiver, the user's receiver is close enough to take advantageway through a restricted channel, in a fog obscuring all vi-ofanyDGPScorrectionsignal.sual navigation aids will certainly appreciate the fact thatThe theorybehind aDGPS system is straightforwardevenadegradedGPSpositionisavailableforthemtoplot.Located on an accurately surveyed site, theDGPS receiver

SATELLITE NAVIGATION 187 where R(f) is the range which differs from the actual range as a function of the carrier frequency. The dual frequency correction method takes two such range measurements, R(L1) and R(L2). Recall that the error term is a function of a constant divided by the square of the frequency. By com￾bining the two range equations derived from the two frequency measurements, the constant term can be elimi￾nated and one is left with an equation in which the true range is simply a function of the two carrier frequencies and the measured ranges R(L1) and R(L2). This method has two major advantages over the ionospheric model method. (1) It calculates corrections from real-time measured data; there￾fore, it is more accurate. (2) It alleviates the need to include ionospheric data on the navigation message. A significant portion of the data message is devoted to ionospheric cor￾rection data. If the receiver is dual frequency capable, then it does not need any of this data. The vast majority of maritime users cannot copy dual frequency signals. For them, the ionospheric delay model provides the correction for the group time delay. 1113. The Ionospheric Delay Model The ionospheric delay model mathematically models the diurnal ionospheric variation. The value for this time de￾lay is determined from a cosinusoidal function into which coefficients representing the maximum value of the time de￾lay (i.e., the amplitude of the cosine wave representing the delay function); the time of day; the period of the variation; and a minimum value of delay are introduced. This model is designed to be most accurate at the diurnal maximum. This is obviously a reasonable design consideration because it is at the time of day when the maximum diurnal time delay oc￾curs that the largest magnitude of error appears. The coefficients for use in this delay model are transmitted to the receiver in the navigation data message. As stated in section 1112, this method of correction is not as accurate as the dual frequency method; however, for the non-military user, it is the only method of correction available. 1114. Multipath Reflection Errors Multipath reflection errors occur when the receiver de￾tects parts of the same signal at two different times. The first reception is the direct path reception, the signal that is received directly from the satellite. The second reception is from a reflection of that same signal from the ground or any other reflective surface. The direct path signal arrives first, the reflected signal, having had to travel a longer distance to the receiver, arrives later. The GPS signal is designed to minimize this multipath error. The L1 and L2 frequencies used demonstrate a diffuse reflection pattern, lowering the signal strength or any reflection that arrives at the receiver. In addition, the receiver’s antenna can be designed to reject a signal that it recognizes as a reflection. In addition to the properties of the carrier frequencies, the high data frequen￾cy of both the P and C/A codes and their resulting good correlation properties minimize the effect of multipath propagation. The design features mentioned above combine to re￾duce the maximum error expected from multipath propagation to less than 20 feet. DIFFERENTIAL GPS 1115. Differential GPS Concept The discussions above make it clear that the Global Po￾sitioning System provides the most accurate positions available to navigators today. They should also make clear that the most accurate positioning information is available to only a small fraction of the using population: U.S. and al￾lied military. For most open ocean navigation applications, the degraded accuracy inherent in selective availability and the inability to copy the precision code presents no serious hazard to navigation. A mariner seldom if ever needs great￾er than 100 meter accuracy in the middle of the ocean. It is a different situation as the mariner approaches shore. Typically for harbor approaches and piloting, the mariner will shift to visual piloting. The increase in accura￾cy provided by this navigational method is required to ensure ship’s safety. The 100 meter accuracy of GPS in this situation is not sufficient. Any mariner who has groped his way through a restricted channel, in a fog obscuring all vi￾sual navigation aids will certainly appreciate the fact that even a degraded GPS position is available for them to plot. However, 100 meter accuracy is not sufficient to ensure ship’s safety in most piloting situations. In this situation, the mariner needs P code accuracy. The problem then be￾comes how to obtain the accuracy of the Precise Positioning Service with due regard to the legitimate security concerns of the U.S. military. The answer to this seeming dilemma lies in the concept of Differential GPS (DGPS). Differential GPS is a system in which a receiver at an accurately surveyed position utilizes GPS signals to calcu￾late timing errors and then broadcasts a correction signal to account for these errors. This is an extremely powerful con￾cept. The errors which contribute to GPS accuracy degradation, ionospheric time delay and selective availabil￾ity, are experienced simultaneously by both the DGPS receiver and a relatively close user’s receiver. The extreme￾ly high altitude of the GPS satellites means that, as long as the DGPS receiver is within 100-200 km of the user’s re￾ceiver, the user’s receiver is close enough to take advantage of any DGPS correction signal. The theory behind a DGPS system is straightforward. Located on an accurately surveyed site, the DGPS receiver

188SATELLITENAVIGATIONalready knows its location, It receives data which tell itsition can be used as the prime input to an electronic chartwherethe satellite is.Knowingthetwolocations,itthensystem,providingan electronicreadoutofpositionaccuratecalculates the time it should take for a satellite's signal toenoughto pilot safelyin the most restricted channel.Thereach it. It compares the time that it actually takes for theU.S.Coast Guard presentlyplans to install DGPS systemssignal to arrive.This difference in time between the theoret-to provide 100% coverage along the eastern seaboard, theical and the actual is the basis for the DGPS receiver'sGulf Coast,and thePacific coast.Alaska and Hawaii willcomputation ofa timing error signal;this difference intimealso be covered with a DGPS network.TheDGPS signaliscausedbyalltheerrorstowhichtheGPssignalissub-will be broadcast using existing radiobeaconsjected; errors, exceptfor receiver error andmultipatherror,DGPS accuracy will revolutionize marine navigation.to which both theDGPS and the user's receivers are simul-It is important to note, however, that, even with the devel-taneously subject.The DGPS system then broadcasts aopment of the electronic chart and the proliferation oftiming correction signal, theeffectofwhich isto correctforaccurate,real-time electronic navigation systems,the mari-selective availability,ionospheric delay,and all the otherner should not let his skills in the more traditional areas oferrorsourcesthetworeceiversshareincommonnavigation, such as celestial navigation and piloting,waneFor suitablyequipped users, DGPS results inpositionsThey will become important secondary methods, any mari-as accurate as if not more accurate than those obtainable byner whohasput hisfaith inelectronicnavigationonlytoseethe Precise Positioning Service.For the mariner approach-the system suffer an electronic failure at sea can attest to theing a harbor or piloting in restricted waters near a site withimportanceof maintainingproficiencyin the moretradi-aDGPS transmitter,theaccuracyrequiredfor ship's safetytionalmethodsofnavigation.However,thereisnodoubtis nowavailablefrom a system otherthanplottingvisualthat theease, convenience,and accuracy of DGPS will rev-bearings.This capability is not limited to simply displayingthecorrectpositionforthenavigatortoplot.TheDGPSpo-olutionizethepracticeofmarinenavigation

188 SATELLITE NAVIGATION already knows its location. It receives data which tell it where the satellite is. Knowing the two locations, it then calculates the time it should take for a satellite’s signal to reach it. It compares the time that it actually takes for the signal to arrive. This difference in time between the theoret￾ical and the actual is the basis for the DGPS receiver’s computation of a timing error signal; this difference in time is caused by all the errors to which the GPS signal is sub￾jected; errors, except for receiver error and multipath error, to which both the DGPS and the user’s receivers are simul￾taneously subject. The DGPS system then broadcasts a timing correction signal, the effect of which is to correct for selective availability, ionospheric delay, and all the other error sources the two receivers share in common. For suitably equipped users, DGPS results in positions as accurate as if not more accurate than those obtainable by the Precise Positioning Service. For the mariner approach￾ing a harbor or piloting in restricted waters near a site with a DGPS transmitter, the accuracy required for ship’s safety is now available from a system other than plotting visual bearings. This capability is not limited to simply displaying the correct position for the navigator to plot. The DGPS po￾sition can be used as the prime input to an electronic chart system, providing an electronic readout of position accurate enough to pilot safely in the most restricted channel. The U.S. Coast Guard presently plans to install DGPS systems to provide 100% coverage along the eastern seaboard, the Gulf Coast, and the Pacific coast. Alaska and Hawaii will also be covered with a DGPS network. The DGPS signal will be broadcast using existing radiobeacons. DGPS accuracy will revolutionize marine navigation. It is important to note, however, that, even with the devel￾opment of the electronic chart and the proliferation of accurate, real-time electronic navigation systems, the mari￾ner should not let his skills in the more traditional areas of navigation, such as celestial navigation and piloting, wane. They will become important secondary methods; any mari￾ner who has put his faith in electronic navigation only to see the system suffer an electronic failure at sea can attest to the importance of maintaining proficiency in the more tradi￾tional methods of navigation. However, there is no doubt that the ease, convenience, and accuracy of DGPS will rev￾olutionize the practice of marine navigation