International Journal of Wireless Information Networks. Vol. I , No. 2, 1994
`
`The Global Positioning System: Signals, Measurements, and
`Performance
`
`Per K. Enge1’2
`
`The Global Positioning System (GPS) is a satellite-based navigation and time transfer system
`developed by the U.S. Department of Defense. It serves marine, airborne, and terrestrial users,
`both military and civilian. Specifically, GPS includes the Standard Positioning Service (SPS) which
`provides civilian users with 100 meter accuracy, and it serves military users with the Precise
`Positioning Service (PPS) which provides 20-m accuracy. Both of these services are available
`worldwide with no requirement for a local reference station. In contrast, differential operation of
`GPS provides 2- to 10-m accuracy to users within 1000 km of a fixed GPS reference receiver.
`Finally, carrier phase comparisons can be used to provide centimeter accuracy to users within 10
`km and potentially within 100 km of a reference receiver. This advanced tutorial will describe the
`GPS signals, the various measurements made by the GPS receivers, and estimate the achievable
`accuracies. It will not dwell on those aspects of GPS which are well known to those skilled in the
`radio communications art, such as spread-spectrum or code division multiple access. Rather,
`it
`will focus on topics which are more unique to radio navigation or GPS. These include code-carrier
`divergence, codeless tracking, carrier aiding, and narrow correlator spacing.
`
`KEY WORDS: Satellite navigation; spread spectrum; global navigation system.
`
`1 . INTRODUCTION
`
`The Global Positioning System (GPS) is a satellite-
`based navigation and time transfer system created by the
`U.S. Department of Defense. As a developmental sys-
`tem, GPS has provided approximately eight years of in-
`creasing service to military and civilian users in a wide
`variety of applications. In September of 1993, GPS in-
`cluded 24 satellites and reached initial operational ca-
`pability (IOC). With IOC,
`the time availability of
`worldwide three-dimensional positioning became vir-
`tually 100%.
`As shown in Fig. 1, GPS consists of a satellite seg-
`ment, a ground control segment, and user receivers. The
`
`'Worcester Polytechnic Institute, Worcester. Massachusetts. Cur-
`rently on leave at Stanford University, Department of Aeronautics
`and Astronautics, Stanford, California.
`3Correspondence should be directed to Professor Per K. Enge, W.
`W. Hansen Experimental Physics Laboratory, Stanford University,
`Stanford, California 94305-4085.
`
`satellite segment consists of 24 satellites placed asym-
`metrically in six orbital planes where each plane is in-
`clined by 55° relative to the equatorial plane. They are
`26559.8 km above the center of the earth, with an or-
`bital period of 12 h and repeating ground tracks as shown
`in Fig. 2. The orbital period is measured in sidereal time
`and not solar time, and so the noontime subsatellite point
`slowly drifts in its fixed track from day to day.
`Each satellite will continuously broadcast direct-
`sequence, spread-spectrum signals on which passive re-
`ceivers can perform precise ranging measurements. Each
`broadcast is also modulated with a navigation message,
`which is developed by the ground control segment and
`describes the satellite location and clock offset. For each
`
`the user equipment measures a
`of several satellites,
`“pseudorange” and demodulates the navigation mes-
`sage. A pseudorange is equal to the true range plus an
`unknown bias equal to the difference between the re-
`ceiver clock and GPS system time. Pseudorange mea-
`surements to four well—spaced satellites are sufficient to
`solve for the user’s three-dimensional position and clock
`
`83
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`1ass-9505/94/0400-oos3so7.oo/o © 1994 Plenum Publishing Corporation
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`PETITIONERS 1007-0001
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`‘viaofiaufidp—d-a¢iu§—-luau-nvwtcwoovpna---nu--uuupDauI—‘
`
`GPS SYSTEM
`
`g--nua-ca»-:-
`
`IIIIIIIIIIIII
`
`L--u-——.......a»»pp—----..»—-»a».\-u-a.a..—-
`CONTROL SEGMENT
`
` User Equipment sot:
`- .. ..I S? 46996.??? ‘I393
`USER SEGIJENT
`
`
`
`ha.»--.
`
`Fig. 1. The Global Positioning System:
`
`the satellite segment, the ground control segment, and the user segment.
`J. Spilker.)
`
`(Courtesy of
`
`
`
`Fig. 2. Ground tracks for four satellites in the GPS constellation.
`
`(Courtesy of]. Spilker.)
`
`SP-WMZFU-U'I3
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`PETITIONERS 1007-0002
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`The Global Positioning System
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`85
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`svm
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`DOE] 5"“
`
`SV#3
`
`VA
`
`
`
`PR1=lXu.1l+(bu_B1)
`
`PRg is the pseudorange to satellite g
`[»Xu‘g|
`is the true distance from the user to satellite g
`bu is the user clock offset measured in meters
`
`Bg is the satellite clock offset measured in meters
`
`Fig. 3. Basic concept of pseudoranging using GPS.
`
`offset. As shown in Fig. 3, if one coordinate of the user's
`position (usually altitude) is known a priori, then three
`pseudorange measurements are usually adequate to solve
`for the user‘s two remaining coordinates and clock olT—
`set.
`
`As shown in Fig. 4, GPS provides a variety of ac-
`curacy levels, where these levels can be broadly char-
`acterized as follows:
`
`Standard Positioning Service (SPS). Civilian users
`are guaranteed access to a l—MHz spreading code (the
`CIA code) which modulates a signal at f,_, = 1575.42
`MHZ. With recent receiver innovations, this chipping
`rate provides a range measurement precision of around
`0.5 m. However, the largest errors are slowly varying
`biases arising from ionospheric refraction, tropospheric
`refraction, and selective availability (SA). SA is the
`largest error source and is intentionally introduced by
`the Department of Defense for national security rea-
`sons. With SA enabled, the SPS provides l00—m hori-
`zontal accuracy (95 percentile level).
`
`(PPS). Authorized
`Precise Positioning Service
`users have access to a 10—MHz code (the P or Y code),
`
`which modulates the signal at f,_, = 1575.42 MHZ and
`a signal at fu = 1227.60 MHZ. This higher chipping
`rate provides better range measurement precision and
`greater protection from multipath. More importantly,
`PPS receivers utilize measurements at the two frequen-
`cies to reduce the effect of ionospheric refraction, and
`PPS users do not suffer from selective availability. For
`these reasons, the PPS provides a horizontal accuracy
`of around 20 m (95 percentile level). Even though the
`P code is published,
`the Department of Defense may
`invoke “antispoofing (AS)” at any time and switch the
`P code to a secure Y code.
`
`C0de~Phase difierential GPS or DGPS. As shown
`in Fig. 5, DGPS places a high-quality GPS receiver and
`an antenna at a known, surveyed location [2]. This ref-
`erence station estimates the slowly varying components
`of the satellite range measurements, and forms a scalar
`correction for each GPS satellite in view. The correction
`
`is broadcast to all DGPS users within range, but its va-
`lidity does decrease with age and the user to reference
`station separation. If the correction is delivered within
`10 s and the user is within 1000 km, then the user will
`
`enjoy position fixing accuracies between 2 and 10 m.
`
`PETITIONERS 1007-0003
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`‘T Carrier Phase
`
`Measurements
`
`Code Phase _,
`Measurements
`
`SPS w/SA
`
`
`
`Code Differential
`
`T1
`
`Worldwide_>2000KmApplicability
`
`
`
`
`Dynamic CDGPS
`i——-—+
`
`Kinematic Survey
`lei
`Upto 100Km
`
`Static Survey
`ljl
`(plus lppm)
`
`
`Horizontal Accuracy
`
`Fig. 4. Levels of accuracy provided by GPS.
`
`Alternatively, networks of reference stations can be used
`to form a vector correction for each satellite. The valid-
`
`ity of this correction still decreases with age, but does
`not decrease as rapidly with distance. These “wide-area
`difierential GPS” systems may provide 5—m accuracies
`over continental areas [16].
`
`Carrier—Phase dzfiferential GPS or CDGPS. Users
`with even more stringent accuracy requirements may be
`able to use a technique called carrier—phase DGPS or
`CDGPS. These users measure the phase of the GPS car-
`rier relative to the canier phase at a reference site and
`achieve range measurement precisions which are a few
`percent of the carrier wavelength.
`As an example of CDGPS, GPS—based phase inter-
`ferometry can be used to determine the attitude of any
`rigid (or semirigid) body by mounting two or more an-
`tennas on the body. Indeed, GPS phase has been used
`to determine the attitude of an aircraft in flight to within
`fractions of a degree [6]. GPS phase comparisons are
`also used in land survey applications, where the anten-
`nas are separated by tens of kilometers. If the antennas
`are fixed, then the survey is static and millimeter rela-
`tive accuracies are possible because long time constants
`
`can be used to average the effects of noise, interference,
`and multipath. If the antennas are moving, then the sur-
`vey is kinematic and shorter time constants must be
`used.
`
`If the antenna separation exceeds one wavelength
`(19 cm), then the estimated position (or attitude) is am-
`biguous, because the number of integer wavelengths
`contained in the phase difference is unknown. Conse-
`quently, canier-phase DGPS requires resolution of a 271'
`or integer ambiguity.
`Survey receivers usually require 30 to 180 min to
`resolve the integer ambiguity, because measurements
`must be made with the satellites at two very different
`locations. If the satellites sweep out a large angle rela-
`tive to the user, then geometric diversity is achieved and
`the integers are observable.
`Many dynamic applications would be well served
`by the accuracy of carrier—phase DGPS, but would also
`require nearly instantaneous resolution of the integer
`ambiguity. For this reason, concepts for identifying the
`integers in real time are being developed [7].
`This advanced tutorial will describe the GPS sig-
`nals, the various measurements made by the user equip-
`ment, and estimate the performance of GPS. It will not
`
`PETITIONERS 1007-0004
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`The Global Positioning System
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`GPS SVtl2
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`El-OD
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`GPS SV#3
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`El-O-Cl
`
`Correction Broadcast
`
`_.:i_4L,:::""__::i:5L__
`
`Reference
`Station
`
`Fig. 5. Differential operation of GPS.
`
`dwell on those aspects of GPS which are well known to
`those skilled in the radio communications art, such as
`spread—spectmm or code division multiple access [29],
`[26]. Rather, it will teach topics which are more unique
`to radio navigation or GPS, including code—carrier di-
`vergence, codeless tracking, carrier aiding, and narrow
`correlator spacing.
`More specifically, Section 2 will describe the sig-
`nals which all the GPS satellites broadcast, and Section
`3 will describe the navigation data which is added to the
`broadcast by the GPS control segment. Section 4 will
`discuss the code and carrier tracking techniques em-
`ployed by many GPS receivers. Section 5 will discuss
`and quantize the errors which trouble code-phase mea-
`surements, and Section 6 will complete our error anal-
`ysis by discussing the navigation equations and geo-
`metric dilution of precision (GDOP). Finally, Section 7
`is a summary and describes some areas of current re-
`search and development.
`This paper will focus on positioning systems that
`are based on measurement of the GPS code phase. Car-
`rier-phase differential GPS will be discussed separately
`in a future paper. Field results which validate the pre—
`dictions of Fig. 4 and the analysis in this paper have
`been obtained by many workers in a wide variety of ap-
`
`plications. Unfortunately, space prohibits a review of
`these results, and the reader is referred to the papers
`listed in the bibliography and recent proceedings of the
`International Technical Meetings of the Satellite Divi-
`sion of the Institute of Navigation, and of the Differ-
`ential Satellite Navigation Symposiums.
`
`2. GPS SIGNAL DESIGN
`
`2.1. Overview
`
`As shown in Fig. 6 [31], each satellite transmits
`navigation signals on two frequencies: f,_, = 1575.42
`MHz and f,_2 = 1227.60 MHz. These L band frequen-
`cies were chosen for three principle reasons. First,
`enough bandwidth could be allocated to send the spread
`spectrum signals needed to obtain precise range mea-
`surements. Second, GPS antennas must be omnidirec-
`tional or hemispherical to serve users with high dynam-
`ics, so space loss and atmospheric attenuation must be
`relatively small. Third, the ranging error due to iono-
`spheric refraction is significantly smaller at L band than
`at lower frequencies.
`As shown in Fig. 6, a single onboard clock pro-
`vides the timing for both carriers, two codes and the
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`PETITIONERS 1007-0005
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`Phase
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`90°
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`
` L1 Signal
`1575.42 MHz
`
`1227.60 MH
`
`F V
`
`x 120
`
` P Coder
` L2 Signal
`
`
`
`
`
`
`+10
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`+ 204600
`
` II
`
`C/ACoder.
`
`
`Fig. 6. Generation of code and carrier signals on the GPS satellite.
`
`data stream. The signal received from each GPS satellite
`is
`
`2.2. Link Budgets
`
`s,_.(t) = x/2C,.D(t)P(t) cos (21rf,_,t + 6”)
`
`+ ~}2CXD(t)X(:) sin (21rf,_,: + GU)
`
`(1)
`
`31.20) = V2CL2D(I‘)P(I) 005 (27rfL2f + 9L2)
`
`(2)
`
`As shown in these equations and Fig. 6, the L1
`broadcast
`is BPSK modulated by two pseudorandom
`noise (PRN) codes in phase quadrature, where X (2) de-_
`notes the C/A code (clear/acquisition or coarse/acqui-
`sition) and P (t) denotes the P code (precision or pro-
`tected) code. The L2 signal is modulated by the P code
`only. The CIA code is a length 1023 Gold code with a
`chipping rate of 1.023 Mcps, which means that it re-
`peats every l ms and yields a null—to-null bandwidth of
`2.046 MHz, In contrast, the P code has a period of one
`week and has a chipping rate of 10.23 Mcps, which
`yields a null—to-null bandwidth of 20.46 MHz. In fact,
`each satellite repeats a one—week section of a single P
`code, which is 37 weeks long. Both the L1 and L2 sig-
`nals are modulated at 50 bps by navigation data (D (t)),
`which is described in Section 3.
`
`The powers in the three received signals are given
`by C,., CX and CL2, and link budgets for these three
`components are given in Table I. As shown, the power
`transmitted in the C/A component is 3 dB greater than
`the power in the P component at L1 and roughly 8 dB
`greater than the power in the P component at L2.
`As shown, the received carrier to noise power spec-
`tral density ratios (C/N0) range from 44.1 dB for the
`C/A signal received from a satellite at zenith down to
`28.6 dB for the L2 signal received at low elevation an-
`gles. These signal-to—n0ise ratios are designed to satisfy
`the ranging accuracy requirement, and they are more
`than adequate for the reliable reception of the 50—bps
`data stream.
`
`2.3. Spread Spectrum
`
`The GPS codes were selected for their auto- and
`
`cross—correlation properties. These properties are well
`described in [26] and only briefly reviewed here.
`As shown in Fig. 7, the C/A codes have autocor—
`relation functions which are four-valued. The maximum
`
`autocorrelation occurs for zero shift, and the largest
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`The Global Positioning System
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`Table I. Link Budgets for the Three GPS Signal Components
`___j._
`
`Zenith
`
`5° Elevation
`
`L1
`
`L2
`
`L1
`
`L2
`
`C/A
`P
`P
`C/A
`P
`P
`
`
`Transmitted power (dBW)
`SV cable and antenna losses
`Polarization losses in the antenna
`
`Satellite antenna gain
`
`Effective radiated power (dBW)
`Space loss (dB)
`Atmospheric loss
`
`Rcvd. power (dBW)
`Rcvr. antenna gain
`
`Rcvr. cable/filter losses
`Other implementation losses
`
`Effective carrier power (C, dBW)
`Boltzmann's constant
`Equivalent noise temp. (71.q)
`Noise PSD (Nu)
`
`14.25
`
`11.25
`
`6.35
`
`1.0 dB
`0.25 dB
`
`14.25
`
`11.25
`
`6.35
`
`28
`182.5
`
`—154.5
`
`15 dB
`
`25
`182.5
`0 dB
`
`—I57.5
`0 dBic
`
`- 156.5
`
`— 159.5
`
`12 dB
`
`22
`184.2
`0.8 dB
`
`-163
`-4 dBic
`
`17.1
`182.3
`
`-166
`
`-169
`
`-172
`
`20.1
`180.6
`
`25
`184.2
`
`—160.5
`
`-160
`
`-1 dB
`— 1 dB
`
`-166
`
`— 162.5
`—228.6 dB/K” Hz
`28 dB
`— 2008.6 dB/K° H2
`
`28.6
`31.6
`34.6
`38.1
`41.1
`44.1
`C/Nu ((113)
`
`
`
`
`
`
`27.1 24.1 21.1 17.6 14.6E,,/N., at 50 bps (dB) 11.6
`
`“side" peak is 24 dB weaker than the main peak. Re-
`markably, the cross-correlation functions between C/A
`codes only take the three values that the autocorrelation
`function takes for nonzero shifts. In other words,
`the
`maximum cross—correlation is also 24 dB weaker than
`
`the main peak of the autocorrelation function.
`The P code has similar properties, but the ratio of
`the main peak to the largest side peaks is much larger,
`because the P code is much longer than the CIA code.
`At the same time, the cross-correlation between differ-
`ent C/A or P codes is also small for any time shift.
`The GPS signal derives the following valuable
`properties from these correlation properties.
`
`taneously without any frequency division. Indeed, GPS
`is a premier application of code division multiple access
`(CDMA).
`
`Antimultipath. Signals which are delayed by more
`than 1.5 times the chip width create correlation peaks
`which are distinct from the peak caused by the direct
`signal. Consequently, the C/A and P codes provide pro-
`tection from multipath with path delays greater than 500
`and 50 m respectively. As described later, advanced re-
`ceivers with so-called narrow correlator spacing are able
`to provide additional protection to C/A code receivers
`[32].
`
`High-Precision Ranging. By tracking the distinct
`and sharp peak of the autocorrelation function, GPS re-
`ceivers can measure C/A code phase with a precision of
`approximately 0.5 m and P code phase with a slightly
`better precision.
`
`Multiple Access. The lack of correlation between
`the GPS codes allow all the satellites to broadcast simul-
`
`Jam Resistance. The military P code provides a
`processing gain of approximately 10 log,0( 10 X
`106/50) or 53 dB. In contrast, the processing gain of the
`C/A code is approximately 10 log,o(1023) or 30 dB.
`These antijam properties exist because GPS receivers
`are matched to the spreading codes. Consequently, the
`magnitude of the receiver’s frequency response is a rel-
`atively flat function of frequency.
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`—1
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`= 0.0616 —> -24dB
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`-1
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`2"~1
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`= -0.001 —> —60dB
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`= —0.0635 —> -24:18
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`Fig. 7. Four—valued autocorrelation function ofa GPS C/A code. The cross-correlation function between C/A codes
`only takes the same three values that the autocorrelation function takes for nonzero shifts.
`
`2.4. Dual Frequencies
`
`The GPS signal uses two frequencies so that the
`receiver can estimate the delay introduced by iono-
`spheric refraction. Indeed, the group delay introduced
`by the ionosphere is approximately
`
`40.3TEC/cfz
`
`where TEC is the unknown total electron content. This
`
`delay can be estimated by tracking the difference in the
`arrival times of the L, and L2 signals, which is
`
`TL: ‘ TL2 —
`
`40.3TEC(fir — fig)
`Cfirfiz
`
`From this dilference observation, the total electron con-
`tent and the ionospheric group delays can be estimated.
`Furthermore, carrier-phase measurements can be
`differenced (OL. - (in) to allow an estimate of the ion-
`ospheric phase delay. Since the ionosphere is disper-
`sive, the group velocity (UK) and the phase velocity (v,,)
`are related by c = x/vgvp, where c is the speed of light.
`Consequently, changes in the total electron content will
`introduce equal but opposite changes in the phase and
`group velocities. This effect is known as code-carrier
`divergence.
`
`If the carrier phases at L, and L3 are dilferenced,
`then the resulting phase delay estimate will have much
`greater precision than the group delay estimate, but will
`suffer from ambiguities proportional to an unknown in-
`teger times the wavelength. However, the rate of change
`of the phase delay is not ambiguous, and so the phase
`dilference measurements can be used to help smooth
`the group delay estimate [8, 30]. This “carn'er—aiding”
`technique significantly improves the estimate of the
`ionospheric delay and delay rate, and will be further dis-
`cussed in Section 5.2.1.
`
`Finally, the L, and L2 signals can be multiplied and
`filtered to yield a signal at the difference frequency. This
`signal has a wavelength of approximately 84 cm and can
`be used to help resolve L, cycle ambiguities when car-
`rier-phase measurements are required for the highest
`possible ranging precision. This technique is known as
`“wide-laning” [13].
`
`3. THE NAVIGATION MESSAGE
`
`As shown in Eqs. (1) and (2), a navigation message
`D(t) modulates both the L, and L2 signals. This mes-
`sage carries data at 50 bps and is required by the re-
`
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`The Global Positioning System
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`ceiver for position fixing. Most of the message is fonned
`by the GPS control segment, which includes five mon-
`itor stations located at Falcon AFB, Hawaii, Ascension,
`Diego Garcia, and Kwajalein Islands. It also includes a
`master control station (MCS), which is colocated with
`the monitor station at Falcon Air Force Base in Colo-
`
`rado Springs. The MCS collects data from all of the
`monitor stations and is responsible for satellite station
`keeping and the generation of the navigation message.
`Finally, the control segment includes uplink ground an-
`tennas, which are located on Ascension, Diego Garcia,
`and Kwajalein Islands. These antennas uplink satellite
`control signals and the contents of the navigation mes-
`sage.
`As shown in Fig. 8, the navigation message is bro-
`ken into 1500-bit frames, which in turn consist of five
`300-bit subframes. Each subframe is composed of ten
`30-bit words where each word has 6 parity bits for error
`detection.
`
`Each subframe begins with a telemetry (TLM)
`word, which contains a synchronization pattern and in-
`
`dicates the status of the uploading process. The second
`word of every subframe is a handover word (HOW),
`which helps the receiver synchronize to the long P code
`after it has synchronized to the short C/A code. These
`two words are generated on the individual spacecraft.
`However, the data carried in the body of the subframes
`is generated by the control segment and uploaded to the
`satellites.
`Subframe 1 carries coefficients for a model of the
`
`satellite clock, and coefficients for an ionospheric delay
`model. The clock model allows the GPS receivers to
`correct for the difference between the individual satel-
`
`lite‘s clock and GPS system time. The model is custom-
`ized to the characteristics of the cesium and rubidium
`
`clock, which the satellites carry. In addition, it includes
`terms to correct for clock drift due to general and special
`relativity. This relativistic drift is due to the high veloc-
`ity of the satellites relative to the users and to the dif-
`ference in gravitational potential.
`The ionospheric model allows a single—frequency
`receiver to estimate the portion of the satellite signal’s
`
`’l‘en, 30 bit words forming a six second subframe
`subframe ————:——%|
`Number
`The five subframes form a 30 second frame with 1500 hits total.
`1
`Block 1 - Clock Correction
`
`Block 2 - Ephemeris
`
`Block 3 - Ephemeris (Cont.)
`
`Block 4 - Message
`
`Block 5 - Almanac (25 frames are required for the complete almanac)
`
`Fig. 8. Summary of the format of the GPS navigation message.
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`travel time which is due to ionospheric refraction. The
`efficacy of this correction is described in Section 5.
`Subframes 2 and 3 contain parameters which de-
`scribe the satellite orbit (ephemeris) and the age of the
`orbital parameters. Keplerian parameters are used to de-
`scribe the orbit because they have a clear physical inter-
`pretation and their accuracy decays slowly and smoothly
`with time. However, they must be transformed to pro-
`vide the location of the satel1ite‘s antenna phase center
`
`()_{g = (xg, yg, zg)) in the earth-centered earth-fixed ref-
`erence frame shown in Fig. 9. In fact, GPS uses the
`WGS-84 ellipsoid for position calculations.
`The body of subframe 4 provides for the transmis-
`sion of 23 eight-bit ASCII characters. These were in-
`cluded to convey alphanumeric information to users of
`GPS.
`Subframe 5 carries an almanac filled with data on
`all the satellites in the constellation. This data include
`
`4. CODE AND CARRIER ACQUISITION AND
`TRACKING
`
`GPS receivers make the following measurements:
`
`0 Code phase, which measures the satellite pseu-
`dorange.
`° Carrier frequency or Doppler shift, which mea-
`sures the time rate of change of the pseudorange.
`0 Change in carrier phase, which measures the
`change in pseudorange (or delta-pseudorange).
`This last measurement maintains phase coher-
`ence and as such should not be confused with the
`
`Doppler measurements.
`
`This section will briefly discuss signal acquisition, and
`then introduce some structures for tracking the L, and
`L2 signals.
`
`ephemeris parameters, clock corrections, satellite health,
`and identification for all the satellites in the constella-
`
`4. 1. Signal Acquisition
`
`tion. The ephemeris and clock data contained in this al-
`manac are less precise than the ephemeris and clock data
`in subframes I through 3. They are provided to aid the
`receivers acquisition of satellite signals and are not ac-
`curate enough for position fixing.
`
`During signal acquisition, the receiver must search
`a time uncertainty corresponding to the 1023 C/A code
`chips, and a frequency uncertainty of up to 15000 Hz.
`The frequency uncertainty is mostly due to the Doppler
`shift of the satellites. The maximum Doppler uncer-
`
` Pseudorange
`
`PR” = |Xu_g|+bu—Bg
`
`= Ix" —xg| +bu -Bg
`
`Fig. 9. Earth-centered earth-fixed (ECEF) coordinate system used by GPS.
`
`PETITIONERS 1007-0010
`
`

`
`The Global Positioning System
`
`93
`
`tainty occurs for a user at the North or South Pole, where
`one satellite can have a radial velocity (11,) of 780 m/s
`and another visible satellite can have a radial velocity
`of -780 m/s. This corresponds to a maximum differ-
`ential Doppler shift off,, = v,fL,/c = i4000 Hz, which
`accounts for the majority of the frequency uncertainty.
`An individual time cell in this time—frequency un-
`certainty region has a width of 1 C/A code chip or 1 as
`and each frequency cell has a width equal
`to the IF
`bandwidth of the receiver, which is typically 1 kHz.
`Consequently, about 10,000 cells must be searched.
`Nonetheless, GPS signal-to-noise ratios are such that this
`search can be executed reliably in about 90 s.
`After the first signal is acquired, further signals can
`be acquired in much less time, because the data in the
`almanac (subframe 4 of the navigation message) can be
`used to reduce the area of the time—frequency uncer-
`tainty. Furthermore, the P code can be acquired rapidly
`after acquisition of the C/A code, because of the hand-
`over word contained in every subframe of the navigation
`message.
`
`4.2. C/A Code and Carrier Tracking
`
`After acquisition, GPS receivers use a delay lock
`loop (DLL) to track the phase of the C/A code from
`each satellite, and such a loop is shown in Fig. 10. As
`shown, the DLL correlates the received signal with a
`slightly early replica of the signal and a slightly late rep-
`lica of the signal. These two correlations are noisy sam-
`ples of the correlation function depicted in Fig. 7. When
`locked to the received signal, the early correlator sam-
`ples the peak of the correlation function on the leading
`edge, and the late correlator samples the falling edge of
`the peak. A null-serving servo slews the two samples in
`time until they straddle the peak of the function. If ad-
`ditive white Gaussian noise (AWGN) is present and the
`precorrelation bandwidth is infinite, then the variance of
`the delay estimate is given by [32]
`
`2
`
`BN(7d Tc)
`C/N0
`
`2
`
`SCAU) = @X(t_T)ej(2"(fLl+fD)t+9)
`
` e—j(2n (f+io> t + 6)
`
`Fig. 10. Coherent delay lock loop (DLL) typically used by GPS receivers to track the CIA or P code.
`
`PETITIONERS 1007-0011
`
`

`
`94
`
`Enge
`
`where -r,, is the correlator spacing shown in Fig. 10, and
`Tc is the code chip width in seconds. Additionally, BN
`is the noise bandwidth of the closed loop.
`As shown, decreasing the correlator spacing (-rd)
`decreases the error variance. If the precorrelation’ band-
`width is approximately equal to 1/ TC, then decreasing
`the 1,, results in very limited improvements, because the
`shape of the autocorrelation function has been smoothed
`by the precorrelation filter. However,
`the C/A code
`bandwidth is a small portion of the overall GPS band-
`width and decreasing the correlator spacing to 7,, z
`0.1T, is an effective strategy. As described later, receiv-
`ers with narrow correlator spacing also enjoy superior
`performance in multipath environments. Accordingly,
`such receivers are currently being investigated for high-
`performance applications [20].
`A noncoherent correlator can track code phase
`without an estimate of the carrier phase. It can be im-
`plemented by taking the magnitude of the outputs from
`the early and late correlators shown in Fig. 10.
`In
`AWGN, the error variance for such a noncoherent DLL
`is given by [32]
`
`O’
`
`g z BN(TdTc) [1 +
`
`C/No
`
`’
`
`1
`
`(1 — -r,,/T,)C/No
`
`]S2
`
`where the term in brackets is the “squaring loss" due
`to the nonlinear operation. As shown, the squaring loss
`depends strongly on B,, which is the bandwidth of the
`processing which precedes the nonlinearity. For C/A
`code tracking, this bandwidth is usually around 50 Hz,
`and so the squaring loss is small. Such a noncoherent
`correlator may be used during signal acquisition before
`the carrier loop is locked.
`Simultaneously,
`the receiver tracks the carrier
`phase and frequency. When the code is aligned or nearly
`aligned, the phase lock loop in Fig. 10 receives an error
`signal which is proportional to exp j(21r( fD — fD)t + 0
`— 3). As described in [28], the variance of the resulting
`phase estimate is approximately given by BN/(C/N0)
`radz.
`'
`
`4.3. P Code and Codeless Tracking
`
`If the P code is being transmitted, then the receiver
`can use the structure shown in Fig. 10 to track the P
`coded signals. As mentioned earlier, such tracking will
`enjoy greater resistance to interference and multipath.
`Moreover, P code observations on L, and L2 can be used
`to estimate the ionospheric delay quite accurately, and
`the carrier—phase difference can be used to help resolve
`the integer ambiguity for ranging on the carrier phase.
`
`However, as mentioned earlier, the P code can be
`switched to the Y code at any time. For this reason,
`many “codeless" receivers attempt to extract the ben-
`efits of dual-frequency tracking without assuming
`knowledge of the wideband code. For example, squar-
`ing loops can be used to estimate the L2 carrier phase.
`These loops simply square the incoming signal to re-
`move the modulation introduced by the unknown code
`and data.
`
`These carrier loops suffer from a squaring loss akin
`to the one described above for the noncoherent DLL.
`
`However, the bandwidth of the filter which precedes the
`squaring operation is set by the P code bandwidth and
`so the loss is much greater. At GPS signal—to—noise ra-
`tios and with B, = 20 X 106, this squaring loss can
`easily be 30 dB.
`Nonetheless, some survey receivers do success-
`fully use squaring loops. After all, the squaring loss is
`mitigated by the increased slope of the error function in
`the carrier—phase loop. It can be further mitigated by
`“rate—aiding” the IQ loop with information from the L,
`channel, which allows the loop bandwidth to be very
`narrow. In addition, these squaring receivers use the dif-
`ference in the Doppler shifts to separate the signals from
`the different satellites [1]. The Doppler shifts are occa-
`sionally equal and so short outages do result.
`An innovative variation on the squaring receiver is
`shown in Fig. 11, where the Y—coded signal on L,
`is
`cross-correlated with the Y-coded signal on L2. (For
`simplicity, Fig. 11 ignores Doppler shift.) As shown,
`the L, signal is subjected to a delay which is adjusted
`by the L3 loop to track the dynamics of the ionosphere.
`The delayed signal
`is used to generate the “early,"
`“late,” and “prompt” signals required for the L2 code
`tracking loop. In addition, the “prompt" signal is mixed
`with the incoming L2 signal to form the error signal for
`the L2 carrier loop.
`This cross—correlating receiver enjoys a number of
`advantages relative to the squaring loop. First,
`the
`Y—coded signal on L, is 5 dB stronger than the Y—coded
`signal on L2. Additionally, the L, noise is uncorrelated
`with the L2 noise, and so the squaring loss is reduced
`by 3 dB. The cross—correlating receiver also provides an
`estimate of the Y code phase, which the squaring re-
`ceiver does not. Further,
`it uses the cross-correlation
`
`properties of the codes to separate the different signals
`and does not rely on the differences in the Doppler shifts.
`Finally,
`the cross—correlating receiver provides a car-
`rier—phase estimate with full-wavelength ambiguities
`rather
`than half—wavelength ambiguities. This
`final
`property is helpful
`in canier—phase DGPS receivers
`
`PETITIONERS 1007-0012
`
`

`
`The Global Positioning System
`
`95
`
`CA code loop
`and
`
`carrier loop
`
`Code Loop
`Filler
`
`'2
`—TL2)9J( If”
`
`t+3 )
`“
`
`Fig. 11. Delay lock loop (DLL) for tracking the Y-coded signal on L2. This structure uses the Y-coded signal from Ll as a reference
`signal.
`
`where the integer wavelength ambiguity must be re-
`solved.
`
`Most recently, two more innovative receivers have
`been described in the patent literature [17, 22]. Both
`make use of the fact that the Y co