In-flight performance analysisof the CHAMP BlackJackGPS ReceiverOliver Montenbruck Æ Remco Kroes

Abstract JPL’s BlackJack receiver currentlyrepresents the most widely used geodetic grade GPSreceiver for space applications. Using data from theCHAMP science mission, the in-flight performanceof the BlackJack receiver has been assessed and theimpact of various software updates performedduring the 2.5 years since launch is described. Keyaspects of the study comprise the channel allocation,anomalous data points, and the noise level of thecode and carrier data. In addition, it has beendemonstrated that the code measurements collectedonboard the CHAMP satellite are notably affected bymultipath errors in the aft-looking hemisphere,which can be attributed to cross-talk between theoccultation antenna string and the primary preciseorbit determination antenna. For carrier smoothed10 s normal points, the code noise itself variesbetween a minimum of 5 cm at high elevations and0.5 m (C/A) to 1.0 m (P1, P2) at 10� elevation.Carrier-phase data exhibit representative errors of0.2 to 2.5 mm. The results of the CHAMP GPS dataanalysis contribute to a better understanding andpossible improvement of the BlackJack receiver andsupport the design of optimal data editing andweighting strategies in precise orbit determinationapplications.

Keywords CHAMP Æ BlackJack Æ Multipath ÆReceiver noise

Introduction

OverviewThis paper contains a thorough discussion and the re-sults of an in-flight performance analysis of the CHAMPBlackJack GPS receiver. The analysis has been carried outin order to obtain a better understanding of the GPSdata, and its quality, produced by JPL’s BlackJack GPSreceiver. Furthermore, the results can be used to developbetter data editing and processing strategies as well ascontribute to a better fulfillment of the CHAMP missionobjectives. An introduction to both CHAMP and theBlackJack GPS receiver is given in the subsequent part ofthis section.The performance analysis mainly focuses on thechannel allocation process and its impact on the overalldata quality, several receiver specific data errors andanomalies, the multipath problem of the BlackJackreceiver and the measurement noise on both the codeand carrier observations. Several new methods havebeen devised in order to perform the different parts ofthe analysis mentioned. Where appropriate, thesemethods are discussed in the text. The final sectionof this publication contains the summary andconclusions.

The CHAMP missionThe Challenging Minisatellite Payload (CHAMP) is aGerman small satellite mission for geoscientific andatmospheric research and applications (Reigber et al.1996). Primary mission objectives comprise the accuratedetermination of the Earth’s gravity field, the estimation ofthe magnetic field including its spatial and temporalvariations, as well as the collection of refraction data formodeling the physical properties of the troposphere andionosphere. To achieve these science goals, the satellite isequipped with a number of highly accurate instruments,such as the STAR accelerometer (ONERA, France), theBlackJack GPS receiver (JPL, USA), a laser retroreflector, aFluxgate magnetometer, an Overhauser magnetometer, anautonomous star sensor and a digital ion driftmeter(AFRL, USA). CHAMP was launched on 15 July 2000 intoan almost circular, near-polar, low-earth orbit, where it isexpected to provide science data for a design lifetime of5 years. For a more detailed description of the CHAMPmission and its scientific goals the reader is referred toReigber et al. (1996) and CHAMP (2001).

Received: 23 February 2003 / Revised: 31 March 2003Accepted: 3 April 2003Published online: 20 June 2003ª Springer-Verlag 2003

O. Montenbruck (&)German Space Operations Center,Deutsches Zentrum fur Luft- und Raumfahrt,82230 Weßling, GermanyE-mail: oliver.montenbruck@dlr.deTel.: +49-8153-281195Fax: +49-8153-281450

R. KroesDelft Institute for Earth Oriented Space Research (DEOS),Kluyverweg 1, 2926 HS Delft, The Netherlands

74 GPS Solutions (2003) 7:74–86 DOI 10.1007/s10291-003-0055-5

Original article

The BlackJack GPS receiverThe BlackJack, or TRSR-2 (TurboRogue Space Receiver 2)GPS receiver, was developed by NASA’s Jet PropulsionLaboratory (JPL), and is a follow-up of the TurboRoguereceiver (Thomas 1995) flown earlier on missions likeMicroLab-1 (GPS/MET), Oerstedt, and SunSat. In contrastto the TurboRogue receiver, which was originally built as aground-based geodetic-grade GPS receiver, the BlackJackhas been specifically designed for orbital applications. Itsupports a total of four antenna inputs, which can beindividually assigned to any of the 48 tracking channelsusing a matrix switch following the amplification anddigital down-conversion of the radio-frequency (r/f) sig-nals (NASA 2001; Meehan 1997). The individual channelscan be allocated in sets of three to track C/A, P1 and P2

code for up to 16 GPS satellites, with a typical limit of tensatellites employed on CHAMP. During Anti-Spoofing apatented, codeless tracking technique is used to estimateP-code from the encrypted Y-code (Meehan et al. 2000).Following power-up, the receiver performs a cold startsearch and achieves three-dimensional navigation withintypically less than 15 min. Using C/A-code measurementsonly, the receiver position is obtained with a representa-tive accuracy of 10–15 m in the absence of SelectiveAvailability. In addition, the velocity of the host satellite isobtained from carrier-phase based range-rate measure-ments. The clock error of the receiver, obtained as part ofthe navigation solution, is used to steer the voltage con-trolled oscillator in such a way as to align the receiver timeto GPS time within a tolerance margin of less than 1 ls(300 m in distance). Aside from the main tracking mode,the receiver can operate in occultation mode to collectmeasurements at a 50 Hz sampling rate when GPS satel-lites set and in altimetry mode to collect ground reflectedGPS signals via a nadir-looking antenna.The BlackJack receiver has a weight of 3.2 kg and a 15 Wpower consumption. While most of the electronic com-ponents are commercial-grade CMOS circuits, it has beendemonstrated by total dose radiation tests that the avail-able shielding is adequate to ensure reliable operationsunder space conditions (Meehan 1997). The receiversoftware is written as a modular, multi-threaded C++application and is stored in flash memory. Software up-dates or patches can be uploaded to the spacecraft in smallsegments without requiring a full replacement. The avail-able spare processor capacity can be used to implementadditional non-GPS related functions as used, e.g., for star-camera processing and K-band ranging inside the GRACEreceiver. Following its initial flight qualification on theShuttle Topography mission (SIRC/X-SAR) (Bertiger et al.2000), the TSRS-2 receiver is currently operational on theSAC-C (Meehan 1997), CHAMP, Jason-1 (Haines et al.2002) and GRACE (Bertiger et al. 2002) satellite missionsas well as the recently launched ICESat (Schutz 1998) andthe Australian FedSat satellite.

CHAMP GPS antenna systemFor the CHAMP mission, the receiver employs a total offour different antennas. A zenith-mounted patch antennaequipped with a choke ring and a typical cone angle of 80�

serves as prime antenna for precise orbit determination(POD). A backup POD antenna and a helix antenna foroccultation measurements are mounted on the rear side,which exhibits a 20� nadir tilt. Finally, a nadir-viewinghelix antenna with left-hand circular polarization for GPSaltimetry (using reflected GPS signals from the sea surface)is mounted on the bottom side of CHAMP. All fourantennas are passive and are operated in combination withsignal amplifiers inside the BlackJack receiver. While thePOD antennas are commercial-grade L1/L2 patch antennas(Sensor Systems S67-1575-14) (Sensor Systems 2002), theoccultation and altimetry antennas have been designedand manufactured by JPL.The exact location of each antenna in the spacecraft ref-erence frame can be found in Table 1 (see Luhr et al.2001). The spacecraft reference frame originates in thecenter of mass and is aligned with the main body axes ofCHAMP, which normally coincide with the orbital frame.The positive z-axis is nadir pointing (bottom), the positivex-axis points in along track direction (towards boom) andthe positive y-axis (towards right) is aligned with thenegative orbital angular momentum vectors thus com-pleting a right-handed system.

Performance analysis

For the remainder of this paper, CHAMP GPS data col-lected by the POD antenna are used to assess the in-flightperformance of the BlackJack receiver. The study extendsan early flight data evaluation given in (Kuang et al. 2001)and complements laboratory based tests of the BlackJackreceiver described in (Williams et al. 2002). Key issuescomprise the channel allocation, outliers and data anom-alies, as well as measurement noise and multipath effectsthat affect the distribution and quality of the obtained GPSdata. Our analysis of the BlackJack receiver does not focuson a particular time period, because one of its goals is tostudy the improvement of the receiver and data qualityover time. Over the 2.5 years that the receiver has beenoperational on CHAMP, several software updates weremade to overcome receiver shortcomings and anomalies.Most of these updates reflect clearly in the data obtainedfrom the receiver.GPS observations from the primary POD antenna em-ployed in this study have been obtained from the CHAMPInformation System and Data Center (ISDC) (CHAMP

GPS Solutions (2003) 7:74–86 75

Table 1Location of the different GPS antennas on CHAMP (Luhr et al. 2001).All values are given in the spacecraft reference system and correspondto an adopted center of the antenna. The offsets of the phase centershave to be determined

Antenna x (mm) y (mm) z (mm)

Main POD )1488.0 0.0 )392.8Reserve POD )1738.9 0.0 )260.6Occultation helix )1643.1 0.0 )64.6Altimetry helix +857.0 241.0 233.0

Original article

2001), which provides data starting as of May 2001. Theseare supplemented by the public data set for day 220/2000(CHAMP 2000) to illustrate the behavior of the earliestBlackJack receiver software. For part of the analysis, IGSprecise (final) orbits in SP3 format supplemented by 5-minute clock data have been used to model the observedpseudoranges. Precise CHAMP reference orbit were pro-vided by DEOS (see Van den IJssel et al. 2003).A total of nine data types are recorded in the RINEXobservations files: the C/A-code (C1) and both P-codemeasurements (P1 and P2) as well as the carrier-phasemeasurements (LA, L1 and L2) and signal-to-noise ratio(SNR) for each of the associated tracking channels (SA,S1 and S2). Here, the designations in brackets have beenchosen in accord with the RINEX 2.20 standard (Gurtnerand Estey 2001) but differ slightly from the notationemployed in the ISCD data files (L1/LP1 versus LA/L1; cf.Kohler 2001). The observations are provided at a stan-dard data interval of 10 s and represent normal pointscreated inside the receiver from 1 Hz samples. In theearly BlackJack receiver versions, the 1 Hz pseudorangedata were fit with a 10 s quadratic polynomial in order toderive the 10 s data points. This has, later on, been re-placed by carrier-phase smoothing of the pseudorangedata and results in a noise of the 10 s normal points thatis a factor of

ffiffiffiffiffi

10p

� 3 smaller than that of the 1 s rawpseudorange data.Throughout this paper, the code and carrier-phaseobservations are described by the relations:

qCA ¼ qþ cDdt þ bCA þ I þMCA þ eCA

qP1 ¼ qþ cDdt þ bP1 þ I þMP1 þ eP1

qP2 ¼ qþ cDdt þ bP2 þ If 21

f 22þMP2 þ eP2

qLA ¼ qþ cDdt � k1NLA þ bLA � I þMLA þ eLA

qL1 ¼ qþ cDdt � k1NL1 þ bL1 � I þML1 þ eL1

qL2 ¼ qþ cDdt � k2NL2 þ bL2 � If 21

f 22þML2 þ eL2

ð1Þ

in which q is the true geometric distance between the phasecenters of the transmitting and receiving GPS antennas.The clock error difference of the GPS satellite and theBlackJack receiver is denoted by cDdt and I denotes theionospheric path delay for the L1 frequency (f1). The car-rier-phase ambiguities are represented by integer multiples(i.e., kN) of the respective wavelengths and b denotesadditional inter-channel differences and line biases presentin the receiver. Finally, the multipath and random noise aredescribed by the M and � terms, respectively.Out of the elementary data types the common linearcombinations:

qP12 ¼ f 21

f 21 �f 2

2qP1 �

f 22

f 21 �f 2

2qP2 � 2:546qP1 � 1:546qP2

qL12 ¼ f 21

f 21 �f 2

2qL1 �

f 22

f 21 �f 2

2qL2 � 2:546qL1 � 1:546qL2

ð2Þ

(Hofmann-Wellenhof et al. 1997) are formed to obtainionosphere-free range measurements (with a roughly 3times larger noise level than the respective single-fre-quency measurements) for point positioning and orbit

determination. Furthermore, the Melbourne-Wubbenacombination:

qMW ¼1

f1 � f2f1qL1 � f2qL2ð Þ � 1

f1 þ f2f1qP1 þ f2qP2ð Þ

ð3Þ

(Melbourne 1985; Wubbena 1985) is used for datascreening and editing. This linear combination of narrow-lane P-code pseudoranges and wide-lane carrier-phasemeasurements results in a geometry-, ionosphere- andtroposphere-free observable. It is less sensitive to codenoise than a simple difference of ionosphere-free pseud-orange and carrier measurements (cf. Eq. 2) and wellsuited for cycle slip and outlier detection.

Channel allocationThe number of available channels for tracking satellites andthe strategy used for channel allocation have a notableinfluence on the quality and usefulness of the data pro-duced by a GPS receiver. To ensure a maximum number ofgood quality observations with a good geometric distri-bution, which is relevant for both the on-board and post-processed navigation solution, the channel allocationalgorithm has to select satellites based on criteria as theelevation angle and the PDOP (Position Dilution Of Pre-cision) value. The exact channel allocation strategy used bythe receiver cannot be determined from the data producedby it. However, it is possible to say something about itseffectiveness, the way improvements were made to it andthe resulting data quality. In order to achieve this for theBlackJack GPS receiver on CHAMP, data from multipletime periods have been used to incorporate the differentsoftware updates relevant for channel allocation issues.Two software updates made so far were identified to berelevant for the receiver channel allocation process. Thefirst update, completed on 26 July 2001 (Meehan 2001),incorporated a change in the cut-off elevation angle of thereceiver. The second update, made on 5 March 2002(Grunwaldt, personal communication), enlarged thenumber of channels used for tracking. The impact of thesetwo software updates on the receiver tracking performanceand data quality is discussed with the aid of Fig. 1. Itshows sky-plots and histograms for selected days before,between and after both software updates.The sky-plots represent the direction of the line-of-sightvector from the receiver to the GPS satellite with respect tothe local orbital frame that is nominally aligned with themain body axes. Its azimuth (A) is measured from the+x-axis (forward, A=0�) to the +y-axis (right, A=+90�) andthe elevation angle E is measured positive towards the zenith(-z-direction). The histograms provide the distribution ofthe number of tracked and useful GPS satellites per epochtogether with the total number of epochs for the given days.The number of useful satellites per epoch is derived fromediting based on the elevation angle (affecting data noiseand multipath), the SNR values (affecting data noise), thePDOP value (affecting single-point positioning accuracies)and the Melbourne-Wubbena combination (indicatingoutliers and cycle slips).

76 GPS Solutions (2003) 7:74–86

Original article

The different histograms immediately show that there areonly eight channels active until the second software update(Fig. 1, top and center); this is then changed to ten (Fig. 1,bottom). The increase in the total number of availableepochs (8,457 on day 143/2001, 8,567 on day 245/2001,8,640 on day 244/2002) over the different time periodsshows that the number of data gaps is decreasing overtime. This is also visible in the different sky-plots wherethe data density increases per time period. The sky plotsalso show that the BlackJack applies an elevation thresholdof approximately 10� for satellite acquisition. This featurehas remained constant over time. Before the first softwareupdate, the receiver tracked satellites far below 0�

elevation, at the cost of higher elevation satellites alsovisible at the same time. The strategy here was clearly tomaintain track of a satellite as long as possible.However, the low elevation satellites deliver observationsof a poorer quality (due to the decreased antenna gain andsignal-to-noise ratio) resulting in less useful data fornavigation for this time period. The first software updatefixes this problem. The receiver now only tracks negativeelevation satellites, sporadically, and acquires new satel-lites at a much earlier stage. As a result, a significantimprovement of the overall amount of good quality data isobtained. This is supported by the change in distributionof the number of useful observations per epoch, which

GPS Solutions (2003) 7:74–86 77

Fig. 1Sky plots illustrating changes inthe channel allocation for days143/2001 (top pronounced for-ward/backwards asymmetry andlarge number of negative eleva-tion observations), 245/2001(center symmetric distribution oftracked satellites), and 244/2002(bottom maximum number oftracked satellites increased fromeight to ten). The associatedhistograms show the statisticaldistribution of the number oftracked satellites per epoch(shaded) and the distribution ofthe number of good observationsper epoch (black). See text forfurther explanation

Original article

changes from an average of six to an average of seven. Thesecond update does not change this average value, butenables up to ten useful observations per epoch.

Outliers and anomaliesThis section provides a discussion of outliers and anomaliesencountered in the CHAMP GPS flight data. It complementsand extends a previous report of BlackJack specific dataanomalies encountered during signal simulators testing ofthe ICEsat spare receiver (Williams et al. 2002).

General outliersAt the 10 s sampling rate, the CHAMP BlackJack receiverprovides a representative number of 60,000 (eight chan-nels active) to 75,000 (ten channels active) pseudorangemeasurements per day. Out of these data, a small fractionexhibits errors far above the 3 r measurement noise. Toidentify such outliers, we employed a kinematic pointpositioning method involving an iterative post-fit residualscheck and data rejection. In total, about 4% outliers witherrors between 10 and 100 m (in P12) and 0.2% outlierswith errors of 100 m and up were encountered in early2001. Following a revision of the channel allocation, thesenumbers later dropped to 1 and 0.1%, respectively. Thisimprovement can mainly be attributed to a decreasedfraction of low elevation observations (E<0–10�; cf. Fig. 1)with unfavorable signal-to-noise ratios (S1, S2<15–25�). Invarious cases (few measurements per day), we observederratic pseudoranges with residuals of tens to hundreds ofkilometers even at high elevations. These may generally beidentified and rejected based on simple integrity checks(e.g., variation of Melbourne-Wubbena combination be-tween epochs).Along with the analysis of code observations in the kine-matic point positioning, we identified carrier-phase out-liers from the post-fit residuals of differential single pointsolutions. Carrier-phase outliers were found to affectroughly 1% of the total number of observations from mid2001 onwards. They are typically confined to errors of lessthan 1 m and can be attributed to integer cycle slips in theL1 and L2 measurements. Again, the erroneous observa-tions are mostly confined to low elevations or SNR valuesand the fraction of affected measurements amounts to lessthan 0.1% when excluding elevations below 10�. Followingthe March 2002 software update, an increased amount ofcarrier-phase outliers (3% total, 0.5% above 10�) may beobserved, which correlates with the increased carrier noiselevel. Among the coarse outliers, both erratic points andsystematic outliers associated with erroneous locks may beobserved. Aside from SNR and elevation-based edit crite-ria, a large fraction of the anomalous carrier measure-ments can well be recognized from discontinuities in theMelbourne-Wubbena linear combination.

Code biasesThe BlackJack GPS receiver occasionally suffers from 15 mcode biases for all or most of a pass (i.e., start of track toend of track). When occurring, all three code observations(i.e., C/A, P1, and P2) as well as the ionosphere-free P12

linear combination experience a common offset of about

15 m (Fig. 2). Based on its magnitude, this bias has pre-viously been interpreted as half a P-code chip in (Williamset al. 2002). On average, two out of roughly 400 dailypasses are affected by a 15 m bias. While the erroneousdata may readily be recognized and rejected in a ground-based processing, they are difficult to discern fromephemeris and ionospheric errors inside the receiver andtherefore affect the built-in C/A-code based navigationsolution.To determine the exact size of the code offset and toenable a possible correction for it, the residuals of theionosphere-free code observations have been obtainedand averaged over a single pass. The analysis has beenconducted for days 140–150/2001 (i.e., the data employedin the IGS low Earth orbit campaign) and days 240–250of 2001. Here, the anomaly occurred for a maximum ofthree passes per day, but some days remained unaf-fected. Results for a representative selection of passescan be found in Table 2. On average, the code biasamounts to 15.5±0.2 m, which is barely consistent with ahalf a P-code chip length and suggests an alternativeinterpretation. In fact, the pseudorange offsets can bestbe attributed to a receiver internal sampling erroryielding a bias of cÆs=15.511 m at the effective samplingrate of 1/s=19.328Æ106 Hz employed in the CHAMPBlackJack receiver (Young, personal communication).Since the sampling error yields a constant offset butdoes not affect the measurement noise and

78 GPS Solutions (2003) 7:74–86

Fig. 2Pseudorange errors (ionosphere-free P12 combination) for selecteddata arcs on day 245/2001 (top) and 142/2001 (bottom). Aside fromscattered outliers, the occurrence of systematic 15 and 75 m codeoffsets may be recognized

Original article

signal-to-noise ratio, its predicted value of 15.511 m canbe used to correct affected measurements if desired.For completeness, we note that a sampling rate of1/s=20.456 MHz is employed in some previous models ofthe BlackJack receiver. Here, the size of one sample cor-responds to a pseudorange error 14.65 m, which perfectlymatches the value of 14.7±0.3 m (Williams, personalcommunication) obtained in the analysis of the ICEsatflight spare (cf. Williams et al. 2002).Table 2 also illustrates the occasional occurrence ofpasses with an approximate bias of 75 m in the iono-sphere-free P12 pseudorange combination (Fig. 2). Inboth of the two cases encountered during days 140–150/2001 the bias coincides with very low SNR values on theL2 frequency, which suggests a different cause than thesampling error described above. Inspection of the indi-vidual code measurements indicates that the P2 mea-surement exhibits a systematic error of about 48 m at theaffected epochs, while the C/A and P1 pseudoranges ap-pear to be error free. Other than the sampling errordiscussed above, the 48 m biases in the P2 pseudorangescannot adequately be corrected in a post-processing dueto a high noise level and the lack of a model explainingthe nature and exact size of this bias.

L2 rampsThe term ‘L2 ramp’ introduced in Williams et al. (2002)denotes a data anomaly during which the L2 carrier-phaseobservation exhibits a rate error of mostly ±6 m/s. L2ramps usually start at the beginning of a satellite passwhen the received signals are still weak and exhibit S2signal-to-noise ratios that are significantly lower than thecorresponding S1 value. The anomaly can easily be visu-alized by forming the time derivative d(qL2)qL1)/dt of theL2–L1 phase difference, which is nominally zero except fora small variation of the ionospheric phase advance. Forautomated data editing, the anomalous data can safely beidentified based on the rate of change of the Melbourne-Wubbena combination.The occurrence of L2 ramps can be attributed (Young,personal communication) to a false L2 carrier lock with afrequency offset of 25 Hz, i.e., one-half of the navigationbit rate. At the L2 wavelength of k=24.4 cm, this yieldsan expected range rate offset of 6.1 m/s in good accord

with the observations. However, due to the irregularnature of the L2 ramps, it is not feasible to correct theresulting error of the L2 observable.In an analysis of selected data arcs collected in 2001 andearly 2002 the L2 ramp anomaly was encountered multipletimes per day on an almost daily basis. Other than de-scribed in (Williams et al. 2002), the P2 code measure-ments were generally found to be valid during the L2ramps. After the software update of 5 March 2002, the L2ramps completely disappear as the result of a new con-sistency check between pseudorange and carrier-phasemeasurements that was added to the receiver software(Young, personal communication).

Sudden SNR drops and low SNR curvesDuring signal simulator testing of the BlackJack sparereceiver for the ICEsat mission (see Williams et al. 2002)numerous outages were encountered near the center of atracking pass, when the elevation and line-of-sightacceleration attained peak values. This anomaly ischaracterized by sudden SNR drops and invalid ormissing pseudorange measurements from the C/A, P1

and P2 tracking channels. In the CHAMP BlackJack flightdata, a similar problem shows up in the data set for day220/2000, but no further indications were found in anyof the examined data sets since the start of the CHAMPISDC in May 2001. Other occurrences of anomalous SNRvalues may still be noted, however, during which eitherS1 or S2 stays low for an entire pass or a large partthereof. As noted above, the occurrence of 48 m P2 codeoffsets appears to coincide with low S2 signal-to-noiseratios but no such correlation could be established forlow S1 values.

Multipath errorsMultipath errors in a GPS receiver are caused by thesuperposition of the direct signal with interfering signalstaking a different signal path. They are typically associatedwith signal reflections in the vicinity of the receiving an-tenna, in which case the resulting errors depend on thepath difference, the strength and polarization of the re-flected radiation as well as receiver internal properties.While carrier-phase multipath is confined to a quarterwavelength, code multipath may be as large as 0.5 codechips for distant reflectors (Leva et al. 1996; Braasch 1995).In case of a spaceborne GPS receiver, multipath reflectionsare exclusively caused by the satellite’s surfaces (if weexclude rendezvous and docking type of applications) andthe maximum path delay is thus of the order of the linearspacecraft dimension.Evidence for code multipath errors is already containedin early analyses (Kuang 2001) of the CHAMP GPS dataquality but has been widely ignored so far. It shows upin a worse-than-expected scatter of geometry- and ion-osphere-free linear combinations as well as pseudorangeresiduals that are inconsistent with the receiver perfor-mance in a lab environment. In the context of thepresent work, multipath errors were first noted from asystematic bias of single point positioning results using

GPS Solutions (2003) 7:74–86 79

Table 2Selected passes with systematic biases in ionosphere-free pseudo-ranges encountered during days 140–150/2001

Day Pass (UTC) PRN Bias (m)

140 20:49 7 )15.56140 16:52 24 )15.42146 08:42 1 )15.33146 06:34 5 +15.56147 12:03 27 )15.62148 20:59 28 +15.23149 21:31 14 )15.18149 00:05 31 +15.52150 15:01 20 +15.73142 00:48 10 )75.30147 02:33 2 )74.91

Original article

dual frequency P-code measurements as compared tocarrier based or dynamically constrained orbit determi-nation solutions. This bias affects the radial positioncomponent by roughly )0.4 m (when consideringobservations down to the 0� elevation) while the along-track and cross-track position are essentially unaffected.

For further analysis of code multipath effects on CHAMP,the respective errors were isolated by forming the linearcombinations:

qCA � 2f 21 �f 2

2f 21 qL2 � f 2

2 qL1

� �

� qL1 � BCA � MCA þ eCA

qP1 � 2f 21 �f 2

2f 21 qL2 � f 2

2 qL1

� �

� qL1 � BP1 � MP1 þ eP1

qP2 � 2f 21 �f 2

2f 21 qL2 � f 2

2 qL1

� �

� qL2 � BP2 � MP2 þ eP2

ð4Þ

in which the receiver-to-satellite geometry and the iono-spheric errors have both been eliminated. Carrier ambi-guities and differential code biases are combined in float

80 GPS Solutions (2003) 7:74–86

Fig. 3a Sky plots of CHAMP multipath errors on C/A-code for days 140–141/2001. b Sky plots of CHAMP multipath errors on P1-code for days140–141/2001. c Sky plots of CHAMP multipath errors on P2-code fordays 140–141/2001. d Sky plots of CHAMP multipath errors on P2-code during deactivation of the occultation antenna string on day 310/2002

Original article

bias parameters BC/A, BP1 and BP2 which are constantsthroughout each pass of uninterrupted carrier-phasetracking. Assuming that carrier-phase multipath and noiseare much smaller than the respective code errors, theabove linear combinations thus provide a direct mea-surement of the C/A and P1/P2 code multipath errors andnoise.Since the bias parameters Bi are not known a priori, theyhave to be adjusted on a per-pass basis to achieve a zero-mean right-hand side of (Eq. 4) using observations thatmay be considered to be free of systematic errors. In caseof measurements collected with the CHAMP Precise OrbitDetermination (POD) antenna one may observe that theionosphere-free code and carrier combinations exhibit anessentially constant offset during the ascent of a GPS sa-tellite but start to be inconsistent prior to its setting. Wehave therefore chosen to adjust the biases using anyobservations with adequate signal-to-noise ratio in theforward hemisphere but include aft looking observationsonly above an elevation threshold of 50�.Sample calibrations for the multipath errors of C/A- andP-code measurements collected with the prime POD an-tenna of CHAMP on days 140–141 of 2001 are shown inFig. 3a–c. Similar results are obtained for other data arcsand no indications of time varying effects have beenencountered in our study. Overall, the multipath effects areconfined to the aft-looking hemisphere and are mostpronounced close to the satellite horizon. However, weaktraces of multipath errors may even be discerned close tothe zenith. For C/A-code measurements extreme multipathvalues of –2.0 m and +0.7 m can be observed and an al-most identical distribution pattern, but roughly 60%smaller amplitude is obtained for the P1-code measure-ments. The P2 multipath effects, in contrast, vary betweenpeak values of –0.6 m and +1.8 m and exhibit a notablyshifted pattern with wider fringes.As illustrated by the sky-plots (Fig. 3a–c), the multipatherrors in the aft-looking hemisphere depend predomi-nantly on elevation and vary only gradually with azimuth.The distribution of errors is not, however, strictly sym-metric around the zenith, but exhibits an apparent polethat is mostly tilted in the forward direction and slightlyoffset to the left. Upon testing various combinations, wefound that a coordinate system (X,Y,Z) resulting from theorbital and nominal body frame (x,y,z) by a roll rotationangle of D# � �7� and a pitch rotation angle ofDw � �27� provides an almost complete decoupling of themultipath dependence on azimuth and elevation angles.For a given unit vector e from the antenna to the observedGPS satellite, the relations:

þ cosðeÞ cosðaÞþ cosðeÞ sinðaÞ� sinðeÞ

0

B

@

1

C

A

¼eT

Xe

eTY e

eTZ e

0

B

B

@

1

C

C

A

¼ R2ðDwÞR1ðD#Þ

eTx e

eTy e

eTz e

0

B

B

@

1

C

C

A

ð5Þ

provide the elevation � above the tilted XY-plane (Fig. 4)as well as the in-plane angle a, (measured positive from theX-axis to the Y-axis). Here, eX, eY and eZ denote unit

vectors along the X-,Y- and Z-axes of the titled frame,while the unit vectors ex, ey and ez describe the main bodyaxes. These can be identified with the along-track, cross-track, and nadir direction vectors:

ex ¼ ey � ez ey ¼ � r�vr�vj j ez ¼ � r

rj j ð6Þ

as defined by the spacecraft position r and inertial velocityv during regular science mode operations.When referred to the tilted (X,Y,Z) frame, the multipatherrors exhibit a fully symmetric distribution and dependonly on the elevation angle �, except for a general decreasein amplitude for azimuth angles far off from 180�. To-gether, these observations suggest that the source ofinterfering radiation causing the multipath effects is lo-cated somewhere along the positive Z-axis relative to thePOD antenna. Denoting the mutual distance by b, thesecondary signal experiences an elevation dependent pathdifference d with respect to the direct signal, which, in itsmost general form, is described by the relation:

d ¼ d0 � beTZ e ¼ d0 þ b sinðeÞ ð7Þ

(Fig. 5). Here, the constant d0 describes the delay at zeroelevation, which equals the baseline in case of a reflectedsignal. On the other hand, Eq. (7) is likewise applicable formultipath effects caused by a secondary antenna, in whichcase d0 accounts for any line or cable length differences onthe way to the receiver (Fig. 5).Following Young (1988), the code multipath error can bedescribed by:

M ¼ dm cosð2pd=kþ D/Þ

1þm cosð2pd=kþ D/Þ �m�1

md cosð2pd=kþ D/Þ

ð8Þ

for multipath delays less than the 15.5 m correlator spac-ing. Here m is the amplitude ratio of the interfering anddirect signal and k is the L1 wavelength (0.1905 m; for C/A-and P1-code) or L2 wavelength (0.2445 m; for P2

GPS Solutions (2003) 7:74–86 81

Fig. 4CHAMP spacecraft coordinate system (x, y, z) and reference frame formultipath analysis (X, Y, Z)

Original article

measurements). Furthermore, DF denotes a supplemen-tary phase shift that may either occur upon signal reflec-tion or in the antenna/receiver electronics.Assuming that m(a,�) varies smoothly and is non-zerothroughout the aft-looking hemisphere, the zones of van-ishing multipath may uniquely be associated with the rootsof the cosine function in (Eq. 8). For a given azimuth a,neighboring roots of M(�) correspond to changes ofDd ¼ k=2 or, equivalently, bD sinðeÞ ¼ k=2. This fact maybe used to infer the length of the baseline b from theobserved multipath pattern.In order to separate multipath effects from measurementnoise, the results of Eq. (4) have been averaged overintervals of ±0.5� in � . Furthermore, the data set has beenconfined to observations within an azimuth range ofa=180�±10� that exhibits the strongest multipath-to-noiseratio (Fig. 6). For observations on the L1 frequency (i.e.,C/A- and P1-code), two consecutive nodes near elevationsof �=)14� and �=+2� can be distinguished, which yields abaseline of:

bL1 ¼ kL1=2ð Þ= sinðþ2�Þ � sinð�14�Þð Þ ¼0:34m ð9Þ

with an expected uncertainty of about ±0.05 m. As a con-sequence, the interfering radiation is found to originatefrom a location near the occultation helix antenna, which ismounted on the aft panel of the CHAMP spacecraft with a20� inclination towards nadir (Luhr et al. 2001, CHAMP2001). For the P2-code, a somewhat larger value of:

bL2 ¼ kL2=2ð Þ= sinðþ8�Þ � sinð�7:5�Þð Þ ¼0:45m ð10Þ

is obtained, which is only marginally compatible with theL1 result, but likewise falls into the vicinity of the occul-tation helix. Both results therefore suggest interferingsignals from the occultation antenna, rather than areflection, as the most likely source of the observed mul-tipath effects. This was substantiated by laboratory testsmade at JPL using the CHAMP engineering model(Meehan, personal communication).In view of remaining uncertainties caused by the incon-sistent baselines and the non-zero roll angle of theempirically determined Z-axis, a test was conducted onday 310 (Nov. 6) of 2002 in which the preamplifier andfront-end connected to the occultation antenna weretemporarily deactivated (Grunwaldt, personal communi-cation). As may be recognized from Fig. 3d, multipatherrors do not show up during this time frame, whichprovides final evidence for attributing the observed errorsto cross-talk between the POD and occultation antennastrings within the BlackJack receiver.Since deactivation of the BlackJack occultation antennastring is not feasible during regular science operation, aneffort has been made to derive a semi-empirical correctionmodel for the code measurements collected with theCHAMP POD antenna. To this end, the variation of themultipath error with azimuth a and elevation � is de-scribed by the expression:

Mða; eÞ ¼ M0 cos a� a0ð Þ � 10�ðe�e0Þ=De10

� cos2pk

d0 þ b sin eð Þ� �

ð11Þ

It denotes the product of a periodic term accounting forthe elevation dependent path delay, an exponential termmodeling the changing ratio of direct and secondarysignal strength with elevation and a cosine termmodeling the azimuth dependence of the signalstrength ratio. The above relation is applied for allobservations in the aft-looking hemisphere (defined bycos(a-a0)>0), otherwise the modeled multipath error isset to zero.A set of suitable model coefficients adjusted from theindividual multipath measurements is summarized inTable 3. The model provides an overall accuracy of betterthan 0.3 m for all observations above an elevationthreshold of E=5� (cf. Fig. 7). When used in dual fre-quency single point positioning solutions, the empiricalmultipath correction was found to remove most of theradial bias observed otherwise and to reduce the overall3D r.m.s. position error by roughly 0.6 m (ca. 20%). Eventhough corrections of individual ionosphere-free pseud-orange may be as large as 4 m (Fig. 7), the overallimprovement of the navigation solution is generally muchsmaller and depends notably on the applied elevationmask as well as other editing criteria.Concerning a physical interpretation of the semi-empir-ical multipath model, we note that no attempt has beenmade to constrain the baseline length b and the 10 dBscale height D�10 to common values for the different

82 GPS Solutions (2003) 7:74–86

Fig. 5Path difference for different forms of interfering radiation mixedwith the prime POD antenna signal

Original article

types of code measurements. This may at least in part bejustified by the assumption of different phase centers andantenna patterns for the L1 and L2 frequency, but isprimarily motivated by a best fit of the observed multi-path pattern. It may also be noted that the measured P1

multipath error is roughly 40% smaller than the corre-sponding C/A-code error and no attempt has been madeto explain this difference in terms of the applied corre-lation process.

Noise analysisA good knowledge of the error distribution of code andcarrier-phase measurements is of relevance for properweighting and data editing in precise orbit determinationapplications. Other than in ground based signal simulatortests, a truth reference is not, however, available todetermine the actual measurement errors of the CHAMP

BlackJack receiver in orbit. Important information on thenoise properties of the individual data types may never-theless be obtained from a comparison of the independentcode and carrier measurements in the C/A, P1 and P2

tracking channels.

Code noiseThe analysis discussed above has shown that multipatherrors only occur in the aft looking hemisphere. Whenconfining oneself to observations in the forward part ofthe hemisphere the multipath terms disappear fromEq. (4), leaving only the noise related error of each codeobservable. In order to allow for a proper interpretationof the code noise, its standard deviation has beendetermined as a function of the carrier-to-noise-densityratio:

GPS Solutions (2003) 7:74–86 83

Fig. 6Individual multipath measure-ments and elevation dependentmean value (solid line) forobservations in the azimuthrange a=180±10� (day 140–141/2001). For the selected observa-tions, the elevation angle � isroughly 27� smaller than theelevation E in the spacecraftframe

Table 3Parameters of semi-empiricalmultipath model for CHAMPcode measurements

Parameter C/A P1 P2

Reference amplitude M0 3.5 m 2.0 m 4.0 mCentral azimuth a0 200� 200� 200�Reference elevation �0 )27� )27� )27�10dB scale height D�10 25� 25� 35�Wavelength k 0.1905 m 0.1905 m 0.2455 mConstant path difference d0 mod k 0.414 m 0.414 m 0.600 mBaseline b 0.36 m 0.36 m 0.45 m

Original article

C�

N0 ¼ 20 � log10

SNRffiffiffi

2p

� �

ð12Þ

(Young, personal communication). Here, SNR is the mea-sured signal-to-noise ratio of the respective code observableas given in the RINEX data file (SA, S1, S2). The carrier-to-noise-density ratio (as well as the SNR value) is well corre-lated with elevation (Fig. 8) and varies between typical val-ues of 40 dB-Hz at a lower threshold of 10� and 55 dB-Hznear the zenith for the C/A-code tracking channels. Thecorresponding P-code, in contrast, ranges from 20 to 53 dB-Hz as a result of the signal squaring required by the codelesstracking process (Young, personal communication).In order to provide a good coverage of the lower C/N0 range,multiple days have been analysed together. Results for days

245 to 248 of 2001 are given in Fig. 9, which shows thatpseudorange noise of the carrier smoothed 10 s normalpoints varies between a minimum of 5 cm at high elevationsand 0.5 m (C/A) or 1.0 m (P1, P2) at 10� elevation. Thecorresponding standard deviation of the unprocessed 1 ssamples is roughly three times

ffiffiffiffiffi

10p� �

higher. No evidence ofchanges in the pseudorange noise distribution have beenobserved for selected data arcs between May 2001 (start ofCHAMP data archive) and the end of 2002, but the codenoise derived from the public Aug 2000 data set (day 220) isroughly twice as high. This may be attributed to the lesseffective normal point algorithm (quadratic pseudorange fitversus carrier smoothing) employed at this time.

Carrier noiseThe BlackJack receiver provides two independent carrier-phase observables on the L1 frequency (denoted as LA andL1), which are generated by the C/A-code and the P1-codetracking channels. These observations are subject to thesame ionospheric and multipath errors (cf. Eq. 1) andexhibit a maximum difference |NL1)NLA| of one cycle countplus a line bias that is confined to less than a wavelength.Consequently, the difference qL1)qLA is nominally constantthroughout each pass, which can be used to assess the noiselevel of the carrier-phase measurements. In the absence ofcorrelations, the standard deviation:

rL1�LA ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r2L1 þ r2

LA

q

> rL1 > rLA ð13Þ

thus provides an upper limit to the noise of the L1 and LAcarrier-phase measurements. In view of squaring lossesinduced by the codeless tracking in the P1 channel, it mayfurther be assumed that the L1 standard deviation exceedsthat of the LA measurements. Thus rL1-LA provides arough estimate of the L1 carrier-phase accuracy.Key results of the carrier-phase noise analysis are pre-sented in Figs. 10 and 11, which indicate notable

84 GPS Solutions (2003) 7:74–86

Fig. 7Observed and modeled multipath errors within the azimuth rangea=180±10�. The dashed curve denotes the predicted multipath errorof the ionosphere-free linear combination P12=2.546ÆP1)1.546ÆP2. Forthe selected observations the elevation angle � is roughly 27� smallerthan the elevation E in the spacecraft frame

Fig. 8Variation of carrier-to-noise-density ratio C/N0 for C/A- and P-codemeasurements with elevation. Each point in the diagram representsthe average C/N0 value for observations collected in a ±0.5� wideelevation interval during days 245–248/2001

Fig. 9Noise (1r standard deviation) of C/A- and P-code measurements as afunction of the carrier-to-noise-density. Each point in the diagramrepresents the average noise for observations within an interval of±0.5 db-Hz (at high C/N0) or ±0.75 db-Hz (at low C/N0) during days245–248/2001

Original article

variations in the carrier tracking performance throughoutthe CHAMP mission. The lowest measurement noise levelis achieved in the Aug 2000 data set, where the standarddeviation of the L1)LA difference ranges from 0.15 mm athigh elevations to 1 mm at low elevations. A roughlydoubled noise level is encountered in carrier-phase mea-surements collected between May 2001 (start of CHAMPISDC) and March 2002. While the noise floor at high C/N0

remained at a constant level of about 0.2 mm during thisperiod, it exhibits notable variations with peak values of0.7 mm in the subsequent months. Even though the sud-den change in the receiver performance is well correlatedwith the instance of the March 2002 software upload, nobandwidth changes have been performed at this time andit is unclear right now, whether other causes (thermal ef-fects, oscillator behavior, etc.) contribute to the apparentdegradation. Further observation of the carrier noise levelis therefore suggested to collect additional informationover the remaining mission lifetime.

Summary and conclusions

The in-orbit performance of the BlackJack dual-frequencyGPS receiver onboard the CHAMP satellite has been ana-lyzed using flight data collected between August 2000 andDecember 2002. Various software upgrades performedduring this period have contributed to an improved datacoverage and integrity, which is demonstrated for selecteddata arcs. At high elevations with good signal conditionsrepresentative noise levels of 5–10 cm for smoothedpseudoranges and 0.2–0.7 mm for carrier-phase mea-surements are achieved, which confirms the excellentoverall quality of the geodetic grade receiver. Varioustypes of data anomalies are discussed out of which theoccasional 15 m code slips can be corrected usingknowledge of the receiver internal sampling frequency.A cross-talk between the prime POD and occultation an-tenna strings has, furthermore, been demonstrated, whichresults in multipath-like pseudorange errors for observa-tions collected in the rear hemisphere. A semi-empiricalmodel is developed to describe the variation of these er-rors as a function of the line-of-sight vector in thespacecraft body frame and to allow a first-order correctionof the affected measurements. It is expected that theresults of the in-flight performance analysis facilitate theselection of adequate data editing and weighting strategiesand contribute to a better understanding as well as furtherrefinements of the BlackJack receiver hard- and software.

Acknowledgments The present study makes use of BlackjackGPS receiver measurements that have been made available for theCHAMP science team by GFZ, Potsdam. Precise reference orbitsof the CHAMP satellite have kindly been provided by J. van denIjssel, DEOS. Tom Meehan, JPL, and Ludwig Grunwaldt, GFZ,have taken the initiative for deactivating the occultation antennastring as part of a test campaign to demonstrate its impact oncode multipath. Their support in this matter is highly appreci-ated. The authors would furthermore like to thank Larry Young,JPL, for his valuable comments and technical discussions duringpreparation of the manuscript.

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Original article

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Original article