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A comparative analysis of measurement noise andmultipath for four constellations: GPS, BeiDou,GLONASS and Galileo

Changsheng Cai, Chang He, Rock Santerre, Lin Pan, Xianqiang Cui & JianjunZhu

To cite this article: Changsheng Cai, Chang He, Rock Santerre, Lin Pan, Xianqiang Cui &Jianjun Zhu (2016) A comparative analysis of measurement noise and multipath for fourconstellations: GPS, BeiDou, GLONASS and Galileo, Survey Review, 48:349, 287-295, DOI:10.1179/1752270615Y.0000000032

To link to this article: http://dx.doi.org/10.1179/1752270615Y.0000000032

Published online: 30 Mar 2016.

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A comparative analysis of measurement noiseand multipath for four constellations: GPS,BeiDou, GLONASS and Galileo

Changsheng Cai1, Chang He1, Rock Santerre2, Lin Pan1, Xianqiang Cui*1 andJianjun Zhu1

With the rapid development of BeiDou system (BDS) and steady progress of Galileo system, the

current GNSS (Global Navigation Satellite System) constellations consist of GPS, GLONASS,

BeiDou and Galileo. The real signals from the four constellations have been available, which allows

us to analyse and compare their measurement noises and multipath effects. In this study, a zero-

baseline test is conducted using two ‘Trimble NetR9’ receivers to assess and compare the noises

and multipath of measurements on multiple frequencies from the four satellite systems. The zero-

baseline double difference approach is utilised to analyse the receiver noises. The code multipath

combination and triple-frequency carrier phase combination approaches are exploited to analyse

a comprehensive effect of the multipath and noises on the code and carrier phase measurements,

respectively. Based on the analysis of the zero-baseline dataset, the results indicate that the code

measurement noise levels range from 5 to 25 cm while the carrier phase noise levels vary within

0.9–1.5 mm for different frequencies and constellations. The code multipath and noise (CMN) level

for GLONASS is the largest with a root mean square (RMS) value of 39 cm on both G1 and G2

frequencies whereas the Galileo code measurements exhibit a smallest level on the E5 frequency

with a RMS value of only 10 cm. The RMS of the carrier phase multipath and noises (PMN) ranges

from 1.3 to 2.6 mm for BeiDou and Galileo satellites. By contrast, the triple-frequency carrier phase

combinations from the GPS Block IIF satellites demonstrate a much larger RMS value of 5.6 mm

owing to an effect of inter-frequency clock biases.

Keywords: GPS, BeiDou, GLONASS, Galileo, Measurement noise, Multipath

IntroductionWith the revitalisation ofGLONASS and the emergence oftwo new Global Navigation Satellite Systems (GNSSs)namely BeiDou and Galileo, the current GNSS familyconsists of GPS, GLONASS, BeiDou and Galileo. TheGLONASS constellation has been completely revitalisedwith 24 operational satellites in orbit since 2012. TheBeiDou system (BDS) has had the capability of providingnavigation and position services over the Asia-Pacificregion with a constellation of 14 operational satellites since27 December 2012, including five GEO (GeostationaryEarth Orbit), four MEO (Medium Earth Orbit) and fiveIGSO (Inclined Geosynchronous Satellite Orbit) naviga-tion satellites (CSNO, 2013). The Galileo system has hadthe capability of independent positioning with four In-

Orbit Validation (IOV) satellites since 12 October 2012(Steigenberger et al., 2013), although the time of simul-taneously tracking the four IOVsatellites is very short.Withcurrent GNSS constellations, the real signals from GPS,GLONASS, BeiDou and Galileo have become possible,which allows us to analyse and compare theirmeasurementnoises and multipath effect. The measurement noises andmultipath effect are a commonly concerned issue in manyapplications such as evaluating the receiver performanceand developing proper stochastic model.The zero-baseline approach has been widely applied for

assessing the receiver intrinsic noise characteristics since itcan remove all other error sources external to the receiverunit. For instance,Yang et al. (2014) analysed the precisionof BeiDou code and carrier phase measurements using thesingle-differenced measurements of zero baselines. Amiri-Simkooei and Tiberius (2007) analysed the receiver noisecharacteristics using both zero baseline and short baselineand reached the same conclusions using the two approa-ches. Freymueller (1992) carried out the zero-baseline testto analyse the possible intrinsic bias caused by differentreceiver types. de Bakker et al. (2012; 2009) used the zero-baseline measurements to assess the thermal noise of GPS

1School of Geosciences and Info-Physics, Central South University,Changsha 410083, China2Departement des Sciences Geomatiques, Universite Laval, Que.G1V0A6, Canada

*Corresponding author, email cuixianqiang@csu.edu.cn

� 2016 Survey Review LtdReceived 05 December 2014; accepted 14 April 2015DOI 10.1179/1752270615Y.0000000032 Survey Review 2016 VOL 48 NO 349 287

and Galileo/GIOVE satellite signals. It is worth notingthat the zero-baseline single-difference (SD) or double-difference (DD) series do not provide any informationon the antenna/preamplifier noises (Gourevitch, 1996).Therefore, the approach can only be used for assessing thenoises of the receiver excluding the antenna/preamplifier.For analysing the code observation multipath, a codemultipath combination (Estey andMeertens, 1999) that isboth geometry-free and ionosphere-free (IF) is commonlyexploited (deBakker et al., 2012;EsteyandMeertens, 1999;Shi et al., 2013; Yang et al., 2014). As for the assessment ofthe carrier phase multipath, a triple-frequency carrierphase linear combination may be utilised (Li et al., 2010;Ma and Shen, 2014; Montenbruck et al., 2013; Wu et al.,2012). Based on the twomultipath assessment approaches,their linear combinations actually still contain an effect ofmeasurement noises. The existing work about the receivernoises and multipath analysis mostly focuses on themeasurements from one satellite system at a time. Thepaper aims at assessing and comparing the receiver noisesand multipath for all four GNSS systems on all availablefrequencies.

Approaches for measurement noises andmultipath analysis

Zero-baseline double differenceReceiver (excluding antenna/preamplifier) noises areusually assessed through zero-baseline tests in which twosame types of receivers are connected to a same antennaby a signal splitter. In the zero-baseline, all error sourcesexcept the measurement noises may be eliminatedthrough a DD operation. The DD carrier phase andcode observations may be expressed as

DDw ¼ ðLp 2 LqÞm 2 ðLp 2 LqÞn¼ Npq

mn þ ð1wÞpqmn ð1Þ

DDP ¼ ðPp 2 PqÞm 2 ðPp 2 PqÞn ¼ ð1PÞpqmn ð2Þ

where DDw and DDP are DD carrier phase and codeobservations in metres, respectively, L is the measuredcarrier phase in metres, P is the measured pseudorange inmetres. The subscripts m, n denotes two receivers and thesuperscripts p, q denotes two satellites, respectively.Npq

mn isthe DD ambiguity in metres; ð1wÞpqmn and ð1PÞpqmn are thenoises of DD carrier phase and code measurements inmetres, respectively.As seen from equation (1), the DD carrier phase

measurements only contain phase measurement noisesand the ambiguity term. Thus, the phase measurementnoises can be derived by removing the ambiguity termfrom the DD phase measurements. For GPS, BeiDouand Galileo constellations, the DD ambiguity that isconverted to the unit of cycles is very close to an integerand thus it can be straightforwardly rounded into itsnearest integer. But this is not the case for GLONASS.The GLONASS DD ambiguity term cannot be expres-sed as a product of a constant wavelength and an integerDD ambiguity cycle owing to different wavelengthsemployed by different GLONASS satellites, whichresults in significant complexity for GLONASS DDambiguity resolution. In order to derive its measurementnoises, the mean values of the GLONASS DD carrierphase series are removed as the ambiguity term in view

that the ambiguity term is constant and the measure-ment noises have a zero-mean statistical characteristic.

Code multipath combinationCode observations on a single frequency and carrier phaseobservationson two frequencies areusuallyutilised to formthe multipath combinations to assess the code multipath.The code multipath combination may be expressed as(de Bakker et al., 2012; Estey and Meertens, 1999)

MPj ¼ Pj 2f 2j þ f 2i

f 2j 2 f 2i�Lj þ 2f 2i

f 2j 2 f 2i�Li

¼M j 2f 2j þ f 2i

f 2j 2 f 2i�mj þ 2f 2i

f 2j 2 f 2i�mi þBj þ 1j ð3Þ

where the subscripts i, j (i?j) denote the carrier frequencies,MP are the code multipath combinations in metres, P is themeasured pseudorange in metres, L is the measured carrierphase in metres, f is the carrier phase frequency in Hertz,M is the multipath effect in the measured pseudorange inmetres, m is the multipath effect in the measured carrierphase in metres, B is a sum of the ambiguity term andhardware delay biases, which is considered as a constant aslong as the phase observations are free of cycle slips, e is thenoise of the combined observations in metres. In equation(3), themultipath combination is both IF andgeometry-free(de Bakker et al., 2012). After removing the constant termBby subtracting themeanvalue of themultipath combinationseries, the residual series are dominated by the code multi-path and noises (CMN) since the carrier phase multipathand carrier phase noises are much smaller in magnitude.Thus, the multipath combination may be applied forassessing the CMN of a receiver including the antenna/preamplifier, unlike the zero-baselineDD approach. Beforethe multipath combination can be utilised for assessing theCMN, the cycle slips have to be first detected as the carrierphase measurements are involved in the multipath combi-nation. When cycle slips are detected out, the computationof the mean value is restarted from the cycle slip occurrenceepoch. In this study, a forward and backward movingwindow averaging algorithm and a second-order, time-difference phase ionospheric residual algorithm are jointlyused to detect cycle slips (Cai et al., 2013).

For triple-frequency or quad-frequency observations,the ith frequency has to be carefully chosen following theprinciple that the coefficients of mj and mi are as small aspossible in order that the carrier phase multipath is notsignificantly magnified. In term of the employedfrequencies of GPS, GLONASS, BeiDou and Galileo,the coefficients of both mj and mi can be smaller than 10provided that a proper ith frequency is chosen. In thisstudy, the following frequency combinations of ( j, i)have been used: (1, 2), (2, 1), (3, 1) and (4, 1). Thefrequencies for the four GNSSs are provided in Table 1.

Triple-frequency carrier phase multipath com-binationDual-frequency carrier phase observations may beexploited to form an IF linear combination, which hasbeen widely utilised in precise point positioning (Koubaand Heroux, 2001; Zumberge et al., 1997). Triple-fre-quency carrier phase observations may form two IFlinear combinations since they can be divided into twogroups of dual-frequency observations. By subtractingone IF combination from the other IF combination, the

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Survey Review 2016 VOL 48 NO 349288

triple-frequency carrier phase combination may beexpressed as (Li et al., 2010; Montenbruck et al., 2013)

DIFðL1;L2;L3Þ ¼ IFðL1;L2Þ2 IFðL1;L3Þ¼ f 21

f 21 2 f 222

f 21

f 21 2 f 23

!�L1 2

f 22

f 21 2 f 22�L2

þ f 23

f 21 2 f 23�L3

¼ f 21

f 21 2 f 222

f 21

f 21 2 f 23

!�m1 2

f 22

f 21 2 f 22�m2

þ f 23

f 21 2 f 23�m3 þ BDIF þ 1DIF

ð4Þ

where DIF is the triple-frequency carrier phase combi-nation inmetres,L is the measured carrier phase inmetres,m is the multipath effect in the measured carrier phase inmetres, BDIF is a sum of the ambiguity term and thehardware delay biases, eDIF is the noise of the combinedphase observations in metres. The triple-frequencycarrier phase combination is both geometry-free and IF(Montenbruck et al., 2012) since the first-order ionosphericeffect and the geometric term have been eliminated. Thephase wind-up and phase centre variation are two signifi-cant error sources for un-differenced carrier phase obser-vations. But considering that the second and the thirdfrequencies are quite close for GPS, BeiDou and Galileo(see Table 1), they are almost cancelled out in the triple-frequency carrier phase combination.Neglecting the phasewind-up effects and phase centre variations and removingthe constant term BDIF, the triple-frequency carrier phasecombination contains a weighted sum of phase multipathand noises (PMN) on each frequency (Montenbruck et al.,2013). The constant term BDIF may be eliminated by sub-tracting the mean value of the triple-frequency combi-nation series. Similar to the code multipath combination,the cycle slip should be first detected before the compu-tation of the mean value. Table 2 provides the coefficients

of triple-frequency carrier phase multipath combination.As the currentGLONASS satellites donot transmit signalsin triple frequencies the triple-frequency combinationapproach does not apply toGLONASS for the time being.Fortunately, the next-generation GLONASS-K satelliteswill add a third frequency (http://www.insidegnss.com/node/2487). The first GLONASS-K satellite was laun-ched on 26 February 2011 but it is still in flight test phase.

Measurement noise and multipathanalysis

Zero-baseline testIn order to analyse and compare the measurement noisesfrom GPS, BeiDou, GLONASS and Galileo systems, azero-baseline test was made on 10 May 2014. The testwas located on the top of Mining Building at the CentralSouth University, China. One pair of ‘Trimble NetR9’receivers were connected to a single choke-ring antennaof ‘TRM55971.00’ using a signal splitter, as displayed inFig. 1. The station coordinates are in the north latitudeof 28u109140 and the East longitude of 112u559 310.The receivers can simultaneously collect GPS, BeiDou,

GLONASS and Galileo measurements on transmitted fre-quencies including triple-frequency GPS and BeiDoumeasurements, dual-frequency GLONASS measurementsand quad-frequency Galileo measurements. Among GPSsatellites, only BLOCK IIF satellites transmit triple-fre-quency data. The signal and measurement information isincluded in Table 1. The displayed code and phase obser-vation types are acquired from Rinex (Receiver Indepen-dent Exchange) version 3, which are different from those inRinexversions 1and2as the lengthof theobservation codesis increased from two to three by adding a signal generationattribute. The attribute represents the tracking mode orchannel. For example, the GPS L1C refers to C/A code-derived L1 carrier phase. The GNSS signal modulationmodes are also provided in Table 1. The BPSK, QPSK,

Table 2 Coefficients of triple-frequency carrier phase multipath combination

Satellite Frequency band Combination coefficient

GPS BLOCK IIF L1–L2–L5 (0.2851, 21.5457, 1.2606)BDS GEO/IGSO/MEO B1–B2–B3 (0.4565, 1.4872, 21.9437)Galileo IOV E1–E5B–E5A (0.1614, 21.4220, 1.2606)

Table 1 GNSS signals and measurements information

Constellation L1/B1/G1/E1 L2/B2/G2/E5B L5/B3/–/E5A –/–/–/E5

Carrier Frequency (MHz) GPS 1575.42 1227.60 1176.45 –BeiDou 1561.10 1207.14 1268.52 –GLONASS 1602 þ k*0.5625 1246 þ k*0.4375 – –Galileo 1575.42 1207.14 1176.45 1191.795

Wavelength (cm) GPS 19.0 24.4 25.5 –BeiDou 19.2 24.8 23.6 –GLONASS 18.7–18.8 24.0–24.1 – –Galileo 19.0 24.8 25.5 25.2

Code, Phase GPS C1C, L1C C2W, L2W C5X, L5X –BeiDou C2I, L2I C7I, L7I C6I, L6I –GLONASS C1P, L1P C2P, L2P – –Galileo C1X, L1X C7X, L7X C5X, L5X C8X, L8X

Modulation GPS BPSK BPSK BPSK –BeiDou QPSK QPSK QPSK –GLONASS BPSK BPSK – –Galileo CBOC AltBOC AltBOC AltBOC

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Survey Review 2016 VOL 48 NO 349 289

CBOC and AltBOC are abbreviations of ‘Binary PhaseShiftKeying’, ‘QuadraturePhaseShiftKeying’, ‘CompositeBinary Offset Carrier’ and ‘Alternative Binary Offset Car-rier’, respectively. A 24-h observation dataset was collectedat a sampling rate of 30 swith an elevationmask angle of 5u.In order to compare the measurement noises betweendifferent types of satellites, the DD carrier phase and codeobservations are formed between the same types of satel-lites. In the zero-baseline test, the tracked satellites includefour GPS satellite types, three BeiDou satellite types, oneGLONASS satellite type and oneGalileo satellite type. Thenumber of visible satellites with different types could bedifferent at each epoch. For consistency, measurementsfrom a pair same type of satellites are used to assess themeasurement noises of the corresponding satellite type. Theused satellite pairs includeGPSBLOCK IIAG08 andG09,IIR G14 and G22, IIRMG15 and G29, IIF G01 and G30,BeiDouGEOC01 andC03, IGSOC08 andC10,MEOC11and C12, GLONASS-M R01 and R11, Galileo IOV E11and E12. These satellite pairs are chosen as representativesbecause they are commonly visible in a long time span(typically more than 4 h). Since these satellites were notconcurrently visible, measurement in a different 4-h sessionis used for this study.Figure 2 illustrates the skyplot of thesesatellite pairs in a 4-h span.

Zero-baseline test result analysisFigures 3 and 4 show the DD carrier phase and codemeasurement noises using the zero-baseline test dataset.

The DD measurement noises from different satellite typesare distinguished by different colours. In Fig. 3, it is seenthat the most phase measurement noises on all availablefrequencies vary in a range of 21 to 1 cm for four con-stellations. The noise distributions for the four differentconstellations are also similar. From Fig. 4, it is clearlyshown that the GPS and BeiDou DD code measurementnoises on three frequencies are distributed in a quite similarbehaviour. By contrast, theGalileoDDcodemeasurementnoises vary in a significantly smaller range while theGLONASS DD code measurement noises are moredispersed. The mean values of the GLONASS DD codeobservations are 0.19 m and 0.06 m on G1 and G2frequencies, respectively. However, the mean values of theDD code observations for other constellations are smallerthan 0.04 m. The relatively larger mean values of theGLONASS DD code observations are likely owing to theresidual inter-frequency code biases.Assuming the noises are at a same level for the

measurements obtained from the same type of satellitesand receivers, the DD measurement noises are magnifiedtwice over the un-differenced ones according to the errorpropagation law. Table 3 shows the un-differenced phaseand codemeasurement noise levels, which are derived fromthe STD (standard deviation) statistical values of DDphase and code measurement noises by dividing with afactor of 2. The results show that the BeiDou GEO phasemeasurements exhibit the highest noise level on all threefrequencies when compared with other satellite systems.In contrast, the phase measurement noises from GPSBLOCK IIF satellites are smallest than other systems aswell as other GPS satellite types. Overall, the phasemeasurement noises for four different satellite systems areat a very close level with a varying range of 0.9–1.5 mm.The noise level differs slightly on different frequencies forall satellite types except theGPSBLOCKIIF forwhich thephasemeasurementnoise level hasa largest inter-frequencydifference of 0.4 mm. As to the code measurement noises,the Galileo code measurements have a noise level of 0.08,0.07, 0.07 and 0.05 monE1, E5B, E5AandE5 frequencies,which are significantly smaller than the noise levels of othersatellite systems. Among quad-frequency Galileo signals,the Galileo E5 signal exhibits the smallest code noise level.This is easily understood because the E5 signal has abroadband of at least 51 MHz using an AltBOC modu-lation (Diessongo et al., 2014). Following Galileo, theBeiDou MEO code measurement shows the second smal-lest noise level on all frequencies. By contrast, the GLO-NASS satellites exhibit the highest noise level partlybecause of its lower Precision (P) code chipping rate at5.11 MHz. Overall, the code measurement noise levelsrange from 0.05 to 0.25 m for all frequencies andconstellations.

Code measurement multipath and noiseanalysisIn order to compare the code measurement multipathfrom four satellite systems, the multipath combinationof equation (3) is used to derive the CMN by removingthe ambiguity term which is computed as the mean valueof the multipath combination series. It should be notedthat the mean value of multipath combination seriesactually contains the constant ambiguity and the partialmultipath effect. After it is removed from the multipathcombinations, the left part reflects a comprehensive

1 Zero-baseline test setup on the top of mining building at

the Central South University, China

2 Sky plot of different types of satellite pairs in a 4-h

session on 10 May 2014

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Survey Review 2016 VOL 48 NO 349290

effect of residual CMN. Based on the code multipathcombination approach, the antenna/preamplifier noise isdetectable whereas it was not the case for the zero-baseline test.Figure 5 shows the CMN for four constellations on all

available frequencies using the dataset fromone receiver of

the zero-baseline test on 10 May 2014. Different coloursrepresent different satellite types. The dataset was collectedon the topofahighbuildingand thus itwasnot tooaffectedby the multipath effects. Figure 5 clearly indicates that theCMN for GPS, GLONASS and BeiDou vary in a similarrange. By contrast, theGalileoCMNvary in a significantly

3 Zero-baseline double-difference (DD) carrier phase receiver noises for four satellite systems on all available frequencies

4 Zero-baseline double-difference (DD) code receiver noises for four satellite systems on all available frequencies

Table 3 Standard deviation (STD) of un-differenced carrier phase and code receiver noises

Frequency L1/B1/G1/E1 L2/B2/G2/E5B L5/B3/–/E5A –/–/–/E5

Phase (mm) GPS BLOCK IIA 1.0 1.4 – –BLOCK IIR 1.0 1.2 – –BLOCK IIR-M 1.0 1.2 – –BLOCK IIF 0.9 1.1 1.1 –

BeiDou GEO 1.4 1.5 1.5 –IGSO 1.4 1.4 1.4 –MEO 1.1 1.2 1.1 –

GLONASS GLONASS-M 1.3 1.2 – –Galileo IOV 1.4 1.4 1.4 1.4

Code (m) GPS BLOCK IIA 0.16 0.15 – –BLOCK IIR 0.15 0.16 – –BLOCK IIR-M 0.15 0.15 – –BLOCK IIF 0.16 0.15 0.14 –

BeiDou GEO 0.16 0.13 0.10 –IGSO 0.19 0.14 0.10 –MEO 0.14 0.12 0.09 –

GLONASS GLONASS-M 0.25 0.22 – –Galileo IOV 0.08 0.07 0.07 0.05

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Survey Review 2016 VOL 48 NO 349 291

smaller range owing to its smaller noise level, especially forthe Galileo E5 frequency. For GLONASS and Galileosatellites, a few spikes at the beginning or the end of theprocessing session is because of the low satellite elevationangles, as seen from Fig. 2.The RMS statistics of the CMN on all frequencies are

made for each single satellite and results are shown inFig. 6, which indicate that theRMSvalues of theCMNaresimilar formost satellite pairs. The obvious differences thatexist in the satellite pairs of (C08, C10) and (E11, E12) aredue to the lower elevation angles of the satellite C10 andE12. Their minimal satellite elevation angles are 11u and15u in their corresponding sessions, respectively.

Table 4 provides the RMS statistical values of the CMNfor each satellite type. The results indicate that the RMS ofthe GLONASS CMN is largest with 0.39 m on both G1andG2 frequencies, respectively. TheGalileo RMS is only0.10 m on the E5 frequency, which is twice or even thricesmaller than other satellite systems. The RMS of BeiDouGEO satellites are slightly smaller than the IGSO andMEO satellites on all three frequencies because the GEOsatellites of C01 and C03 are always in view at higher

satellite elevations, as seen from Fig. 2. In addition, theRMSsof theBeiDouCMNon theB1 frequencyare slightlylarger than the ones on other frequencies. TheRMSs of theGPS CMN are similar for four different satellite types,varying between 0.25 and 0.31 m. It is worthwhile to noticethat RMS statistical values in Table 4 are computed usingall-epoch data regardless of the differences of satelliteelevation angles.Generally, the CMNmagnitude increasesas the satellite elevation angles decrease to a lower value.In order to examine the dependence of the CMN on

the satellite elevation angles, the RMS of the CMNagainst the elevation angles is shown in Fig. 7. The RMSis calculated for each increment of 5u in satelliteelevation angles. For instance, the RMS at the 12.5urepresents a statistical value of the CMN at satellite el-evation angles from 10u to 15u. Figure 7 clearly illus-trates the obvious dependence of the CMN on thesatellite elevation angles for all constellations andfrequencies except the Galileo E5 frequency. The RMSsof the GLONASS CMN on the G1 and G2 frequenciesare larger than those from other constellations in mostsatellite elevations angles. In contrast, the Galileo CMN

5 Code multipath combinations on all available frequencies for GPS, GLONASS, BeiDou and Galileo satellites

6 RMS statistics of code multipath and noise for different types of satellites on all available frequencies

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on the E1 and E5 frequencies exhibit the smallest RMSvalues regardless of the elevation angles. In addition, theRMSs of the BeiDou CMN are comparable to the GPSones on three frequencies.

Carrier phase measurement multipath and noiseanalysisThe triple-frequency carrier phase measurements may beused to form both geometry-free and IF combinations forassessing the PMN. As the GPS BLOCK IIA, BLOCKIIR, BLOCK IIR-M and GLONASS-M satellites do nottransmit triple-frequency measurements, their obser-vations cannot be used for triple-frequency combinations.The Galileo carrier phase measurements on the E1, E5B,andE5A frequencies are utilised to assess itsmultipath andnoise level. Figure 8 shows the triple-frequency carrierphase combinations in which the combined ambiguitieshave been removed as a mean value of the combinations,using the dataset from one receiver of the zero-baseline test

on 10 May 2014. The residuals reflect a comprehensiveeffect of the PMN. In Fig. 8, the PMN vary within+2 cmfor all satellite types except the GPS Block IIF. The smallfluctuation of PMN for BeiDou and Galileo satellitesexhibits a short periodical variation characteristic of themultipath effect. By contrast, significant systematic errorsare found from GPS satellites of G01 and G30, based onthe triple-frequency carrier phase combinations. Thesystematic errors may not attribute to the multipath effectsince the corresponding code multipath combinations donot indicate an obvious systematic bias. As addressed in(Montenbruck et al., 2012), the significant systematicvariation for theGPSBlock IIF satellites is an indication ofthermally dependent inter-frequency clock biases.Figure 9 provides the RMS statistics of the PMN on a

single satellite basis, which indicates that the Galileo IOVsatellites have the smallest PMN level whereas the GPSBLOCK IIF satellites have the largest PMN level. Thecoefficients of triple-frequency carrier phase combinations

7 RMS of the code multipath and noises (CMN) against elevation angles for four constellations on all available frequencies

Table 4 RMS statistics of code multipath and noises (CMN) for GPS, BeiDou, GLONASS and Galileo satellites on all availablefrequencies

L1/B1/G1/E1 (m) L2/B2/G2/E5B (m) L5/B3/–/E5A (m) –/–/–/E5 (m)

GPS BLOCK IIA 0.28 0.31 – –BLOCK IIR 0.25 0.28 – –BLOCK IIR-M 0.28 0.28 – –BLOCK IIF 0.26 0.28 0.30 –

BeiDou GEO 0.23 0.19 0.19 –IGSO 0.36 0.30 0.26 –MEO 0.34 0.29 0.27 –

GLONASS GLONASS-M 0.39 0.39 – –Galileo IOV 0.17 0.27 0.27 0.10

8 Triple-frequency phase multipath and noises (PMN) on all available frequencies for GPS, BeiDou and Galileo satellites

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have been provided inTable 2.Assuming that the PMNonthe used three frequencies are equal and uncorrelated, theRMS of the PMN on each frequency can be derived bydividing the root sum square of the combination coeffi-cients. The acquired RMS values on a single frequency forall three satellite systems are provided in Table 5.Obviously, the RMSs of the PMN from BeiDou andGalileo satellites are smaller with a variation from 1.3 to2.6 mm whereas the one from GPS satellites is largest by5.6 mm owing to a significant inter-frequency clock bias(Montenbruck et al., 2013).

ConclusionsWith the availability of real signals from GPS, BeiDou,GLONASS and Galileo constellations, the multi-systemintegrated applications will be a trend of future GNSSdevelopment. The paper analyses and compares themeasurement noises and multipath on multiple fre-quencies from the four satellite systems. The zero-base-line double difference, code multipath combination andtriple-frequency carrier phase combination approachesare utilised to analyse the receiver thermal noise, codeand phase multipath effects, respectively. The analysis ofmeasurement noise and multipath is useful in manyapplications such as evaluating the receiver performanceand developing proper measurement stochastic model.A zero-baseline test was carried out using the ‘Trimble

NetR9’ receivers which can produce four-GNSS

measurements on multiple frequencies. The zero-base-line double difference results indicate that the receiverphase measurement noises for four different satellitesystems are at a very close level with a varying range of0.9–1.5 mm. The receiver code measurement noise levelsrange from 0.05 to 0.25 m for four satellite systems.Galileo code measurements have a relatively smallernoise level of 0.08, 0.07, 0.07 and 0.05 m on E1, E5B,E5A and E5 frequencies whereas the GLONASS satel-lites exhibit the highest code noise level with values of0.25 m and 0.22 m on G1 and G2 frequencies, respect-ively. The multipath analysis results indicate that theRMS of the CMN for GLONASS is largest with 0.39 mon both G1 and G2 frequencies, respectively, while theone for the Galileo E5 frequency is only 0.1 m which istwice or even thrice smaller than other satellite systems.The RMS of the PMN ranges from 1.3 to 2.6 mm forBeiDou and Galileo phase measurements. By contrast,a significant systematic variation trend is found from theGPS satellites of G01 and G30 with a RMS value of5.6 mm due to a significant inter-frequency clock biasfor the GPS BLOCK IIF satellite type. It should benoted that the conclusions are drawn based on the testresults from the receivers and antennas that we used andcould be different for other receiver and antenna types.

AcknowledgementsThe financial supports from Scientific Research Fund ofHunan Provincial Education Department (No. 13K007),China Postdoctoral Science Foundation (No.2014M550425, No. 2013M540641), Teacher ResearchFund at Central South University (2013JSJJ004) andState Key Laboratory of Geo-information Engineering(No. SKLGIE2013-M-2-4) are greatly appreciated.

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