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Performance evaluation of single-frequency pointpositioning with GPS, GLONASS, BeiDou andGalileo

L. Pan, C. Cai, R. Santerre & X. Zhang

To cite this article: L. Pan, C. Cai, R. Santerre & X. Zhang (2017) Performance evaluation ofsingle-frequency point positioning with GPS, GLONASS, BeiDou and Galileo, Survey Review,49:354, 197-205, DOI: 10.1080/00396265.2016.1151628

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Performance evaluation of single-frequencypoint positioning with GPS, GLONASS, BeiDouand GalileoL. Pan1, C. Cai∗2, R. Santerre3 and X. Zhang1

The single point positioning (SPP) mode has been widely used in many fields such as vehiclenavigation, Geographic Information System and land surveying. For a long period, the SPPtechnology mainly relies on GPS system. With the recent revitalisation of the GLONASSconstellation and two newly emerging constellations of BeiDou and Galileo, it is now feasible toinvestigate the performance of quad-constellation integrated SPP (QISPP) with GPS, GLONASS,BeiDou and Galileo measurements. As a satellite-based positioning technology, the QISPP isexpected to improve the accuracy and availability of positioning solutions due to the increasednumber of visible satellites and the improved satellite sky distribution. In this study, a QISPPmodel is presented to simultaneously process observations from all four Global NavigationSatellite System (GNSS) constellations. Datasets collected at 47 globally distributed Multi-GNSSExperiment (MGEX) stations on two consecutive days and a kinematic experimental dataset areemployed to fully assess the QISPP performance in terms of positioning accuracy andavailability. Given that most navigation users are using single-frequency receivers, only theobservations on a single frequency are utilised. The results indicate that the QISPP improves thepositioning accuracy by an average of 16, 13 and 12% using the MGEX datasets, and 43, 31and 51% using the kinematic experimental dataset over the GPS-only case in the east, northand up components, respectively. The availability of the QISPP solutions remains 100% even fora mask elevation angle of 40°, whereas it is only 37% for the GPS-only case. All these results areachieved using geodetic-type receivers and they are possibly optimistic for users who usenavigation-type receivers.Keywords: Single point positioning, GPS, GLONASS, BeiDou, Galileo

IntroductionGPS single point positioning (SPP) technology has beenwidely used for civil navigation since the mid-1980s dueto its simple operation and data processing (Lee, 1986;Parkinson and Axelrad, 1988). However, the positioningaccuracy of the GPS SPP was limited to tens of metresbecause of the contamination of various error sources.Many efforts have been made to improve the performanceof the GPS SPP, such as improving the quality of civilcode measurements and broadcast satellite ephemeris.On the way to GPS modernisation, remarkable progresshas been made in the two aspects. Currently, the precision

of GPS C/A code measurements is approximately 0.3 m(Yang et al., 2014) and the signal-in-space ranging error(SISRE) of broadcast ephemeris is approximately 0.7 m(Montenbruck et al., 2015), which results in a significantimprovement on the positioning accuracy. The currenthorizontal and vertical accuracy of GPS SPP are typicallyat a level of 1–2 and 2–3 m, respectively (Cai et al.,2014a). Efforts are also made to improve the SPP per-formance by combining GPS with other Global Naviga-tion Satellite Systems (GNSS) (Cai et al., 2014a;Angrisano et al., 2013). Multi-constellation integratedSPP has the potential to significantly improve the posi-tioning accuracy due to the increased number of visiblesatellites and the improved satellite sky distribution,especially when positioning is performed in areas withGNSS signal blockages.In recent years, GLONASS, BeiDou and Galileo sys-

tems have been booming. A full GLONASS constellationconsisting of 24 operational satellites has been completelyrevitalised since 2012. BeiDou was declared to provide

1School of Geodesy and Geomatics, Wuhan University, Wuhan 430079,China2School of Geosciences and Info-Physics, Central South University,Changsha 410083, China3Département des Sciences Géomatiques, Université Laval, Québec,Canada G1V0A6

∗Correspondingauthor, email cscai@hotmail.com

© 2016 Survey Review LtdReceived 11 September 2015; accepted 3 February 2016DOI 10.1080/00396265.2016.1151628 Survey Review 2017 VOL 49 NO 354 197

navigation and position services over the Asia-Pacificregion with a constellation of 14 operational satelliteson 27 December 2012. A new generation of BeiDou sat-ellite was first launched successfully on 30 March 2015,which marks the start of the BeiDou system expansionfrom the regional to global scale. Soon after, two morenew generations of BeiDou satellites were launched suc-cessfully on 25 July 2015. The Galileo constellation hashad four In-Orbit Validation (IOV) satellites and fourFull Operational Capability (FOC) satellites since 27March 2015. The current GNSS constellations enablethe GNSS users to use simultaneously quad-constellationsignals. This provides an opportunity to investigate themulti-constellation integrated positioning performance.Ryan et al. (1998) first implemented the multi-constel-

lation integrated SPP but only GPS and GLONASS sys-tems were available at that time. With the revival ofGLONASS, more investigations on combined GPS/GLONASS SPP have been made (Cai and Gao, 2009;Angrisano et al., 2013). The combination with BeiDouor Galileo has also been attracting increasing attentionsin recent years (Cai et al., 2014a,b,c; Ryan and Lacha-pelle, 2000; Zhao et al., 2005). However, most of theseresearch works focused on the combination of only twoGNSSs at a time. Undoubtedly, the joint use of quad-con-stellation signals will be becoming the trend of GNSSdevelopment. In this study, a positioning model for thequad-constellation integrated SPP (QISPP) is presentedand its performance is investigated in terms of positioningaccuracy and availability.

Positioning model with quad-constellationsIn the QISPP, a key issue is to align the coordinate andtime references for the four GNSS systems. Regardingthe coordinate references, the broadcast orbits of WGS-84, PZ90.11, CGCS2000 and GTRF are adopted for pos-ition determination of GPS, GLONASS, BeiDou andGalileo satellites, respectively. Although the four GNSSsystems employ different coordinate references, theirdifferences are at a level of only several centimetres (Mon-tenbruck et al., 2015; Torre and Caporali, 2015). Such asmall difference is negligible in our analysis of code-based positioning solutions that use broadcast ephemeriswith metre-level accuracy. In other words, the satellitecoordinates of the four GNSS systems can be directlyused in the QISPP and no transformations are needed.On the other hand, the time scales used by the fourGNSS systems are different. The GPS time is establishedby the GPS Master Control Station and referenced toUnited States Naval Observatory (USNO) CoordinatedUniversal Time (UTC) with a small difference of lessthan 1 μs. Apart from this, GPS time differs from UTC(USNO) because the latter is periodically corrected withinteger leap seconds (GPS Directorate, 2012). The GLO-NASS time is based on an atomic time scale UTC (SovietUnion, SU) maintained by Russia with an integer differ-ence of 3 h and a fractional difference of less than 1 ms(RISDE, 2008). Thus, GLONASS time differs fromGPS time by leap seconds in addition to a tiny fractionaldifference. The BeiDou Time System was synchronisedwith UTC within 100 ns at 00:00:00 on 1 January 2006,whereas there exists a constant offset of 14 s to the GPS

time (CSNO, 2013). The Galileo System Time (GST) isnearly identical to the GPS time apart from a differenceof tens of nanoseconds (EU, 2010). Unlike the coordinatereference frame, the difference between the time refer-ences cannot be ignored and must be properly handledin the QISPP since they will significantly affect the posi-tioning solutions.Since the four GNSS systems adopt different time

scales, a receiver clock parameter with respect to itstime scale has to be estimated for each satellite systemeven if only a physical clock exists in the multi-GNSSreceiver. Alternatively, a system-time-difference par-ameter with respect to a reference time scale may be intro-duced instead of adding a receiver clock parameter (Caiand Gao, 2009). If the GPS time scale is chosen as thereference, the GPS receiver clock offset is directly esti-mated as an unknown parameter, whereas the receiverclock offsets of the other satellite systems are expressedas a sum of the GPS receiver clock and the system-time-difference parameters. The QISPP observation modelcan be depicted as

Pg = rg + cdtg − cdTg + dgorb + dg

trop + dgion + 1g (1)

Pr = rr + cdtg + cdtr,gsys − cdTr + drorb + dr

trop + drion

+ 1r (2)

Pb = rb + cdtg + cdtb,gsys − cdTb + dborb + db

trop + dbion

+ 1b (3)

Pe = re + cdtg + cdte,gsys − cdTe + deorb + de

trop + deion

+ 1e (4)

where the superscripts g, r, b and e refer to GPS, GLO-NASS, BeiDou and Galileo satellites, respectively. P isthe measured pseudorange in metres, ρ is the geometricrange in metres, c is the speed of light in vacuum in metresper second, dtg is the GPS receiver clock offset in seconds,dtr,gsys, dtb,gsys and dte,gsys are the GPS-GLONASS, GPS-BeiDou and GPS-Galileo system time differences inseconds, respectively, dT is the satellite clock offset inseconds, dorb is the satellite orbit error in metres, dtrop isthe tropospheric delay in metres, dion is the ionosphericdelay in metres, and ɛ is the measurement noise includingmultipath in metres.In equations (1)–(4), the satellite position and clock off-

set are computed using the broadcast ephemeris data. Thetropospheric error is corrected using the Saastamoinenmodel (Saastamoinen, 1973). The ionospheric error iscorrected using the Klobuchar model (Klobuchar, 1987)for GPS, GLONASS and BeiDou systems, whereas forGalileo the ionospheric error correction is made usingthe second version of the NeQuick model (Nava et al.,2008). Compared with the Klobuchar model, theNeQuick model is better suited for Galileo ionosphericerror corrections (Oladipo and Schüler, 2012). Hence,the unknown parameters include three receiver coordi-nates, one GPS receiver clock offset and three systemtime differences in the QISPP model. In view that mostSPP users are using single-frequency receivers due totheir low cost, only the pseudorange measurements onthe L1/G1/B1/E1 frequencies are used in this study.Owing to the fact that the broadcast satellite orbits andclock offsets refer to the ionosphere-free code

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198 Survey Review 2017 VOL 49 NO 354

combination on two frequencies, the satellite positionsand satellite clock offsets derived from the broadcastephemeris will contain hardware delay biases in a formof ionosphere-free combination. For dual-frequencyusers, the hardware delay biases can be cancelled outwhen the ionosphere-free code combinations are used.But for single-frequency users, the hardware delay biasesmust be corrected. Fortunately, the time group delayshave been provided in the broadcast navigation messageson a satellite-by-satellite basis. Hence, they can be appliedto correct the hardware delay biases in the single-fre-quency pseudorange-based positioning. The code obser-vations “C1C” for GPS and GLONASS, “C1I” forBeiDou and “C1C” or “C1X” for Galileo are adoptedin this study. The above code observation types aredefined in Receiver Independent Exchange (Rinex) ver-sion 3.02.As to the stochastic model for the QISPP, the following

covariance matrix of observations is adopted:

Cov =Qg 0 0 00 Qr 0 00 0 Qb 00 0 0 Qe

⎡⎢⎢⎣

⎤⎥⎥⎦ (5)

Q =

s21 0 · · · 00 s2

2 · · · 0

..

. ... . .

. ...

0 0 · · · s2n

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦ (6)

where the subscript n is the number of satellites for eachsatellite system, and σ2 is the variance of the code obser-vations, which can be expressed as

s2 = s20/( sinE)

2 (7)

where σ0 is the standard deviation (STD) of code obser-vations, which is different for each satellite system, andE is the satellite elevation angle.

The precision of the GPS code observations is set to0.3 m (Cai et al., 2014b). Based on our previous analysisin Cai et al. (2014c), an initial weight ratio of 1:1 is appro-priate for GPS and BeiDou code observations. Therefore,the precision of the BeiDou code observations is also set to0.3 m. The precision of the GLONASS code observationsis set to 0.6 m due to its twice lower code chipping rate thanthe GPS code observations. In view that the accuracy ofGalileo broadcast ephemeris is relatively lower (Monten-bruck et al., 2015), its measurements are down-weightedby a factor of four. That is, the precision of the Galileocode observations is also set to 0.6 m.

Results and analysisData descriptionDatasets collected at 47 globally distributed Multi-GNSSExperiment (MGEX) stations on 7 and 8 April 2015 areused to assess the performance of the QISPP. The distri-bution of stations is shown in Fig. 1. All stations wereequipped with multi-GNSS geodetic-type receivers,which can produce the observations from GPS, GLO-NASS, BeiDou and Galileo constellations. All obser-vations were recorded and post-processed at a samplinginterval of 30 s and the satellite elevation mask anglewas set to 10°. A quad-constellation mixed broadcastephemeris file “brdmdddf.yyp” provided by InternationalGNSS Service (IGS) is adopted for QISPP processing(available at: ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/rinex3/). Since the precise coordi-nates of manyMGEX stations are not available, the refer-ence coordinates for QISPP accuracy assessment areobtained by an online positioning user service, whichcan provide centimetre-level or even millimetre-level posi-tioning accuracy (Ghoddousi-Fard and Dare, 2006)(available at: http://www.ngs.noaa.gov/OPUS).

1 Geographical distribution of 47 MGEX stations

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Survey Review 2017 VOL 49 NO 354 199

QISPP results analysisFirst, the dataset from the MGEX station NNOR locatedin Australia during the GPS time 2:15–6:15 on 8 April2015 was processed for the QISPP analysis. This periodof time is chosen because three Galileo satellites andabout 10 BeiDou satellites were visible. It should benoted that although four Galileo IOV satellites and twoGalileo FOC satellites can be tracked successfully, onlythree Galileo IOV satellites have their broadcast ephe-meris data, namely E11, E12 and E19. Thus, observationsfrom these three satellites are processed. For the purposeof comparison, the dataset is processed in different con-stellation combinations, i.e. GPS-only, GPS/GLONASS,GPS/GLONASS/BeiDou and GPS/GLONASS/BeiDou/Galileo. In the data processing, the receiver coordinatesas well as other unknown parameters are estimatedepoch-by-epoch without imposing any constraintsbetween the epochs in order to analyse the single-epochSPP performance. In addition, only the single-frequencyoriginal code observation rather than carrier-phasesmoothing code is adopted. For brevity, GLONASS, Bei-Dou and Galileo systems are represented by “GLO”,“BDS” and “GAL” in the following figures and tables,respectively.Figure 2 shows the epoch-wise positioning errors in the

four different combination cases. The variations are con-sistent for the four cases in the east, north and up

directions, but the positioning errors for the triple- andquad-constellation cases show less fluctuation. It isobvious that the GPS/GLONASS SPP achieves smallerpositioning errors than the GPS-only case. By combiningwith BeiDou, the positioning errors of GPS/GLONASS/BeiDou SPP are further reduced at almost all epochs.The blue line is almost completely covered by the orangeline, indicating that there is no significant change byincluding the Galileo observations. Table 1 provides theroot mean square (RMS) statistics of positioning errorsin the east, north and up coordinate components for allthe four cases. The improvement rates given in brackets(columns 3–5) refer to the accuracy improvement by add-ing a further satellite system. Besides, the improvementrates (columns 6–7) refer to the accuracy improvementof the triple-constellation and quad-constellation casesover the GPS-only case, respectively. The results indicatethat the GPS/GLONASS case improves the positioningaccuracy by 16, 7 and 12% over the GPS-only case inthe east, north and up components, respectively. By intro-ducing BeiDou, a further accuracy improvement of 14, 16and 12% compared with the GPS/GLONASS case in thethree coordinate components is achieved. The furtherintegration with Galileo only improves the positioningaccuracy by less than 8%. The improvement of theQISPP on the positioning accuracy is 34, 25 and 25%over the GPS-only SPP in the three coordinatecomponents.The number of visible satellites and Position Dilution

of Precision (PDOP) for the four cases are also plottedin Fig. 2. It is seen that the multi-constellation combi-nation obviously increases the number of visible satellitesand simultaneously decreases the PDOP value. The aver-age number of satellites and PDOP are given in Table 1.For the quad-constellation integrated case, the averagenumber of visible satellites increases from 6.9 to 27.8,leading to a significant decrease in average PDOP valuesfrom 2.3 to 1.1. The increased satellite number anddecreased PDOP explain why the positioning accuracycan be improved in the multi-constellation integratedcases.Observation residuals that contain measurement noises

and other unmodelled errors may be used to evaluate theinner accuracy of the QISPP model. Figure 3 shows thecode observation residuals in the quad-constellation inte-grated processing case. The different colors representdifferent satellites. It can be seen that most GPS, GLO-NASS and BeiDou code residuals vary within a similarrange of −3 m to +3 m, whereas the Galileo coderesiduals vary in a significantly smaller range. The RMSstatistics are displayed in each panel. The statisticalresults clearly demonstrate that GLONASS has the lar-gest RMS residuals of ± 2.42 m. The RMS statistics ofthe BeiDou code residuals are almost half of GLONASSresiduals. GPS and Galileo RMS residuals are smallerwith values of ± 0.72 m and ± 0.46 m, respectively.These residuals show a comprehensive effect of remainedsatellite orbit and clock error, ionospheric delay error, ran-ging error and other unmodelled errors, which are differ-ent for different constellations. The smallest residualsfrom Galileo are partly due to the lower measurementredundancy and the higher satellite elevation angles.Overall, the code residuals for all four GNSS systemsappear in an acceptable level, suggesting that variouserrors and biases in code observations from different

2 Positioning errors, number of satellites and PDOP for theprocessing at NNOR on 8 April 2015

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200 Survey Review 2017 VOL 49 NO 354

constellations have been properly handled in the QISPPmodel.As the four GNSS systems adopt different time scales,

three system time difference parameters are introducedinto the QISPP processing. In order to investigate theirtime-varying characteristics, the system time differenceestimates (STDE) are obtained and plotted in Fig. 4. Itis obvious that the GPS-GLONASS, GPS-BeiDou andGPS-Galileo STDE all demonstrate clock stability. TheGPS-BeiDou and GPS-Galileo STDE values vary withina range of 5 ns while the varying range of the GPS-GLO-NASS STDE is almost twice. Their statistical results interms of mean values and STDs are also given in Fig. 4.The STDs of the GPS-GLONASS STDE are 1.47 ns,while the GPS-BeiDou and GPS-Galileo ones are 0.66and 0.83 ns, respectively. On the other hand, the multi-constellation mixed broadcast ephemeris file “brdmdddf.yyp” generated by IGS provides daily updated offset ofeach system time to UTC time, which can be applied tocompute the system time differences by an operation ofsubtraction. The obtained GPS-BeiDou and GPS-Galileosystem time differences from the broadcast ephemeris are5.68 and −2.97 ns, respectively. Uniquely, the GPS-

GLONASS system time differences are directly availablefrom the broadcast ephemeris with a value of −7.45 ns.By comparison, the mean values of STDE given in Fig.4 are far different from the system time differences derivedfrom the broadcast ephemeris. The reason for thephenomenon is that the former contains partial codehardware delay of the satellite and the receiver, which isdependent on specific receiver/antenna types (Cai et al.,2014a). As the code hardware delay bias is not availablein the broadcast ephemeris, only applying the correctionsof system time difference data from the broadcast ephe-meris is insufficient to compensate the code biasesbetween GPS and other GNSSs. Therefore, three systemtime difference parameters are indeed necessary to be esti-mated in the QISPP model.In order to investigate the performance of the QISPP in

a constrained visibility environment, Fig. 5 illustrates theRMS statistics of three-dimensional (3D) positioningerrors, availability, average number of visible satellitesand PDOP under different elevation mask angles. It isclearly seen that the 3D positioning errors for any constel-lation combination increase as the elevation mask angleincreases. However, the increase in the positioning errorsfor GPS-only and GPS/GLONASS cases is more signifi-cant. For the elevation mask angle of 40°, the 3D posi-tioning accuracy for the QISPP is improved by 75%from 15.74 to 3.95 m over the GPS-only SPP. In addition,the number of satellites increases from an average of 4.0 to12.7, leading to a decrease in PDOP values from 8.0 to3.6. The availability refers to the percentage of the epochsat which the position solutions can be acquired over thetotal epochs. For the GPS-only case, the availabilitybegins to decrease when the elevation mask angle

3 Code observation residuals for QISPP at NNOR

Table 1 RMS statistics of positioning errors and average number of satellites and PDOP at NNOR

GPS GPS/GLO GPS/GLO/BDS GPS/GLO/BDS/GALImprovement ratew.r.t. GPS (%)

East (m) 0.50 0.42 (16%) 0.36 (14%) 0.33 (8%) 28 34North (m) 0.60 0.56 (7%) 0.47 (16%) 0.45 (4%) 22 25Up (m) 1.95 1.72 (12%) 1.52 (12%) 1.47 (3%) 22 25No. of Sats. 6.9 13.3 (93%) 24.8 (86%) 27.8 (12%) 259 303PDOP 2.3 1.6 (30%) 1.2 (25%) 1.1 (8%) 48 52

The percentages in the brackets (columns 3–5) refer to the improvement over the nearest former case. The percentages (columns 6–7)refer to the improvement of the triple- and quad-constellation cases over the GPS-only case.

4 Estimated system time differences for QISPP at NNOR

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Survey Review 2017 VOL 49 NO 354 201

increases to 30°. For a mask angle of 40°, the availabilitydrops to 37%. By contrast, the availability for the GPS/GLONASS case is 52% and remains 100% for the tri-ple-constellation and quad-constellation cases. Onceagain, the multiple constellations outweigh the single con-stellation in terms of the availability of positioningsolutions.

Global QISPP accuracy assessmentIn order to assess the positioning accuracy of the QISPP,each solution is compared with GPS-only, GPS/GLO-NASS and GPS/GLONASS/BeiDou SPP solutionsusing datasets collected at 47 MGEX stations over twoconsecutive days. In order to ensure the contributions ofBeiDou and Galileo measurements, only the solutionsat specific epochs that include at least two BeiDou satel-lites and two Galileo satellites are used for the globalaccuracy statistics. The average time at the 47 stations is5.0 and 6.5 h for the two days, respectively.The RMS statistics of positioning errors, average num-

ber of satellites and PDOP in the four different constella-tion combinations at 47 stations on 7 April 2015 areshown in Fig. 6, which illustrates that the positioningerrors are reduced continuously in all three coordinatecomponents as more constellations are included in theSPP processing. The average positioning errors, numberof satellites and PDOP for the 47 stations are displayedin Table 2. The average satellite numbers of GPS, GLO-NASS, BeiDou and Galileo are 8.6, 7.0, 5.5 and 2.3,

5 RMS statistics of 3D positioning errors, availability, aver-age number of satellites and PDOP under differentelevation mask angles at NNOR

6 RMS statistics of positioning errors, average number of satellites and PDOP at 47 stations on 7 April 2015

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202 Survey Review 2017 VOL 49 NO 354

respectively. The average PDOPs for the above four pro-cessing cases are 2.0, 1.4, 1.2 and 1.1. The combinationof GPS and GLONASS improves the positioning accu-racy over the GPS-only case by 0.06, 0.11 and 0.17 m inthe east, north and up directions, respectively. In the tri-ple-constellation SPP, an accuracy improvement of 0.07,0.12 and 0.21 m over the GPS/GLONASS case in thethree directions is achieved. The positioning accuracy isonly improved by 0.02, 0.04 and 0.05 m in the three direc-tions after a further integration with Galileo.The statistical results on 8 April 2015 are also given in

Table 2. According to the average improvement rates ofthe two days, the combined GPS/GLONASS SPPimproves the positioning accuracy by 8, 5 and 5% overthe GPS-only case in the east, north and up directions,respectively. The accuracy improvement for the GPS/GLONASS/BeiDou case is 6, 6 and 6% over the GPS/GLONASS case in the three directions. After inclusionof Galileo observations, the further improvement on posi-tioning accuracy is 3, 2 and 2% in the three directions.Compared with GPS-only SPP, the QISPP improves thepositioning accuracy by 16, 13 and 12% in the three direc-tions. The average horizontal positioning accuracy at allstations over the two days for the four different constella-tion combinations is 2.02, 1.91, 1.79 and 1.76 m, respect-ively. It should be noted that all results were obtainedusing geodetic-type receivers. The positioning accuracycould degrade for navigation-type receivers.BeiDou satellites are not evenly distributed globally

because the current BeiDou system is in the stage of globaldeployment. Thus, the visibility of BeiDou satellites isdifferent at the global scale. In order to evaluate the con-tributions of BeiDou system, Fig. 7 shows the improve-ment in 3D accuracy against the PDOP improvementafter adding BeiDou observations to the GPS/GLONASSSPP processing. The red curve shown in Fig. 7 is thesecond-order fitting of the blue points. A total of 94 bluepoints correspond to the positioning solutions at 47stations on two days. The red curve reveals a trend thatthe 3D accuracy improvement rates increase as thePDOP improvement rates increase. This demonstratesthat the improvement of the positioning accuracy is depen-dent on the improvement of the satellite sky distribution.

Kinematic results and analysisIn order to assess the QISPP performance in the real kin-ematic mode, a kinematic data test was conducted on the

new campus of the Central South University in Chang-sha, China, on 16 August 2014. The kinematic test lastedfor 3 h with a beginning time at the local time 17:00:00(GPS time 9:00:00). In order that all three operationalGalileo IOV satellites could be tracked in the experimen-tal area, the experiment time was planned in advance.Figure 8 shows the equipment setup and field environ-ment.At the rover station, a “Trimble NetR9” receiverwith a “Trimble Zephyr Model 2” geodetic antenna wascarried by an electric bicycle to collect kinematic datafrom four constellations. The moving vehicle was drivenat a speed of approximately 10 km/h. At the base station,the same type of receiver with a “Trimble Zephyr Geode-tic 2” antenna and a radome was set up on the roof of theMining Building of the Central South University to helpdetermine the reference coordinates of the rover station atcentimetre-level accuracy using a double-difference real-time kinematic approach. The distance between the baseand rover stations is less than 2.5 km.The kinematicdata were collected at a sampling rate of 1 s with anelevation mask angle of 10°.Figure 9 presents the positioning errors, number of sat-

ellites and PDOP using the single-frequency code obser-vations for the kinematic test. It is obvious that thepositioning errors are significantly reduced for the GPS/GLONASS case over the GPS-only case, especially inthe vertical direction. The positioning accuracy is further

Table 2 Average positioning errors, number of satellites and PDOP for the 47 stations on 7 and 8 April 2015

GPS GPS/GLO GPS/GLO/BDS GPS/GLO/BDS/GAL

Improvementrate w.r.t. GPS

(%)

7 April 2015 East (m) 0.81 0.75 (7%) 0.68 (9%) 0.66 (3%) 16 19North (m) 2.05 1.94 (5%) 1.82 (6%) 1.78 (2%) 11 13Up (m) 3.13 2.96 (5%) 2.75 (7%) 2.70 (2%) 12 14No. of Sats. 8.6 15.6 (81%) 21.1 (35%) 23.4 (11%) 145 172PDOP 2.0 1.4 (30%) 1.2 (14%) 1.1 (8%) 40 45

8 April 2015 East (m) 1.04 0.96 (8%) 0.93 (3%) 0.91 (2%) 11 13North (m) 1.55 1.47 (5%) 1.38 (6%) 1.36 (1%) 11 12Up (m) 3.58 3.44 (4%) 3.30 (4%) 3.22 (2%) 8 10No. of Sats. 9.4 16.5 (76%) 21.1 (28%) 23.6 (12%) 124 151PDOP 1.8 1.3 (28%) 1.2 (8%) 1.1 (8%) 33 39

The percentages in the brackets (columns 4–6) refer to the improvement over the nearest former case. The percentages (columns 7–8)refer to the improvement of the triple- and quad-constellation cases over the GPS-only case.

7 Dependence of 3D accuracy improvement on the PDOPimprovement after adding BeiDou observations to theGPS/GLONASS SPP processing

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improved after a further combination with BeiDou. How-ever, the integration with Galileo did not significantlyimprove the positioning accuracy. The positioning errorsin the north component are larger than those in the eastcomponent due to the uneven satellite sky distribution.Table 3 provides the RMS statistics of the positioningerrors and the average number of satellites and PDOPin the kinematic test. The results indicate that theimprovement for the GPS/GLONASS case on the posi-tioning accuracy is 20, 15 and 32% over the GPS-onlycase in the east, north and up components, respectively.Furthermore, the improvement of the GPS/GLONASS/BeiDou case over the GPS/GLONASS case is 29, 17and 23% in three coordinate components, respectively.The positioning accuracy is only improved by less than7% after adding Galileo. In contrast to the GPS-onlycase, the QISPP improves the positioning accuracy by43, 31 and 51% in the three coordinate components,respectively.

ConclusionsThe BeiDou and Galileo have already begun to transmitreal signals for navigation and positioning applications,which have extended the GNSS family to quad constella-tions. The quad-constellation integrated single point posi-tioning (QISPP) has become feasible. In this study, aQISPP model is presented to simultaneously processobservations from GPS, GLONASS, BeiDou and Gali-leo. Datasets from 47 globally distributedMGEX stationson two consecutive days as well as a kinematic experimen-tal dataset are employed on a single epoch basis to assessthe performance of the QISPP in terms of positioningaccuracy and availability. The performance of the

8 Equipment setup and field environment for the kinematic quad-constellation SPP experiment on 16 August 2014

9 Positioning errors, number of satellites and PDOP for thekinematic test

Table 3 RMS statistics of positioning errors and average number of satellites and PDOP for the kinematic test

GPS GPS/GLO GPS/GLO/BDS GPS/GLO/BDS/GALImprovement ratew.r.t. GPS (%)

East (m) 1.09 0.87 (20%) 0.62 (29%) 0.62 (0%) 43 43North (m) 3.99 3.38 (15%) 2.80 (17%) 2.76 (1%) 30 31Up (m) 4.15 2.82 (32%) 2.17 (23%) 2.02 (7%) 48 51No. of Sats. 8.8 14.7 (67%) 24.4 (66%) 27.3 (12%) 177 210PDOP 1.8 1.4 (22%) 1.1 (21%) 1.0 (9%) 39 44

The percentages in the brackets (columns 3–5) refer to the improvement over the nearest former case. The percentages (columns 6–7)refer to the improvement of the triple- and quad-constellation cases over the GPS-only case.

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QISPP is compared with single-, dual- and triple-constel-lation combined SPP. In view that most navigation usersare using single-frequency receivers, only single-frequencymeasurements are employed in our SPP processing.Using the MGEX datasets, the statistical results indi-

cate that the combined GPS/GLONASS SPP improvesthe positioning accuracy by an average of 8, 5 and 5%over the GPS-only case in the east, north and up com-ponents, respectively. By introducing BeiDou, a furtheraccuracy improvement of 6, 6 and 6% is achieved. The per-formance improvement is more significant using the realkinematic experimental dataset. The GPS/GLONASScase improves the positioning accuracy by 20, 15 and32% over the GPS-only case in the three coordinate com-ponents, respectively. With inclusion of BeiDou, a furtheraccuracy improvement of 29, 17 and 23% is achieved. Theimprovement on the availability is also obvious. The avail-ability for the GPS-only case is only 37% at a maskelevation angle of 40° while it is increased to 52% for theGPS/GLONASS case and further to 100% for the triple-constellation and quad-constellation cases. Under the cur-rent Galileo constellation, no significant performanceimprovement is found after adding Galileo observations.In the next few years, both the BeiDou and Galileo con-stellations will be fully deployed. Greater benefits fromthe quad-constellation integration can be expected.It should be noted that the presented results are

obtained using geodetic-type receivers rather than naviga-tion-type receivers. If the latter is used, the positioningaccuracy could degrade due to relatively lower receiverperformance.

AcknowledgementsThe financial supports from the Scientific Research Fundof Hunan Provincial Education Department (No.13K007), the Hunan Provincial Innovation Platformand Talents Program (No. 2015RS4007) and the TeacherResearch Fund at Central South University (No.2013JSJJ004) are greatly appreciated.

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