G E O M A T I C A

NETWORK REAL-TIME KINEMATICPERFORMANCE ANALYSIS USING RTCM 3.0AND THE SOUTHERN ALBERTA NETWORK

Kyle O’Keefe, Minmin Lin and Gérard Lachapelle, Department of Geomatics EngineeringSchulich School of Engineering, University of Calgary, Calgary, Alberta

The RTCM 3.0 data transmission format is introduced and described as it applies to multiple referencestation real-time kinematic differential GPS positioning, or network RTK. The new format provides a moremodern and flexible message structure that accommodates network RTK data transmission, while requiring upto 80% less bandwidth for the transmission of RTK correction messages. Based on this reduced bandwidth, weinvestigated moving the correction interpolation step of the network RTK procedure from the network to therover user. The RTCM 3.0 format is implemented and tested in both network and user software. Three inter-polation methods are implemented and compared with single baseline processing using real data collectedusing reference stations from the Southern Alberta Network. Under moderate ionospheric conditions, thenetwork RTK solution outperforms the single baseline approach in both the observation and position domains.The three interpolation methods are found to be comparable. Under severe ionospheric conditions, networkambiguity resolution becomes difficult, making the network corrections unreliable. It is recommended thata network ambiguity resolution status flag be added to the RTCM 3.0 network correction message format toalert users when network corrections are unreliable.

1. Introduction

In single baseline real-time kinematic (RTK)differential GPS surveying, the highest accuracyrover positions are only achieved when double dif-ference ambiguities are successfully resolved. Theability to resolve ambiguities depends mainly onthe level of errors remaining after observationshave been differenced between the reference androver receivers. Because differential atmospheric(ionospheric and tropospheric) errors are spatiallycorrelated, double difference errors will increase as

a function of distance from the reference station.Once differential errors are in the order of a carrierphase wavelength, ambiguity resolution becomesdifficult and, as a result, typical RTK operations arelimited to within a radius of approximately 10 kmfrom the reference station. In order to provide RTKservice to a larger area using this approach, a largenumber of very densely spaced reference receiversare required.

GEOMATICA Vol. 61, No. 1, 2007, pp. 29 to 41

Le format de transmission de données RCTM 3.0 est introduit et décrit en ce qu’il s’applique au posi-tionnement GPS cinématique différentiel à stations de référence multiples, ou réseau RTK. Le nouveau formatoffre une structure de message plus moderne et souple qui accommode la transmission de données du réseauRTK, tout en nécessitant une largeur de bande jusqu’à 80 % moindre pour la transmission des messages decorrections RTK. Grâce à cette largeur de bande réduite, nous avons étudié la possibilité de faire passerl’étape de l’interpolation de corrections de la procédure du réseau RTK du réseau à l’utilisateur du véhicule.Le format RTCM 3.0 est mis en œuvre et à l’essai dans le logiciel du réseau et de l’utilisateur. Trois méthodesd’interpolation sont appliquées et comparées avec le traitement de lignes de base simples utilisant les donnéesréelles collectées à l’aide de stations de référence du réseau du sud de l’Alberta. Dans des conditionsionosphériques modérées, la solution du réseau RTK surpasse l’approche de lignes de base simples dans lesdomaines de l’observation et de la position. Les trois méthodes d’interpolation sont considérées comparables.Dans des conditions ionosphériques sévères, la résolution de l’ambiguïté du réseau devient difficile, rendantles corrections du réseau peu fiables. Il est recommandé qu’un indicateur d’état de la résolution de l’ambiguïtédu réseau soit ajouté au format du message de corrections de réseau RTCM 3.0 afin d’avertir les utilisateurslorsque les corrections du réseau sont peu fiables.

Kyle O’Keefeokeefe@geomatics.

ucalgary.ca

Gérard Lachapellelachapelle@geo-

matics.ucalgary.ca

G E O M A T I C A

Alternative methods, often referred to as net-work RTK, have been developed where a sparsenetwork of permanent reference stations is used toestimate the spatially correlated observation errorsover a large region. These error estimates can beeither interpolated to the rover location, or modeledas a surface whose parameters are then transmittedto the rover user.

The case where network corrections are interpo-lated to the user location is called the VirtualReference Station (VRS) implementation [Vollath etal. 2000; Landau 2003; Alves 2004]. The correctionsare transmitted to the user in a format that makes theuser receiver think it is receiving corrections from asingle nearby reference station. Generally, these cor-rections are transmitted in a standard format, such asRTCM 2.3 messages, that are readily understood bycommercial off-the-shelf rover receivers. In the sec-ond approach, where a reference correction surfaceis modeled and a parameterization of the model sur-face is sent to the rover, proprietary message formatssuch as Flächen Korrektur Parameter (FKP) aregenerally employed to send correction informationto the rover [Wübbena et al. 2001, 2002].

The VRS and FKP approaches both suffer fromtheoretical and operational difficulties. The networkobservations are generalized, resulting in a loss ofinformation, and the network configuration is hiddenfrom the user, making it difficult to make informeddecisions about how to employ the network. VRSrelies on a data transmission standard that was notdesigned for network data dissemination, and FKPuses a proprietary standard that is not implementedin many commercial receivers.

Subcommittee SC104 of the Radio TechnicalCommission for Maritime Services (RTCM) isdeveloping a new standard called RTCM 3.0 toreplace RTCM 2.3. It will include specific supportfor network RTK message types, in addition to sup-port for multiple GNSS, and improvements in effi-ciency and reliability of data transmission for singlebaseline differential code and RTK applications.

In this paper, the proposed RTCM 3.0 messagestructure is reviewed and compared with RTCM2.3, with specific emphasis on network RTK appli-cations. One notable feature of the RTCM 3.0model is that the task of interpolating network cor-rections is shifted to the user. To investigate this,three different interpolation methods are introducedand compared, using real network and user dataobtained with the University of Calgary SouthernAlberta Network over two different data-collectionperiods representing different ionospheric condi-tions. Conclusions and recommendations about theproposed message format and the three interpola-tion methods are then made.

2. RTCM 3.0 Format andProcessing Model2.1 RTCM 2.3 and RTCM 3.0 forSingle Baseline RTK

RTCM Version 2.3, though widely acceptedfor single baseline RTK, is not without its prob-lems. Two of the most common complaints arefirst, that it uses inefficient and awkward 30-bitwords (with 6 bits of parity similar to the GPS nav-igation message), and second, that the format is notable to accommodate new message types for newfrequencies and systems.

Its proposed replacement, RTCM 3.0, address-es both issues, in addition to supporting networkRTK specific message types.

Instead of using 30-bit words with 24 bits ofdata followed by 6 bits of parity, the parity schemeuses a 24-bit Cyclic Redundancy Check (CRC) atthe end of a variable length message. This is a majorimprovement for three reasons. First, it makes eachmessage independent from the others, unlike the24/6 scheme where the parity calculation includesbits from the previous word. Second, the 24-bitCRC, which is also used in Wide Area AugmentationSystem (WAAS), provides protection against burst,as well as random errors with a probability of unde-tected error < 2–24 (5.96 x 10–8) for all channel biterror probabilities < 0.5 (FAA-E-2963, 2002). Third,moving to a modern parity algorithm greatly increas-es the efficiency of data transmission since only thefinal 24 bits of each message are used for parity, asopposed to 6 out of every 30 bits transmitted.

For example, RTCM 3.0 defines a messagetype 1003 that contains all of the information pre-viously sent in RTCM 2.3 messages 18 and 19. Theupper plot in Figure 1 shows the number of bitsrequired to transmit using these two standards ver-sus number of satellites. The lower plot shows thepercentages of bits devoted to useful informationby using these two standards. RTCM 3.0 is clearlymore efficient than RTCM 2.3 since only 80% ofRTCM 2.3 data bits are useful, while the efficiencyof RTCM 3.0 increases from 88% to 98% as datafrom more satellites are transmitted. RTCM 3.0will also make it possible to transmit 1-second cor-rections for up to 10 satellites on connections asslow as 1200 bits per second.

2.2 Processing Models forNetwork RTK

A typical Network RTK system consists of fiveprocessing steps, as shown in Figure 2.

30

…a sparsenetwork ofpermanentreference sta-tions is usedto estimatethe spatiallycorrelatedobservationerrors over alarge region.

G E O M A T I C A

First, assuming known network station coordi-nates, the network software or control centre willestimate the double-differenced network ambigui-ties, and subsequently estimate the corrections ateach station for each double-difference pair. Thecorrections are then arbitrarily undifferenced andinterpolated to a virtual reference station near therover, and then the VRS corrections are transmittedto the rover receiver using the RTCM 2.3 format.Finally, the rover computes a single baseline solu-tion between itself and the VRS.

The RTCM 3.0 implementation of networkRTK shifts all but the first step to the rover. Thenetwork’s only task is to collect observations andestimate network ambiguities and corrections foreach station. These corrections are then transmittedto the user as correction differences between eachreference network station and one designated masterstation. The user is left to interpolate and apply thecorrections and, in doing so, can generate the cor-rection to be applied relative to the master station ofthe network.

Excluding multipath and measurement noiseeffects, the correction difference contains the tro-pospheric and orbit (non-dispersive) single differ-ence error differences, as well as ionospheric (dis-persive) single difference error differences betweenthe two stations.

The RTCM 3.0 scheme further requires that apair of L1 and L2 correction differences to be repa-rameterized into dispersive and non-dispersive partsnamed, respectively, Ionospheric Carrier PhaseCorrection Difference (ICPCD) and GeometricCarrier Phase Correction Difference (GCPCD)[RTCM 2004]. This is done by forming the geome-try-free and ionosphere-free combinations of the L1and L2 correction differences.

Breaking the L1 and L2 correction differencesinto dispersive and non-dispersive parts yields afurther reduction in the bandwidth, since the dis-persive and non-dispersive parts can be transmittedat different rates; i.e., the GCPCD of auxiliary sta-tions could be updated as infrequently as every 10seconds. Additionally, since these two quantitiesrepresent errors, not absolute values, the data range

of these two parts is defined in RTCM 3.0 as ±24m, compared to the data range of ±32,768 cyclesfor phase corrections defined by RTCM 2.3. Usingthe ICPCD and GCPCD thus dramatically decreas-es the bandwidth by up to 80% compared to usingmessages 20/21 in RTCM 2.3.

Figure 3 shows the throughput required fortransmitting ICPCD and GCPCD or, instead, trans-mitting RTCM 2.3 messages 20/21 as a function ofthe number of satellites tracked and the number ofnetwork stations used. Of course, this comparisonassumes that information from all of the networkstations is being transmitted to the user, as pro-posed by the RTCM 3.0 data processing model, andclearly demonstrates why this kind of processingmodel is not recommended when using RTCM 2.3format corrections.

31

Figure 1: Bandwidth and efficiency comparison between RTCM 3.0 messagetype 1003 and RTCM 2.3 message types 18/19.

Figure 2: Division of Functions in Network RTK implementations.

ICPCD = k 1L1CD – k 1L2CD

=∆I t

f12 = ∆I1 t

GCPCD = k 2L1CD + k 1L2CD (1)

= ∆T t + ∆δr t

k 1=f2

2

f22 – f1

2 = – 1.545728, k 2=f1

2

f12 – f2

2 = 2.545728

G E O M A T I C A

In operational practice, two groups of RTCM3.0 messages will be transmitted to support net-work RTK. First, RTCM 3.0 single baseline RTKmessages will transmit the coordinates and rawobservations of the network master station, thenRTCM 3.0 network correction messages will pro-vide the ICPCD and GCPCD of each auxiliary sta-tion, and coordinate differences between them andthe master station. Using the master station obser-vations and the correction differences, the rover canreconstruct the observations from each of the otherreference stations. The rover can then combinethese with the coordinate differences of each of thereference stations to interpolate and obtain networkcorrections at the rover location.

3. Southern AlbertaNetwork Tests

As described above, the major feature of theRTCM 3.0 approach to Network RTK is that it

allows the user receiver to manage the interpolationof the reference station observations. In previouswork, this was often seen as a disadvantage, sinceoff-the-shelf receivers would require modificationsin order to be used in network applications.However, this can also be an advantage since itallows users to select their own interpolation meth-ods based on their needs and available computingpower. In this section, two data sets collected withthe Southern Alberta Network are processed fol-lowing the RTCM 3.0 model. RTCM 3.0 messagesare generated by the control centre and transmittedto the user, where they are decoded and then inter-polated using three common interpolation methods.

3.1 Data CollectionNetwork data was collected and processed

using the University of Calgary (U of C) SouthernAlberta Network and University of Calgary net-work software, MultiRef™ [Lachapelle and Alves2002]. In this paper, results from two separate peri-ods are presented. The first test uses data collectedon May 24, 2004, between 1h00 and 3h00 MDT.During this test, the local K index, as observed atthe Meanook Geomagnetic Observatory, approxi-mately 400 km north of Calgary, remained between3 and 4, indicating relatively benign ionosphericconditions. A second data set was collectedbetween 23h00 MDT on April 20, 2005, and 3h00MDT on April 21, 2005. During this test, the Kindex was 6, representing more challenging ionos-pheric conditions.

In both cases, MultiRef™ was used to collectdual frequency code and carrier phase observationsfrom the same five network stations: IRRI, COCH,STRA, BLDM and AIRD, as shown in Figure 4. Astation located at the University of Calgary servedas the rover receiver in this test. The MultiRef™was then used to estimate network ambiguities andgenerate RTCM 3.0 format messages.

A separate decoder and an interpolation func-tion were implemented at the rover to interpret andinterpolate the corrections. The interpolated correc-tions were applied to the master station (IRRI)observations, and these corrected master stationobservations were processed in double-differencemode with the raw rover observations usingGrafNav™ 7.01, a commercial baseline processingpackage developed by NovAtel Waypoint. Dataflow for this test is summarized in Figure 5.

3.2. Network Ambiguity Resolution In the RTCM 3.0 network RTK processing

scheme, the only estimation task of the network is32

Figure 4: Southern Alberta Network stations used inthis test.

Figure 3: Data throughput requirement for RTCM2.3 vs. RTCM 3.0 in a network RTK applicationwhere all network observations are being transmittedto the user.

G E O M A T I C A

to determine the network ambiguities. Networkdouble differences are formed by using the shortestbaseline set connecting all of the reference stations.In general, the highest satellite is selected as thebase satellite. MultiRef™ then attempts to solveambiguities between interconnected stations.Figure 6 shows the L1 and L2 ambiguity status ofthe four baselines in the network for local time01:00 to 03:00 on May 24, 2004. The green pointsdenote the base satellites, the blue ones denote thefixed satellites, and the red ones represent satelliteswith float ambiguities.

During the first test, network ambiguities arefixed 90% of the time. Especially in the case of thebaseline IRRI-AIRD, almost all the ambiguities arefixed. This scenario is a good example of a casewhere network ambiguities are well resolved. Thesecond data set, with more challenging ionosphericconditions, demonstrates the limitations of networkambiguity resolution when spatially correlatederrors are large. Figure 7 shows the network ambi-guity resolution status for the second test whereambiguity resolution remains excellent on theIRRI-AIRD baseline, but significantly worse on thelonger baselines.

3.3. Simulated Data Transmissionand Messaging Schedule

In this particular network configuration, sixtypes of RTCM 3.0 messages are transmitted:1004—Raw observations of the master station;1006—Coordinates of the master station; 1008—Antenna information; 1101—Coordinates of theauxiliary stations relative to the master stations;1102—ICPCD of the auxiliary stations; and1103—GCPCD of the auxiliary stations.

The raw observations made by the master sta-tion IRRI are transmitted every second, while thecoordinates and antenna information of the masterand auxiliary stations are transmitted every 10 sec-onds at different epochs. The ICPCD of all auxiliarystations are updated every second; the GCPCD ofstations COCH and STRA are transmitted on oddseconds; and the GCPCD of stations BLDM andAIRD are transmitted on even seconds to equitablydistribute the data within the operation period. Forthis five-station network, the maximum bandwidthrequired for this schedule would be 3752 bits persecond when ten satellites are observed.

An example of ICPCD and GCPCD for one ofthe network stations, BLDM, during the first test, isshown in Figure 8. Figure 9 shows the correspon-ding double-differenced corrections between theauxiliary station and the master station, IRRI.

33

Figure 5: Data flow used to test RTCM 3.0 format using the Southern AlbertaNetwork. MultiRef™ is used to collect data and resolve network ambiguitiesand generate an RTCM 3.0 data stream. An RTCM decoder and interpola-tion module is used at the other end to provide corrections that can be usedby the commercial post-processing package GrafNav™.

Figure 6: Network ambiguity resolution status during May 24, 2004 test.

G E O M A T I C A

These are obtained by subtracting the base satellitecorrection difference from each of the other correc-tion differences. The double-differenced correctionsare clearly similar to the correction differences them-selves, since the correction differences for the high-elevation base satellite are generally small. Thebaseline between BLDM and IRRI is about 70 kmlong, meaning that the ionospheric misclosures rang-ing from 0.5 to 2 cycles indicate that the differentialionospheric errors range from 1 to 5 ppm. It must benoted that the non-dispersive correction differencesand double-difference misclosures shown here havenot being reduced with a tropospheric model, lead-ing to particularly large correction differences andmisclosures for low-elevation satellites. The reasonis that the RCTM 3.0 standard specifies that tropos-pheric models only be applied by the user, to avoidthe possibility of introducing systematic errors dueto the reference network and the user applyingincompatible tropospheric models.

3.4. Interpolation MethodsOnce ICPCD and GCPCD messages have been

received by the rover, the next step is to interpolate

these corrections to the user location so they can beapplied. Three different interpolation methods:Plane Interpolation, Distance Weighted, and Least-Squares Collocation, are compared. All of these arecommon in Network RTK literature and each hascertain advantages and disadvantages.

One of the simplest linear interpolation meth-ods is to fit a plane to the available data. The cor-rections at the rover are assumed to be lying on aplane defined by the corrections at the auxiliary sta-tions. The advantage of this method is its conceptu-al simplicity. One drawback is that a minimum ofthree reference stations is required, yet when morethat three points are used for the interpolation, theinterpolating plane will no longer match theobserved corrections at the reference stations.

Euler and Zebhauser [2003] utilize a distanceweighted interpolation function. In this scheme, theinfluence of a given reference station is inverselyproportional to the distance between the referencestation and the user. The final correction at the useris a weighted average of all of the reference stationcorrections.

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Figure 7: Network ambiguity resolution status during April 20-21, 2005 test.

Figure 8: ICPCD and GCPCD of auxiliary stationBLDM.

Figure 9: Double-difference dispersive and non-dis-persive misclosures with full tropospheric error.

G E O M A T I C A

(2)

Where: 1 denotes master station;2 to n denote auxiliary stations;Si denotes the distance between the rover and

auxiliary station i.Though slightly more complicated, this

method is very convenient since, unlike plane inter-polation, it generalizes to the case where only onereference station is available.

The final method discussed in this paper isLeast-Squares Collocation. In this method, the cor-rection differences at rover location are treated“signal” in a least-squares collocation problemusing measurements containing both signal andnoise. Least-squares collocation has been usedextensively in Geodesy and a detailed descriptioncan be found in Moritz [1980]. The method wasfirst applied to the network RTK problem byRaquet [1998].

Although more computationally expensive, thecollocation method has several advantages. It pro-vides a smooth interpolation surface; it does notdepend on the number of reference stations avail-able; and, most importantly, it provides a rigorousestimate of the uncertainty of the interpolated valueas a function of the uncertainly of the reference sta-tion observations.

The general equations of collocation areshown as follows:

dln = – C1nBT [BC1n

BT]–1(Bln – ∇∆N)dln = – C1n1n

BT [BC1nBT]–1(Bln – ∇∆N) (3)

C1n= C* – C* BT [BC* BT]–1BC*

where dln are the corrections at the network points,dln are the corrections at the user points, ln are thenetwork observations, ∇∆N are the double differ-ence network ambiguities and B is the double dif-ference transformation matrix. The covariancematrices are related as

(4)

Where C1nis the covariance matrix of the correc-

tions at the user, i.e., the signal, C1nthe covariance

is the covariance between the corrections at the net-work stations and at the user. In order to performleast-squares collocation, the form of this covariancematrix must be known. In practice, this is obtained

from a covariance function. In this paper, thecovariance function due to Raquet [1998] is used.

As an example, Figure 10 shows the plane sur-face determined by four reference stations with amaster station located at [0,0] and having, by defi-nition, a correction difference of zero. This interpo-lation can be compared with Figure 11 and Figure12, which show the results of distance-weighted

35

CDrover=CDi ⁄ SiΣ

i = 2

n

1 ⁄ SiΣi = 2

n

C* =Cln

ClnlnClnln

Cln

Figure 10: Plane interpolation surface.

Figure 11: Distance-weighted interpolation surface.

Figure 12: Collocation Interpolation Surface.

matrix of the network observations and Clnln= Clnln

T

G E O M A T I C A

and least-squares collocation using the same fourreference stations.

3.5. User Results: Observations,Ambiguity Resolution, andPositioning Accuracy

In this section, the three interpolation methodsare compared using real data. Figure 13 presentsthe original double-difference, geometry-free mis-closures between the master station and the roverstation, as well as the corrected misclosures

obtained using each of the interpolation methodsfor the first data set. All three interpolation methodsresult in an improvement for the geometry-freecomponent on the order of 60%. In this data set, thecollocation method achieved the best results interms of percentage of improvement, followed bythe plane and distance weighted methods. Table 1gives the percentage improvement of all the satel-lites after applying the network corrections. Exceptfor PRN 19, the collocation method produced a70% to 80% improvement of all the other fixedsatellites; the plane method, around 70%; and thedistance weighted method, around 60%. Afterapplying network corrections, the magnitude ofgeometry-free misclosures of all satellites is suc-cessfully lowered to less than 0.3 L1 cycles.

However, the ionosphere-free misclosures,which have been reduced by the troposphericmodel, have very small magnitudes. As shown inFigure 14, the magnitude of the misclosures is nor-mally less than 0.5 L1 cycles. Comparing Figure 14and Figure 13, it is clear that the improvement innon-dispersive misclosures after correction is notas obvious as the effect on dispersive misclosures.However, an improvement on the order of 10% to30% can still be obtained through the application ofcorrections.

For the first test, network-corrected user datawas processed using GrafNav™ starting at epoch115200, 1:00 local time when medium-level ionos-pheric errors were observed.

Twenty-four kilometres from the rover UOFC,the nearest reference station, AIRD, is used for sin-gle-reference station processing. Three interpolationmethods are used in the network approach. Thenorth, east and vertical errors are shown in Figure 15and their accuracies after ambiguity resolution areshown in Table 2. The first fixing time for plane andcollocation methods is the same, while the distance-

36

Figure 13: Dispersive “raw” and “corrected” misclo-sures using distance-weighted, plane and collocationinterpolation methods

Without Distance weighted Plane Collocationcorrection

PRN RMS RMS RMS RMS(L1 cycle) (L1 cycle) Imp. (L1 cycle) Imp. (L1 cycle) Imp.

7 0.7527 0.210 62% 0.1484 69% 0.1026 74%8 0.8660 0.2785 67% 0.1719 79% 0.1373 83%19 0.4925 0.2032 33% 0.1799 35% 0.1587 38%26 0.8159 0.2365 66% 0.1508 76% 0.1162 80%27 0.8737 0.3271 63% 0.2540 70% 0.2028 76%29 0.8248 0.2461 66% 0.1643 75% 0.1213 80%31 0.8407 0.3393 57% 0.2495 67% 0.222 70%

Table 1: First data set geometry-free, double-difference misclosures (in L1 cycles) by satellite using each inter-polation method.

G E O M A T I C A

weighted method takes twenty seconds longer to fix.As compared to the single-reference stationapproach, which takes more than half an hour to fixambiguities, the network approach exhibits a signif-icant advantage in reducing the convergence timeunder medium ionospheric situations. Even after thesingle-reference station solution is fixed, positionerrors still increase with time; most likely due toincorrect ambiguity resolution due to ionosphericeffects. All three interpolation methods are effectiveand demonstrate similar result in positioning accura-cy, while the collocation method shows slightlybetter 3D positioning accuracy.

Figure 16 and Figure 17 present the uncorrect-ed and corrected geometry-free and ionosphere-free misclosures between IRRI and UOFC for thesecond test. In this case, the network ambiguitiesare generally not resolved, meaning that the mis-closures do not represent their true ionospheric andgeometric errors.

However, it should be noted that, as shown inFigure 7, the ambiguities between IRRI, STRA,AIRD and COCH are resolved well, above 60% ofthe time during the period of interest. MultiRef™only encounters difficulty in resolving COCH-BLDM ambiguities, in which case the percentage islower than 20%.

Since the correctness and appropriateness of“float” corrections cannot be evaluated in the

observation domain and “float” corrections do notreflect the true errors at the reference stations, theinterpolated corrections are questionable and,hence, the results of employing these correctionsare unpredictable.

Once corrections are received from the rover,ambiguity resolution by the rover can be attempted,regardless of the ambiguity resolution status of the

37

Figure 14: Non-dispersive “raw” and “corrected”misclosures using distance weighted, plane and collo-cation interpolation methods

Figure 15: North, east and vertical position errors over time for the single ref-erence station and multiple reference station approaches using three interpo-lation methods.

Table 2: First data set RMS position errors of the single reference stationapproach and multiple reference station approach using three interpolationmethods.

Interpolation Methods RMS After Fix (cm) First Fixing Time (s)

North 4.80AIRD East 8.55 2379

Up 8.73(Single Baseline) 3D 13.13

North 3.32Distance weighted East 1.38 491

Up 4.543D 5.79

North 2.11Plane East 2.46 470

Up 4.113D 5.23

North 2.44Collocation East 1.61 470

Up 3.783D 4.78

G E O M A T I C A

network; however, the results will not necessarilybe reliable.

In the following analysis, position domainresults are considered with rover ambiguity resolu-tion both enabled and disabled. North, east and ver-tical error components obtained with ambiguityresolution enabled are shown in Figure 18.

Table 3 summarizes the RMS positioningerrors for epochs with fixed ambiguities. The sin-gle-station approach fixes the ambiguities at epoch2814, while the network approach using the dis-tance-weighted interpolation method achieved fixat epoch 1803. The network approach, using planeand collocation interpolation methods, both fix atepoch 3604, which is later than the single-stationapproach. Moreover, it is obvious from Figure 18that the ambiguities have been incorrectly fixedusing the plane interpolation method. A comparisonof the RMS north, east and vertical errors after theambiguities are fixed reveals no improvementusing the network approach. For this data set, the3D RMS position errors of the network approachusing the distance-weighted interpolation methodare the best, followed by the single-baselineapproach and the network approach using the col-location interpolation method. In this case, theplane interpolation method shows a distinct bias inall three directions, and the corresponding RMSerrors are not reported in Table 3.

Figure 19 shows the position errors obtainedwith the rover is processing data using an iono-sphere-free float combination, i.e., the ionosphere-free observable is formed and ambiguities are notresults. Table 4 lists RMS position accuracies withthe first hour excluded to allow for float ambiguityconvergence. The plane interpolation method per-forms best in this scenario, while exhibiting a min-

38

Figure 16: Dispersive “raw” misclosures and interpo-lated corrections using distance-weighted, plane andcollocation interpolation methods.

Figure 17: Non-dispersive “raw” misclosures andinterpolated corrections using distance-weighted,plane and collocation interpolation methods.

Figure 18: North, east and vertical position errorsover time for the single reference station approachand multiple reference station approach using threeinterpolation methods with KAR enabled inGrafNav™.

G E O M A T I C A

imum 3D error of 5.11 cm for the four tests. Thedistance-weighted interpolation method performedsecond-best, followed by the collocation methodand, finally, the single baseline method. Overall, amaximum improvement of 3 cm can be observedusing the network approach.

In summary, when the network ambiguities aremostly resolved (fix percentage is 90% or above),the interpolated network corrections effectivelyreduce master-rover misclosures. Among all threeinterpolation methods, the collocation method showsthe highest improvement. In the position domain, allthree interpolation methods are effective anddemonstrate similar results in positioning accuracy.

However, when network ambiguities are onlypartially resolved, no effective analysis can be per-formed in the observation domain, and results inthe position domain with ambiguity resolutionenabled do not show a distinct advantage to net-work RTK over the single-baseline approach.When rover ambiguity is disabled, the three net-work methods all show slightly better positioningaccuracy than the single-baseline method.

4. Conclusions

In this paper, the RTCM 3.0 data format and itsapplications to network RTK are discussed andcompared with the current RTCM 2.3 format. TheRTCM 3.0 format contains several improvementsover RTCM 2.3, as it is designed to compress databy up to 80% and accommodate network RTK spe-cific messages.

In order to test the new format, RTCM 3.0 mes-sage generation capabilities were added toMultiRef™, the network RTK software developed atthe University of Calgary. An RTCM 3.0 decoderand interpolation functions were also implementedat the rover end to allow the new format to be usedwith commercial carrier phase-processing software.

When network ambiguities are resolved above90% of the time, the majority of the corrections ateach station are equivalent to the true value of

39

Table 3: Second data set RMS position errors of the single reference stationapproach and multiple reference station approach using three interpolationmethods.

Interpolation RMS After Fix (cm) First Fix Time (s)Methods

AIRD North 9.62 2814East 1.62

Vertical 9.09(Single Baseline) 3D 13.33

North 7.25 1803Distance weighted East 5.40

Vertical 7.713D 11.88

North N/A 3604Plane East N/A

Vertical N/A3D N/A

North 8.93 3604Collocation East 8.72

Vertical 5.993D 13.84

Figure 19: North, east and vertical position errorsover time for the single reference station approachand multiple reference station approach using threeinterpolation methods with KAR disabled inGrafNav™.

Interpolation Methods RMS After 1 hour (cm)

AIRD North 2.64East 1.02

(Single Baseline) Vertical 7.513D 8.03

North 3.04Distance weighted East 0.92

Vertical 5.543D 6.39

North 1.52Plane East 1.16

Vertical 4.743D 5.11

North 3.92Collocation East 0.85

Vertical 6.743D 7.84

Table 4: IF-float RMS position errors after allowing 1 hour for float ambi-guity convergence.

G E O M A T I C A

ionospheric and tropospheric errors. The threeinterpolation methods proposed herein present sim-ilar results when interpolating the network correc-tions to the location of the rover. Analysis of thesample data set observed in Southern Alberta dur-ing relatively benign ionospheric conditions indi-cates that network corrections can efficientlyreduce the master-rover dispersive errors by 60% to80%, and non-dispersive errors by 10% to 30%. Inall cases, the network approach, regardless ofwhich interpolation method is used, takes less timeto fix the ambiguities than does the single-referenceapproach. There is no significant difference amongthe three interpolation methods in the positiondomain using the above data set.

When the assumption that all the networkambiguities are resolved correctly holds true, thecorrections at each physical station should be equalto the true errors at the respective stations.However, errors may be introduced in the correc-tions via float network ambiguities or incorrectlyfixed network ambiguities, which result in the cor-rections departing from the true value. The ambi-guity resolution status of the network generatingthe corrections should be transmitted to the roverreceiver so that the rover can distinguish betweenthe “fixed” and “float” corrections.

In RTCM 3.0, a 2-bit field named the“Ambiguity Status Flag” is defined for each correc-tion, but no value is reserved for float indication. Forthe network service providers who want to utilize“float” corrections to rovers, RTCM 3.0 does notprovide a corresponding field. An alternativeapproach would be to transmit only the “fixed” cor-rections to the rover. However, this would introduceavailability problems in longer baseline networks orunder high ionospheric conditions. Alves et al.[2005] have proposed a geometry-based qualityindex to monitor network RTK quality. However, thequality index is still based on the assumption that thetrue errors are determined; i.e., that network ambi-guities are correctly resolved. More effort is neededto indicate the quality of the corrections; in particu-lar, corrections based on float ambiguities.

Acknowledgements

The authors would like to acknowledge thesupport of the RTCM Sub-committee 104 for theirassistance and support of this project.

References

Alves, P. 2004a. Development of two novel carrierphase-based methods for multiple Reference stationpositioning. PhD Thesis, published as Report No.20203, Department of Geomatics Engineering, TheUniversity of Calgary (http://www.geomatics.ucal-gary.ca). Date Accessed: November 20, 2005.

Alves, P., I. Geisler, N. Brown, J. Wirth and H.-J. Euler.2005. Introduction of a Geometry-Based NetworkRTK Quality Indicator. Proceedings of the 18thInternational Technical Meeting of the SatelliteDivision of the Institute of Navigation, September21-24, 2005, Long Beach, California.

Euler, H.-J., B.E. Zebhauser, B. Townsend and G.Wübbena. 2002. Comparison of Different Proposalsfor Reference Station Network InformationDistribution Formats. Proceedings of the 15thInternational Technical Meeting of the SatelliteDivision of the Institute of Navigation, September24-27, 2002, Portland, Oregon.

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Moritz, H. 1980. Advanced Physical Geodesy.Wichmann. Karlsruhe-West. Abacus Press,Tunbridge, England.

Raquet, J.F. 1998. Development of a Method forKinematic GPS Carrier-Phase AmbiguityResolution Using Multiple Reference Receivers.PhD Thesis, published as Report No. 20116,Department of Geomatics Engineering, TheUniversity of Calgary. (http://www.geomatics.ucal-gary.ca) Date Accessed: November 20, 2005.

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Authors

Dr. Kyle O'Keefe is an Assistant Professor ofGeomatics Engineering at the University of CalgarySchulich School of Engineering. He completed hisPhD and BSc degrees in the same department in2004 and 2000. He has worked in positioning andnavigation research since 1996. His major researchinterests are GNSS system simulation and assess-ment, space applications of GNSS, carrier phasepositioning, and local and indoor positioning withGPS and other wireless technologies.

Ms. Minmin Lin completed an MSc. inGeomatics Engineering at the University of CalgarySchulich School of Engineering in 2006. In 1999,she completed her BSc. degree in Control Scienceand Engineering at Huazhong University of Scienceand Technology. In 2002, she received her MSc.degree in Navigation and Control at BeijingUniversity of Aeronautics and Astronautics. She ispresently employed by NovAtel Inc. in Calgary.

Dr. Gérard Lachapelle is a Professor ofGeomatics Engineering at the University ofCalgary where he is responsible for teaching andresearch related to location, positioning, and navi-gation. He has been involved with GPS develop-ments and applications since 1980. He has held aCanada Research Chair/iCORE Chair in wirelesslocation since 2001 and heads the PLAN Group atthe University of Calgary. o

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