Using a Virtual Reference Station to Compensate for Coordinate Transformations in GPS Surveying

Bryan R. Townsend, Roberton Enterprises Ltd., Anna B. O. Jensen, National Survey and Cadastre, Denmark

BIOGRAPHY datum, this not the preferred mode of operation. The Network is used to model the ionospheric, tropospheric, Bryan Townsend received his Master of Science degree in and orbit errors over a region. Using reference station 1993 from the Department of Geomatics Engineering at coordinates that are in another datum than WGS84 will the University of Calgary. Since then he has worked in reduce the ability of the Network RTK software to model several areas of GPS including GPS surveying, GPS these errors. receiver design and wide area reference systems. Most recently he is involved in the development of multi- This paper investigates using the VRS position to correct reference RTK systems. for local datum effects. With this method the reference station coordinates remain in WGS84 and the rover Anna B.O. Jensen holds an M.Sc. in surveying from the coordinates are maintained in the local system. This University of Aalborg in Denmark, and has since 1995 method allows the user to work in the local earth fixed been employed in the Department of Geodesy at the system for several years and not suffer any significant National Survey and Cadastre – Denmark (KMS). She is degradation in accuracy. presently doing her Ph.D at the University of Copenhagen and KMS. INTRODUCTION

ABSTRACT The introduction of multi-reference station based RTK (Network RTK) offers several advantages to GPS The introduction of multi-reference station based RTK surveying. RTK coverage over regional areas is made (Network RTK) offers several advantages to GPS possible while using fewer reference stations, with more surveying. RTK coverage over regional areas is made ease to the user, and at a lower cost than by traditional possible while using fewer reference stations, with more single baseline methods. A regional network that can ease to the user, and at a lower cost than by traditional cover areas of several hundred kilometers square has single baseline methods. A regional network that can introduced new problems related to coordinate cover areas of several hundred kilometers square has transformations between WGS84 and the earth fixed introduced new problems related to coordinate regional reference system, which is often preferred by the transformations between WGS84 and the earth fixed user. regional reference system. This paper investigates this problem and presents a way it In single baseline RTK the position of the rover is can be solved using the Virtual Reference Stations calculated relative to the reference station. Therefore, it is (VRS’s). possible to enter the reference station coordinates in the local datum. As long as the baseline between the rover NETWORK RTK AND VIRTUAL REFERENCE and reference station is short, the coordinates output by STATIONS the rover can be used directly in the local datum without significant errors. Network RTK is an approach of using a network of reference receivers for centimeter level positioning In Network RTK the situation is more complicated. While [Raquet, 1998a and 1998b]. This method estimates the it is possible to have the reference stations in the local distribution of the differential carrier phase and datum, and thereby obtain rover coordinates in the local pseudorange errors over the area covered by the network.

The errors are used to compute corrections for the The reference station data is corrected to compensate for reference station data based on the location of the rover the differential errors associated with the rover location. receiver. To do this the Network RTK software needs to know the approximate position of the rover. In MultiRefTM the rover Figure 1 is a functional diagram for the MultiRefTM position is reported back using the GPGGA message Network RTK software. MultiRefTM is a Network RTK format (see Figure 2). The GPGGA message is part of the software currently being developed by the University of NMEA 0183 Standard for Interfacing Marine Electronic Calgary and Roberton Enterprises Ltd. Devices [NMEA, 1997]. Most GPS receivers support this format. GPS RS Network Control Centre Rover Virtual reference stations (VRS’s) are often used in GPS Rx Network RTK. A VRS is virtual because it does not Two-way connection (eg Mobile Phone) physically exist at the location reported by its coordinates. VRS function at control centre. It is generated using data from a real reference station and therefore has the same characteristics as a real reference station. From a GPS positioning algorithm point of view, GPS Rx RS Communication Broadcast TCP/IP (eg ASC) it is not technically necessary to use VRS’s but using Serial Com Port VRS function at Rover. Dial-up VRS’s offers several advantages. Some of these are:

1) The number of VRS’s that can be generated is Figure 1: Network RTK functional diagram limitless. 2) The virtual reference station can be placed anywhere The raw GPS data from the reference stations is within the network of reference stations. transmitted in real-time to a central processing computer 3) For large networks, the VRS can be tailored for a (the Control Centre in Figure 1). The differential specific broadcast area. ionospheric, tropospheric, and orbit errors are calculated 4) The virtual reference station can be used for for the region covered by the network. The RTK data is coordinate transformation between WGS84 and other sent to rover receiver via wireless communications, and is geodetic systems. corrected based on the location of the rover. Figure 3 shows a VRS placed relative to the rover receiver The communication with the rover can be bi-directional within a network of reference stations. (one rover per connection) or broadcast (multiple rovers receive the same data). Each method has their own advantages and these will be discussed later in the paper. RS1 RS2

Almost all RTK receivers use the RTCM standard for receiving reference station data [RTCM, 1998]. Figure 2 shows a diagram representing the data interface between the Network RTK system and the rover GPS receiver.

RTCM

GPS Rover Receiver GPGGA VRS RS3

RS5 Figure 2: Interface to GPS RTK receiver

The RTCM messages contain the L1 and L2 pseudorange and carrier phase measurements for a single reference RS4 station plus the reference station coordinates. MultiRefTM uses message types 18 and 19 for the measurement data and message types 3 and 22 for the VRS position. Figure 3: Virtual reference stations (VRS)

There are several methods for VRS placement. Some determined from the broadcast ephemerides are given in Network RTK software place the VRS directly on the user WGS84. position. This has a disadvantage because the rover receiver will think the reference station is very close and When performing absolute GPS single point positioning therefore may be over optimistic about solving using broadcast ephemerides the position will therefore ambiguities. As a result, more missed fixes (i.e. wrong also be given in WGS84. ambiguity solutions) are likely. ITRF The MultiRefTM software places the VRS on the line between the rover position and the nearest reference The International Earth Rotation Service (IERS) is in station. Using the distance to the nearest reference station charge of providing realizations of worldwide celestial as a guide, the distance between the VRS and the rover is and terrestrial reference systems for instance the calculated by the equation, International Terrestrial Reference System (ITRS), which is considered to be the best reference system defined to

DVRS = DRS/α (1) date. The ITRS is realized in the form of reference frames (ITRF) whenever necessary. where DVRS is the distance between the rover and VRS, DRS is the distance between the rover and nearest RS, and When GPS is used for geodetic and geodynamic purposes α is between 1.0 and 3.0 depending on the atmospheric where high accuracy is required, the ITRF is used as the conditions. reference frame, and the relative GPS positions are determined using precise orbit information e.g. from the REFERENCE SYSTEMS International GPS Service where the satellite positions are given in the ITRF. By using precise orbits and reference The advantage of using VRS’s to correct for coordinate station coordinates given in the ITRF at the same epoch in transformations is the main subject of this paper. Before time, geometrical misalignments are eliminated in the going further a discussion of reference system is positioning process, whereby the positions of the rover necessary. An increasing number of reference systems are will be free of any errors originating from reference frame being used for GPS positioning, and the following 5 mix-ups. sections describe the systems relevant for this paper. TRANSFORMATION BETWEEN WGS84 and ITRF WGS84 In 1996 and 1997 NIMA carried out a number of The World Geodetic System 1984 (WGS84) is a investigations with the purpose of the determining of set conventional terrestrial reference system defined to be of transformation parameters between ITRF94 and used in connection with GPS. The definition and WGS84 [Malys et. al, 1997a, and 1997b]. They came up realization of WGS84 is described in National Imagery with two sets of parameters for a 7-parameter datum and Mapping Agency (2000). transformation. The authors of the papers were however not completely satisfied with the results, and in the 1997b- WGS84 was originally realized, i.e. coordinates for a paper they are recommending that any transformation number of physical reference stations were determined in between the reference frames should be avoided because the reference frame, using the TRANSIT system in 1987. of the lack of statistical significance in the determination This realization of WGS84 was used until 1994 when a of the parameters. new GPS based realization was introduced called WGS84 (G730). This was based on data from a number of In this paper we are however using the parameters permanent GPS stations, including some IGS stations, and anyway, since they are giving an indication of the size of in the data processing the IGS stations were kept fixed at the translation and rotation between the two reference their ITRF92 coordinates. Thereby WGS84 became close frames to coincident with the ITRF92. ETRF In 1996 a new realization was introduced called WGS84 (G873), determined using the same procedure. This time The European Terrestrial Reference System (ETRS) was however the IGS stations were kept fixed at their ITRF94 introduced in Europe in 1990, and the first realization of coordinates. the ETRS was coincident with the ITRS at epoch 1989.0. But since ETRS is fixed to the Euroasian Tectonic Plate WGS84 was defined as the reference frame to be used in the reference system moves with the plate away from its connection with GPS and thus the satellite coordinates original definition.

3) Use WGS84 coordinates for the reference stations ETRS89 has been realized a number of times through and adjust the VRS coordinates to compensate for the connections to the ITRS, the first realization being coordinate transformation. ETRF89 and the latest being the ETRF2000. Method 1) may work as long as the difference between the ETRF92 epoch 1989.0 has during the 1990’ies been local system and WGS84 is small. When performing introduced in most European countries as the reference relative GPS positioning, where the reference station is frame for surveying and mapping, based on a located in a point with known position, the reference recommendation from the EUREF commission under the frame will be a combination of WGS84 and the reference International Association of the Geodesy. During the frame in which the coordinates for the reference station latest years the name EUREF89 has been adopted for this are given. If high accuracy positioning is carried out it is reference frame. The name originates from the first GPS thus important that the reference frame used for the survey campaign initiated by the EUREF commission in coordinates of the reference station is in a good 1989. concordance with the reference frame used for the satellite coordinates. If that is not the case a geometrical TRANSFORMATION BETWEEN WGS84 AND misalignment will be present in the positioning process, EUREF89 resulting in higher residuals for the positions of the rover.

Transformation of coordinates from WGS84 to EUREF89 Leick (1995) sets up a rule of thumb for this: can be carried out using the following three steps: db dR 1) Convert coordinates from WGS84 to ITRF94 (epoch = (2) 1997.2) using the 7-parameter transformation derived by b ρ Malys et al. (1997b) where db is the error in the baseline, b is the length of the baseline, dR is the error in the position of the reference 2) Convert coordinates from ITRF94 (epoch 1997.2) to station, and ρ is the distance from the satellite to the ETRF92 (epoch 1997.2) using the procedure given by reference receiver. Boucher and Altamimi (2001). Using Equation (2), Figure 4 plots the residual errors for 3) Convert coordinates from ETRF92 (epoch 1997.2) to reference station errors of 1, 10, and 100 metres. ρ is ETRF92 (epoch 1989.0) using the procedure given by assumed to be an average of 23000000 metres. Boucher and Altamimi (2001).

0.050 The size of the transformation in the last step is dependent 100 m 0.040 Reference Station on local crustal movements and station displacements, and Coordinate Error is therefore station (location) specific. 0.030

10 m

COORDINATE TRANSFORMATION USING (m) Error 0.020 Reference Station VIRTUAL REFERENCE STATIONS Coordinate Error 1 m 0.010 Reference Station Coordinate Error The GPS system is designed to provide user position 0.000 coordinates in the WGS84 reference system. The users 0 5 10 15 20 25 30 35 40 45 50 often need coordinates in a different geodetic reference Baseline Distance (km) frames. For example, in North America NAD83 is used Figure 4: Differential residual errors caused by for surveying and mapping purposes and in Europe most reference station coordinate errors countries use EUREF89. The residuals errors will affect both the network RTK In Network RTK this issue can be dealt with in several processing as well at the RTK processing in the user ways: receiver. The Network RTK software is attempting to estimate the differential errors within the network at sub- 1) Use reference station coordinates that are in the local centimetre level. Often the baseline distance within a system. Network exceed 50 km and for this reason it is safest to 2) Use WGS84 coordinates for the reference stations have the reference station coordinates in WGS84. and implement a transformation algorithm in the rover GPS receiver. Method 2) is the probably most ‘correct’ method to use. Establishing the rover coordinates in WGS84 will prevent

any modeling problems with the Network RTK software For any practical surveying and mapping purposes and the GPS receiver RTK processing. The drawback of WGS84 and EUREF89 are considered as being identical this method is that it requires the user to enter the local since the difference between the two systems is relatively transformation parameters into the GPS receiver and, small in Denmark. depending the on reference frame, the transformation is often not trivial. Using the above formulas for transformation of the coordinates from WGS84 to EUREF89, the difference Method 3) meets both requirements. The reference between the two reference frames can be determined. stations coordinates are left in WGS84 and the user is working in the regional or local reference frame. Figure 5 In Figure 6 the difference between WGS84 and EUREF89 illustrates this method. is shown for the six stations. The vectors in the plot indicate the size and direction of the horizontal difference. The difference in ellipsoidal heights is between 1 and 2 cm and is not shown in the plot because of the relatively VRSLocal small size compared to the horizontal differences. The RoverLocal horizontal coordinates are determined using the UTM map projection. The scale of the map and of the difference vectors are shown by means of scale bars in the plot. Coordinate Translation (∆X,∆Y,∆Z)

VRSWGS84 RoverWGS84

Figure 5: Coordinate Translation Using VRS’s

The coordinate difference (∆X, ∆Y, ∆Z) between the local system and WGS84 is calculated for the rover position. The coordinate difference is added to the VRS coordinates reported in the RTCM type 3 and 22 messages. Since the baseline geometry between the VRS and the rover remains the same and, because the distance between the stations is small, the same transformation will be realized in the rover position. Figure 6: Difference between WGS84 and EUREF89 With this method the transformation parameters and in Denmark reference station coordinates can be updated by the Network RTK service provider without inconveniencing The coordinate differences for the three components are the user. The coordinates of a given point on the ground given Table 1. will always be reported in the local earth fixed system. With transformation parameters continually being updated Table 1: Difference between EUREF89 and WGS84 the coordinates will remain the same for many years. Station ∆Northing ∆Easting ∆Height DISCUSSION OF METHOD [metre] [metre] [metre] STAG 0.172 0.130 0.015 EUREF89 was introduced in Denmark based on a five- HVIG 0.170 0.127 0.017 day survey campaign where coordinates for six reference stations (see Figure 6) were determined. The data MYGD 10.172 0.124 0.018 processing was carried out at the University of Bern VAEG 0.175 0.129 0.015 [Frankhauser and Gurtner, 1995]. TYVH 0.174 0.126 0.017

BUDD 0.176 0.127 0.016 The original six station network has now been densified so more than 500 national reference points are coordinated in EUREF89, which makes the reference frame easily Considering the rule of thumb given in Formula (2), an accessible for relative GPS positioning. error of 20 cm in the reference stations coordinates implies an error of about 1 mm in the rover station.

1924 also called the Hayford ellipsoid) made it possible to If the six stations in Figure 6 were used as reference define the new datum as a best possible fit to the actual stations in connection with a network RTK it could thus shape of the earth in Europe at the time. be expected that the rover positions would be experiencing 1 mm errors because of the inconsistency in Even though a number of combined adjustments have the reference station coordinates. been carried out in order to unify ED50 all over Europe, the datum should be considered as a different datum in the More important from a Network RTK software point of different countries where it has been realized, when it is view is to look the deformations within the network. Since being compared to WGS84 or EUREF89. geodetic systems like EUREF89 are earth fixed, orientation and scale within the network may change over The accuracy of ED50 is today suffering from the time. Table 2 lists the differences in the coordinate shifts accuracy of the observations forming the basis for the between EUREF89 and WGS84 for the six stations from realization of the datum. Since the accuracy of the Table 1. observations are poorer than the GPS observations used to realize EUREF89, the Danish realization of ED50 does Table 2: Coordinate error differences for EUREF89 suffer from a lot of tension or stress when compared to the realization of EUREF89. Station ∆Northing ∆Easting ∆Height [metre] [metre] [metre] Further the observations were mainly horizontal, making it STAG 0.000 0.000 0.000 in reality a two-dimensional datum. The height was later HVIG -0.002 -0.003 0.002 added as a third component through leveling.

MYGD 0.000 -0.006 0.003 Because of the big differences in accuracy between ED50 VAEG 0.003 -0.001 0.000 and EUREF89 in Denmark, a transformation between the TYVH 0.002 -0.004 0.002 two systems cannot be carried out with sub-centimeter accuracy using closed analytical formulas. The best 7- BUDD 0.004 -0.003 0.001 parameter transformation derived, gives a mean transformation error of 20 cm which is not sufficient for These values were calculated by taking the values for surveying purposes. station STAG and subtracting it from the values in Table 1. The conversion from EUREF89 to ED50 is therefore carried out using first the 7-parameter transformation for Table 2 shows that the difference between WGS84 and removing the main difference between the two systems. EUREF89 is relatively constant throughout Denmark, Then a transverse Mercator map projection is introduced, since there are no major crustal deformations going on and by applying a number of regionally defined regular and therefore all three methods outlined in the previous polynomials the coordinates are finally converted to the section could be used. UTM map projection (datum ED50). From here the coordinates can be converted to geodetic latitude and In other parts of the world with more crustal movements longitude in ED50 if necessary. Using this procedure the situation can be much different. Certainly in northern coordinates can be converted between EUREF89 and Norway and Sweden where there is large glacial rebound ED50 with a mean error of 1.6 cm in Denmark [Jensen affecting the heights (~1 cm/year) and some rotation and Madsen, 1998]. affecting the positions in the horizontal, we would not see a constant shift in the coordinates. Since centimetre level The transformation parameters are all derived using the positioning is required, relative shifts of a couple of original observations defining ED50 and EUREF89, and centimetres is significant and cannot be ignored. therefore the transformation accuracy is degraded considerable as soon as it is used outside the area covered A more severe example is to look at applying the method by the observations. to the European Datum ED50. ED50 is the predecessor to EUREF89 and was the datum used throughout Europe for By using this conversion procedure the height information mapping and some surveying purposes. is lost. But the height can be handled separately by introducing the known difference between the surfaces of ED50 was realized through astronomical observations, the reference ellipsoids of the two systems. and terrestrial distance and direction observations between the defining geodetic reference points. The observations, and the chosen ellipsoid (the International Ellipsoid of

In Figure 7 the difference between coordinates given in Using method 3) would work well as long as the baseline WGS84 and ED50 for the six Danish stations mentioned distance between the VRS and the rover receiver is short. before is shown. The plots in Figure 4 indicate that the baseline distance should not be more than 1 or 2 kilometres. This would limit the placement of the VRS to a small area relative to the rover. Since the VRS position can be updated frequently it would not be any problem for the Network RTK system to accommodate this requirement. The disadvantage would be that the baseline between the VRS and the rover would be quite short. As discussed earlier, this may degrade the ambiguity fixing performance of the rover.

Using ED50 is an extreme example since most countries have adopted more modern reference systems. There is however still a significant number of maps and other data which is referenced to these older systems and therefore their use is still relevant.

DISCUSSION OF IMPLEMENTATION ISSUES

The method of transforming coordinates using VRS’s is

straightforward. The implementation is more com- Figure 7: Difference between WGS84 and ED50 in plicated. The critical factor is whether the Network RTK Denmark. system in using a bi-directional or broadcast (one-way) communication with the rover receiver. The scales of the map and of the difference vectors are shown by means of scale bars in the plot. Bi-directional communication with the rover gives the most flexibility. The transformation calculations are done Table 3: Coordinate error differences for ED50 at the control centre and it does not matter whether the transformation algorithms are simple or complicated. The system can accommodate either. Station ∆Northing ∆Easting ∆Height

[metre] [metre] [metre] If the Network RTK system is using one-way broadcast STAG 0.000 0.000 0.000 communication with the rover, the implementation of HVIG -1.074 0.128 -0.686 using VRS’s for coordinate transformation is more MYGD -1.762 -1.527 -4.041 difficult. In this type of implementation the VRS function VAEG 0.342 -1.010 -1.648 is performed by the data receiver which receives the broadcast data from the control centre. Therefore in order TYVH -0.708 -1.142 -2.984 for this method to be used, the data receiver must have BUDD -0.145 -1.224 -3.290 access to the coordinate transformation information.

Table 3 lists the differences in the coordinate shifts One way of doing this is to upload the transformation data between ED50 and WGS84 for the six stations. These to the rover data receiver before going to the field. This values were calculated using the same procedure as Table may be possible for some users but not for all. Another 2. This shows that there are significant differences in scale way is to include the information in the data broadcast to and orientation between the two reference frames. For the rover. this reason, along with the overall shift in coordinates (see Figure 4), method 1) as described in the previous section The simplest and possibly the most efficient way to send would not work very well. this transformation data to the rover is to send the coordinate shift values for several points throughout the Converting coordinates from WGS84 to ED50 is a coverage area. The data receiver could then utilize a complicated procedure and would be difficult to simple interpolation algorithm to compute the coordinate implement in any RTK equipment. For this reason method shifts for a given user location. 2) would not be desirable.

If transforming coordinates between WGS84 and A further extension of this technique may be to use it for EUREF89 in Denmark, only a few points would be conversion from ellipsoidal heights to mean sea level required. Therefore including the information in the data heights. broadcast would be feasible. In the ED50 case the situation is much different. The amount of data that can be DISCLAIMER sent to the rover is limited due the data link bandwidth. This paper represents the opinion of the authors and does not represent the official policy of the National Survey Figure 8 shows the absolute coordinate differences and Cadastre - Denmark. between WGS84 and ED50 (colour coded) overlaid by a grid with 10 km spacing between the points. The weird REFERENCES features in the NW and NE of the plot arise because the grid points are located outside the area covered by the Boucher, C. and Z. Altamimi, (2001) Specifications for polynomials. reference frame fixing in the analysis of a EUREF GPS campaign, version 5: 125-04-2001. Memo from Observatoire de Paris, 2001.

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