Use of Multiple Reference GNSS Stations - CiteSeerX

Use of Multiple Reference GNSS Stations for RTK Positioning Gérard Lachapelle, M. Elizabeth Cannon, Luiz Paulo Fortes, and Paulo Alves Department of Geomatics Engineering, University of Calgary

BIOGRAPHY Dr. Gérard Lachapelle is Professor and Head of the Department of Geomatics Engineering where he is responsible for teaching and research related to positioning, navigation, and hydrography. He has been involved with GPS developments and applications since 1980. Dr. M. Elizabeth Cannon is Professor of Geomatics Engineering at the University of Calgary. She has been involved in GPS research and development since 1984, and has worked extensively on the integration of GPS and inertial navigation systems for precise aircraft positioning. Dr. Cannon is a Past President of the ION. Luiz Paulo Fortes holds a M.Sc. degree in Computer Science and is currently a Ph.D. student at the University of Calgary. He had been working for IBGE’s Department of Geodesy in Brazil since 1982 where he was responsible for the Research and Analysis division, and as the head of the department during the period 1995-98. Paulo Alves received a BSc in Geomatics Engineering from the University of Calgary in 2000 and is currently enrolled in the MSc program where he is focussing his research efforts on the use of multiple reference stations for RTK GPS. ABSTRACT The accuracy performance of carrier phase based realtime kinematic (RTK) DGPS positioning depends on the ability of the algorithms and software to resolve the integer ambiguities and to model the differential errors that occur between the reference station(s) and the remote. The use of a network of reference stations

is effective in enhancing the solution to both problems. An effective method called "NetAdjust" developed and tested at the University of Calgary during the past few years is reviewed. The use of this approach increases the minimum distance requirement between reference stations and remote through effective modeling of the differential errors, which are dominated by the ionospheric and tropospheric errors. The effectiveness of the method is demonstrated through a field test conducted in the St.Lawrence River region, Canada, to assess its viability for 3D marine navigation in constricted waterways. INTRODUCTION Carrier phase real-time kinematic (RTK) DGPS positioning can be performed using either an integer or a real number (float) ambiguity resolution approach. In order to resolve the ambiguities, many conditions must exist, including a relatively short distance (e.g. < 10 – 20 km) between the reference station and the mobile unit and relatively small differential errors between the two receivers. A dense network of reference receivers can be used to maintain the short distance requirement, but this approach is expensive and can be complex to implement operationally. A solution to this problem is to use a sparser network of reference receivers in an interactive manner to better model the differential errors. Thus the behavior of correlated errors (orbital and atmospheric) can be modelled throughout the region covered by the network, while the uncorrelated errors (multipath and noise) can be averaged out through filtering. The reference station density required with this approach is a function of the magnitude of the uncorrelated errors and the predictability of correlated errors. Early experiences suggest a decrease by a factor of two to three. The method described and used herein is the NetAdjust method developed at the University of Calgary during

Presented at the World Congress of the International Association of Institutes of Navigation, San Diego, June 26-28, 2000

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1996-98 [e.g. Raquet & Lachapelle 1997, Raquet 1998]. MULTI-REFERENCE STATION (MRS) APPROACH

The equations used to compute the corrections to the carrier-phase observables are as follows:

δˆl = C δl B T (BC δl B T ) −1 (BΦ − λ∆∇N)

is the covariance matrix of the carrier-phase observables collected at the reference stations, and

C δl r , δl is the cross-covariance matrix between the

The NetAdjust multi-reference station approach uses a linear least-squares predictor, namely least-squares collocation, to estimate the differential code and carrier phase errors in the region covered by the network of reference stations [Raquet 1998, Raquet et al., 1998a; Townsend et al., 1999]. The principle of the method is that as long as the code and carrierphase observable errors are predicted using a leastsquares principle, it is possible to resolve integer ambiguities over longer distances, which increases the achievable accuracy of the user.

δˆl r = C δlr ,δl B T (BC δl B T ) −1 (BΦ − λ∆∇N)

C δl

(1) (2)

where δˆl r

is the correction vector to carrier-phase observables collected at the user receiver, in metres,

δˆl

is the correction vector to carrier-phase observables collected at the reference stations, in metres,

Φ

is the measurement-minus-range carrier-phase observable ( Φ = Φ − ρ ), in metres, assuming that the reference station coordinates are known in order to compute the geometric range ρ

∆∇N is the double difference integer ambiguity vector

between the reference stations (assumed to be known), in cycles

λ

is the carrier-phase wavelength, in metres

B

is the double difference matrix ( B = ∂∆∇ Φ / ∂Φ ) (made up of the values +1, -1 and 0)

carrier-phase observables collected at the user receiver and at the reference stations. The above equations can be derived using the principle of least-squares prediction (collocation), as shown by Fortes [1998]. Examining Eq. (1) and (2), it can be seen that the double difference ambiguities between the reference stations must be known, along with precise coordinates for the reference stations. It is important to note that these ambiguities can either be solved either as integer or real numbers. Integer ambiguities are expected to yield a higher level of performance. However, if the integer ambiguities cannot be resolved because the inter-reference station distance and/or the differential errors are too large, the real number ambiguities in the network can be used and converge to the integer ambiguities over time. (The convergence time is tens of minutes to hours, depending on the network configuration and other parameters). The method is therefore very robust in that sense. Once error corrections to the measurements for the reference stations and the mobile user have been estimated, the ambiguities between the user and anyone reference station can be resolve either as integer or real numbers. Since the errors are estimated at every reference station, the use of anyone reference station will yield the same level of accuracy. This singular advantage further increases the robustness of the real-time differential corrections. Once the measurements have been corrected by the estimated errors at both a reference station and at the user station, a standard ambiguity resolution method can be used. The spatial decorrelation of carrier phase errors in a reference station network was investigated by Fotopoulos & Cannon [2000]. The covariance matrices C δl and C δl r , δl are also required to apply NetAdjust (this is actually a requirement of least-squares prediction). The procedure used to determine the ambiguities is described in the next sections. Raquet [1998] and Raquet et al. [1998b] describe how to derive the covariance function that supports the computation of the covariance matrices.

Presented at the World Congress of the International Association of Institutes of Navigation, San Diego, June 26-28, 2000

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FIELD TEST An observation campaign was undertaken in August 1999 in the St.Lawrence River Region to assess the multi-reference station approach. From August 2 to 7, four temporary NovAtel MiLLennium GPS receivers were used in Grand-Mère, Deschaillons, Thetford-Mines and Sorel, in addition to the CCG radiobeacons located in Lauzon, Trois-Rivières and St-Jean-sur-Richelieu, as shown in Figure 1. All stations were static, as simulating any of the reference stations as a “user” was deemed to be adequate to illustrate the concept. Relatively short baselines were involved in this test, as a way to overcome remaining differential errors mainly due to the ionosphere. Since all observations were made in the static mode, a data rate of 15 s was used for the data reduction. The ionosphere was found to be relatively active during the test, with a RMS differential effect of 2 to 3 ppm and a maximum differential effect in excess of 7 ppm in the position coordinate domain.

generate network corrections. Since Grand-Mère is the closest station to Trois-Rivières, the 30-km baseline defined by these two stations was processed using single and multi-reference station observations. (Actually the selection of the closest reference station is necessary for the single-reference station approach, whereas for the multi-reference station approach, the use of any reference station with corrected observations gives the same results). The second configuration (Figure 2b), implemented to test the impact of the method when using longer baselines, consisted of choosing Deschaillons as the “user”, with all the remaining stations but Trois-Rivières used to compute network corrections. Grand-Mère was again the closest station to Deschaillons and then, the 46-km baseline formed by these two stations was processed using successively the single and multiple reference station approach. 47oN Lauzon

Two days for which all seven stations were simultaneously tracking satellites were selected for processing and analysis, namely August 4 and 5. The QC program [UNAVCO, 1994] was used as a preprocessing step and showed a high data quality in general. The Bernese GPS Software, version 4.0, [Rothacher and Mervart, 1996] was used to reduce the GPS data in order to generate precise coordinates for the new reference stations, and to resolve integer ambiguities between the reference stations. Most of the L1 and L2 integer ambiguities were resolved. The covariance function described in Fortes et al. [1999] was used.

Grand-Mère

40'

30 km 20'

64 km

77 km

33 km

Deschaillons Trois-Rivières

Thetford-Mines

Sorel

46oN

79 km

82 km 40'

20'

St-Jean-sur-Richelieu

Improvement Using the Multi-Reference Station Approach Comparisons between the Single Reference Station and Multi-reference Station approaches were made for the observation, position and ambiguity domains. The objective was to assess how much improvement the multi-reference station approach produces over the single reference station approach. To assess the improvement using the multiple reference station approach, two network configurations were analyzed, as shown in Figure 2. In the first configuration (Figure 2a), Trois-Rivières was treated as the “user” receiver and all the remaining stations acted as reference stations to

45oN30'

73oW

30'

72oW

30'

71oW

Figure 1: Reference Network for August 1999 test In the observation domain, the single reference station (raw) L1 and WL double difference misclosures were compared with those generated after applying the corrections. The RMS values of the single and multireference station misclosures for Grand-Mère to Trois-Rivières (30 km) and Grand-Mère to Deschaillons (46 km), as well as the improvement percentage are shown in Table 1. The improvement obtained using the multi-reference station approach is 50%. The agreement between the two days was found

Presented at the World Congress of the International Association of Institutes of Navigation, San Diego, June 26-28, 2000

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to be excellent. With this network density and layout the results are improved with respect to previous ones using a more sparse reference network (November 1998 test in Fortes et al. [1999]). Figure 3 shows the double difference L1 and WL misclosures using single and multi-reference station observations for GrandMère to Trois-Rivières on August 5.

Table 1: Single (SRS) and multi-reference (MRS) station Improvement in Observation Domain – Double Difference Misclosures L1 RMS (cm) SRS MRS Imprv 5 2.5 50%

WL RMS (cm) SRS MRS Imprv 7 3.5 50%

47oN Lauzon Grand-Mère

40'

30 km 20'

Deschaillons Trois-Rivières Thetford-Mines

Sorel

46oN

40'

20'

St-Jean-sur-Richelieu 45oN30'

o

73 W

30'

o

72 W

30'

o

71 W

(a) o

47 N Lauzon Grand-Mère

40'

46 km

Deschaillons 20'

Thetford-Mines

Sorel

46oN

40'

20'

St-Jean-sur-Richelieu 45oN30'

73oW

30'

72oW

30'

71oW

(b) Figure 2: Network configurations used to test the improvement brought by the multi-reference station approach. The “user” stations are represented as a square and the shown baselines connect them to the closest reference network station

Figure 3: Single and multi-reference station L1 and WL double difference misclosures for Grand-Mère to Trois-Rivières baseline (30 km) - Aug 5, 1999 In the position domain, the known double difference integer ambiguities (resolved previously) were used, since the objective was to verify how much improvement the method brings independent of the ambiguity fixing process. Single and multi-reference station observations were used in FLYKIN, an OTF software program developed at the University of Calgary [Lu et al, 1994]. In order to use the known ambiguities, the software was modified to read ambiguities from a file instead of trying to resolve them. Coordinates of Grand–Mère and Deschaillons, computed by FLYKIN using single and multireference station observations for August 4 and 5 were compared with the known values. The results are summarized in Table 2. The multi-reference station approach improves the results by up to 60%. Table 2: Single (SRS) and multi-reference (MRS) station Position Domain Performance L1 RMS (cm) WL RMS (cm) Coord

Lat Lon Hgt

SRS

MRS

Imprv

SRS

MRS

Imprv

5 5 8

3 2 5

40% 60% 38%

6 6 10

4 3 7

33% 50% 30%

Presented at the World Congress of the International Association of Institutes of Navigation, San Diego, June 26-28, 2000

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The fixed integer WL mode with the multi-reference station approach, which would be the easiest integer mode to use operationally, yields an RMS agreement better than 10 cm for any coordinate component. Because the differential effects of the atmosphere and orbital errors were modeled effectively with the multireference station approach, the use of ionospheric-free observables, while still improving the accuracy by a few cm, is not critical. For the ambiguity domain analysis, both baselines were processed using single and multi-reference station observations for the two 24-hour periods with the ambiguity computations re-starting every ten minutes in order to generate about 144 samples for each day. FLYKIN Suite [GEOsurv, 1999] was used for this purpose. The resolved integer ambiguities were then compared with the ones obtained independently with the Bernese software in a batch mode. The results for the WL integer ambiguities, which are summarized in Table 3, show the improvement in terms of percentage of corrected fixes, mean number of epochs to fixed ambiguities and percentage of ambiguities reliably converted to L1. It can be seen that, by using the multi-reference approach, improvements in all three types of comparisons are achieved. The percentage of corrected fixes, even using single reference observations, was above 88%, which can be explained by the use of WL observables over relatively short baselines. The conversion to L1 ambiguities is important if one wants to derive accurate IF solutions. Resolution of L1 integer ambiguities is however relatively difficult due to an unfavorable ratio between wavelength and differential errors. This is why the success rate was only 21% or less when using the SRS approach. The use of the MRS approach improved L1 ambiguity resolution by about 10%. Table 3: Ambiguity domain improvement % of corrected fixes of WL ambiguities

Mean number of epochs (15 s interval) to fix WL ambiguities

% of WL ambiguities reliably converted to L1

SRS 92%

SRS 12

SRS 19%

MRS 95%

MRS 9

MRS 28%

In order to assess if and how much accuracy degradation occurs in the position domain when using real number ambiguities, two additional tests were performed using the two network configurations

described earlier and shown in Figure 2. The two configurations were used to generate real number ambiguity corrections. The real number ambiguities were computed in batch mode. The use of a batch mode should be representative of the real-time case after the network ambiguities have been “initialized”. In the first test, real number ambiguities in the network were first estimated. Fixed integer solutions between one of the reference stations, namely GrandMère, and the two stations selected as users, namely Trois-Rivières and Deschaillons, were then computed using successively the single reference and multireference station approach. A correct integer ambiguity file was provide to FLYKIN™ to perform the computations in order to assess the improvement in the position domain, with no external influence from the ambiguity resolution process. The results are summarized in Table 4. The position coordinate RMS agreement is better than 5 cm in all cases. The average improvement over the single reference station mode, whose results are summarized in Table 2, is about 37%. When network integer ambiguities were used (Table 2), the average improvement was about 42%. This shows that the accuracy degradation is minimal when network real ambiguities are used. This provides more operational flexibility. Table 4: Single (SRS) and multi-reference (MRS) station Position Domain Improvement Using Real Number Ambiguities in the Network L1 RMS (cm) WL RMS (cm) Coord

SRS

MRS

Imprv

SRS

MRS

Imprv

Lat Lon Hgt

5 5 8

3 2 6

40% 60% 25%

6 6 10

4 3 7

33% 50% 30%

In the second test, the Grand-Mère to Trois-Rivières baseline was processed using the real number ambiguity mode, with both the SRS and MRS approaches. In the latter case, the integer and real ambiguity mode were successively used to derive the network corrections. The results were derived using GPSurvey™ [Trimble, 1996] and are summarized in Table 5. Since a continuous sequence of 24 hours of data was processed, the single reference station approach is likely to yield optimistic results. Nevertheless, the multi-reference station approach yields an average improvement of about 28% to 40% over the single reference station approach. The improvement when using integer ambiguities instead of real number values in the network is only about

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7%. The IF RMS results with the MRS approach, not shown in the Table, are 2 cm in the latitude and longitude component, and 5 cm in the height component. A comparison of the real number ambiguity results with those obtained when using integer ambiguities everywhere (Table 2) shows a degradation of 16%, for the same baseline in the same day.

GEOsurv Inc., for his help on using FLYKIN Suite for this special application.

Table 5: SRS and MRS Position Domain Improvement Using Real Number Ambiguities Between the Reference Station and User

Fortes, L.P., G. Lachapelle, M.E. Cannon, G. Marceau, S. Ryan, S. Wee and J. Raquet (1999) Testing of a Multi-Reference GPS Station Network for Precise 3D Positioninng in the St.Lawrence Seaway. Proceedings of GPS99 (Session A4, Nashville, 14-17 September), The Institute of Navigation, Alexandria, VA., 12591269[http://www.ensu.ucalgary.ca/GPSRes/multire f. html]

L1 RMS (cm) Coord SRS MRS Improv Integer Number Ambiguities in the Network Lat 4 3 36% Lon 4 2 41% Height 12 9 29% Real Number Ambiguities in the Network Lat 4 3 28% Lon 4 3 28% Height 12 9 28% CONCLUSIONS The results of the test demonstrate the improvement brought by the multi-reference station approach over the single-reference station case in all of the observation, position and ambiguity domains. Although the percentage improvement is significant, the absolute improvement is small in this case, due to the relatively dense network configuration. With a sparser network, the absolute improvement would be larger. Since this work was carried out, sophisticated software to resolve the network ambiguities (e.g. Sun et al 1999) and to estimate measurement corrections in real time has been completed and is being tested using a variety of network configurations. ACKNOWLEDGMENTS The authors would like to express their gratitude to Kyle O’Keefe and Jayanti Sharma, from the University of Calgary, for the data collection; to Hua Huang, Georgia Fotopoulos and Anna Jensen, from the University of Calgary, for their valuable help during the processing phase; and to Paul Mrstik,

REFERENCES Fortes, L. P. (1998) GPS Kinematic Carrier-Phase Positioning Collocation. ENGO629 Minor Seminar, Department of Geomatics Engineering, Univ. of Calgary.

Fotopoulos, G., and Cannon, M.E. (2000) Investigation of the Spatial Decorrelation of GPS Carrier Phase Errors Using a Regional Reference Station Network. Proc. of World Congress of International Association of Institutes of Navigation, (San Diego, June 25-28), Inst. of Navigation, Alexandria, VA. GEOsurv. Flykin Suite & Flykin Suite+ User’s Manual, Rev. 1.12 (1999) GEOsurv Inc., Nepean, Ontario.. Lu, G., Cannon, M. E., Chen, D., Lachapelle, G. (1994) FLYKIN Operator’s Manual, Version 2.0. Department of Geomatics Engineering, The University of Calgary. Raquet, J. (1998) Development of a Method for Kinematic GPS Carrier-Phase Ambiguity Resolution Using Multiple Reference Receivers. PhD Thesis, UCGE Report Number 20116, University of Calgary [http://www.geomatics. ucalgary.ca/GradTheses.html] Raquet, J., and G. Lachapelle (1997) Long-Distance Kinematic Carrier-Phase Ambiguity Resolution Using A Reference Receiver Network. Proceedings of GPS97 (Session B6), The Institute of Navigation (Kansas City, 16-19 September), The Institute of Navigation, 1747-1756. [http://www.ensu.ucalgary.ca/GPSRes /multiref.html] Raquet, J., Lachapelle, G., and Melgård, T. (1998a) Test of a 400 km x 600 km Network of Reference Receivers for Precise Kinematic Carrier-Phase Positioning. Proceedings of GPS98 (Session A5,

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Nashville, 15-18 September), The Institute of Navigation, 407-416. [http:// www.ensu. ucalgary.ca/GPSRes/multiref. html] Raquet, J., Lachapelle, G., Fortes, L. P. (1998b) Use of a Covariance Technique for Predicting Performance of Regional Area Differential Code and Carrier-Phase Networks. In Proceedings of the 11th International Technical Meeting of the Satellite Division of the Institute of Navigation, Nashville, September. [http://www.ensu.ucalgary. ca/GPSRes/multiref. html] Rothacher, M., Mervart, L. Bernese (1996) GPS Software, Version 4.0. Astronomical Institute, University of Bern. Sun, H., T. Melgard and M.E. Cannon (1999), Realtime GPS Reference Network Carrier Phase Ambiguity Resolution, Proceedings of the ION National Technical Meeting, San Diego, January 25-27, pp. 193-199 [http://www.ensu.ucalgary.ca /GPSRes/multiref.html]

Townsend, B., Lachapelle, G., Fortes, L. P., Melgård, T., Nørbech, T., Raquet, J. (1999) New Concepts for a Carrier Phase Based GPS Positioning Using a National Reference Station Network. Proceedings of the National Technical Meeting, The Institute of Navigation, San Diego. [http://www.ensu.ucalgary.ca/GPSRes/multiref.html]

Trimble. GPSurvey Software User’s Guide (1996) Surveying & Mapping Division, Trimble Navigation Limited, Sunnyvale. UNAVCO. QC v3 Users Guide (1994) University NAVSTAR Consortium, Boulder.

Presented at the World Congress of the International Association of Institutes of Navigation, San Diego, June 26-28, 2000

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