New Concepts for a Carrier Phase Based GPS Positioning ... - CiteSeerX

New Concepts for a Carrier Phase Based GPS Positioning Using a National Reference Station Network Bryan Townsend, Kværner Marine Automation Gérard Lachapelle and Luiz Paulo Fortes, The University of Calgary Tor Egil Melgård, Kværner Marine Automation Torbjørn Nørbech, Norwegian Mapping Authority Captain J. Raquet, AFIT, Wright-Patterson AFB

BIOGRAPHY Bryan Townsend received his B.Sc. in 1989 and M.Sc. in 1993 from Geomatics Engineering , the University of Calgary. He has experience in several areas of GPS and surveying. Currently he is under contact to Kvaerner Marine Automation as the development coordinator for a wide area RTK system. 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. Luiz Paulo Fortes, holds a MSc degree in Computer Science applied to Cartography. He is currently a PhD student at the University of Calgary. He has been working during the last 16 years for Brazil’s IBGE’s Department of Geodesy where he was responsible for the Research and Analysis branch. Tor Egil Melgård graduated in 1994 from the Norwegian Institute of Technology (NTH) with a Master degree in electrical engineering. Since then he has continued his work in the area of GPS and navigation. Currently he is employed at Kværner Marine Automation (KMA) located near Oslo, Norway, where he is Project Manager for the development of a Wide Area RTK system for Norway. Torbjørn Nørbech graduated in 1976 from the Norwegian Institute of Technology (NTH) with a Masters degree in photogrammetry. Then he was a research assistant and a lecturer at the same institute, and received a Ph.D. in 1982. Since 1983 he has been working at the Norwegian Mapping Authority. Currently he is responsible for the SATREF® system.

Captain Raquet is an assistant professor in the Department of Electrical and Computer Engineering at the Air Force Institute of Technology, where he is responsible for teaching and research related to GPS and inertial navigation systems. He received his Ph.D. in Geomatics Engineering from The University of Calgary, an M.S. in Aero/Astro Engineering from MIT, and a B.S. in Astronautical Engineering from the U.S. Air Force Academy. ABSTRACT Kværner Marine Automation (KMA) along with the Norwegian Mapping Authority (NMA) has put together a project to deploy a national DGPS RTK service in Norway. The project, named DeciPos, was initiated in early 1997. DeciPos is an augmentation to the existing GPS reference station network (SATREF®) operated by SK. SATREF® currently consists of 10 reference stations linked with high-speed data lines to a control center in Hønefoss, Norway. The GPS methodology incorporated in DeciPos is being developed in close cooperation with the University of Calgary. This approach uses a network of GPS reference stations to correct for the effect of correlated atmospheric and orbital errors on RTK positioning. Previous work has shown that a network approach provides more RTK coverage per reference receiver than the traditional single reference station approach. A comparison of data collected in September 97 and September 1998 shows that the method proposed is stable despite the increase in the level of ionospheric activity. Some real-time implementations issues are discussed. The latency of carrier phase data corrections based on the network is shown to have little effect on the quality of the results.

INTRODUCTION Kværner Marine Automation (KMA) along with the Norwegian Mapping Authority (SK) have teamed together on a project to deploy a national DGPS RTK service in Norway. RTK implies the service provides for carrier phase based GPS positioning. The project, named DeciPos, was initiated in early 1997. The service will be completed in stages starting with southern Norway until the entire country is covered. The service will provide essentially two levels of positioning accuracy – sub-metre and sub-decimetre. The sub-metre accuracy equates to a position solution where the carrier phase ambiguities are left floating and not fixed. Similarly, the sub-metre accuracy equates to a position solution where the carrier phase ambiguities are fixed. These accuracies will meet the requirements of a wide variety of user groups involved in land, marine, and air applications.

They are Trondheim (Tron), Oslo, Kristiansand (Kris), Stavanger (Stav), Bergen (Berg), and Alesund (Ales). These stations cover an area of 400 km in the east-west direction and 600 km in the north-south direction. The GPS methodology incorporated in DeciPos is being developed in close cooperation with the University of Calgary. This approach uses a network of GPS reference stations to correct for the effect of correlated atmospheric and orbital errors on RTK positioning. The following section briefly explains the methodology behind this approach. THE NETWORK RTK APPROACH The Network RTK or DeciPos approach method is an approach for using a network of reference receivers for centimeter level positioning [1,2]. This method corrects the reference receiver measurements, as opposed to providing differential range corrections to be applied to the mobile receiver's measurements. With this approach, all of the information from the reference receiver network is “encapsulated” into the measurements from a single reference receiver. Standard differential positioning or ambiguity resolution is then performed between a mobile receiver and one of the adjusted reference receivers, as shown in Figure 2. 1) Calculation of Measurement Corrections Raw Measurements Reference 1 Reference 2 …Reference n

Corrected Measurements Computation Point

Reference 1 Reference 2 …Reference n

2) Ambiguity Resolution Raw Measurements Mobile Receiver (near Computation Point)

Figure 2:

Figure 1:

Map of Norway

DeciPos is an augmentation to the existing GPS reference station network (SATREF®) operated by the Norwegian Mapping Authority. SATREF® currently consists of 11 reference stations linked with high-speed data lines to a control center in Hønefoss, Norway. The current evaluation and analysis is based on six stations based in southern Norway. These stations are shown in Figure 1.

Corrected Measurements Reference n

The Network RTK Approach

This method is attractive from an implementation point of view, because it can be used with existing code or carrierphase differential positioning software that utilizes single reference receiver raw measurements. After the network adjustment is completed, the corrected measurements are essentially more accurate versions of the original raw measurements (with the errors reduced by the network). This distinction is especially important for network carrierphase ambiguity resolution, because all ambiguity resolution algorithms require some form of the ``raw'' measurements from both the mobile and reference receivers. Additionally, only one set of integer ambiguities must be calculated (as opposed to calculating

the ambiguities between the mobile receiver and all of the reference receivers). Other advantages of the basic network RTK approach are as follows: 1) 2)

3)

4)

5)

6) 7)

It can be used to reduce both code and carrier-phase differential measurement errors. It is performed on an epoch by epoch basis, so there are no assumptions about error dynamics and there is no required initialization time. It can be performed in real-time. All that is required to do this is to combine the data from each of the reference receivers together in real-time, which is generally not difficult because the reference receivers are at fixed locations on the ground. Errors (including multipath) are isolated and assigned to specific measurements. This can provide insight into the cause of the multipath at a reference receiver site. It is computationally efficient. For each computation point, a measurement vector is multiplied by a single matrix which is only periodically recalculated. It can be used with measurements from any GPS receiver that outputs raw measurements. It can be used in combination with other multipath reduction methods.

The algorithm is based upon a linear minimum variance of error estimator which minimizes the differential error between a mobile receiver located at the specified “computation point” and any of the reference receivers. At the heart of this estimator is a differential measurement error covariance matrix which describes the second moment (covariance) DGPS error statistics for the network. The parameters used to calculate this covariance matrix are determined by the measurements from the network itself. Essentially, by analyzing the differential measurement errors between each of the reference receivers (which are at known locations), it is possible to characterize the spatial characteristics of these errors over the entire network. This procedure is described in more detail in [1,3]. By embedding the DGPS error characteristics within the covariance matrix, the network RTK method does not require any explicit parameterization of the errors themselves as a function of position. Figure 2 represents the use of network RTK for positioning a mobile receiver which is located in the vicinity of the “computation point” (i.e., the point for which the differential errors are minimized). These corrections applied to the reference receiver measurements change as the computation point changes. In order to handle the general case where the mobile receiver can be anywhere within the network, it is necessary to calculate

the corrections for a number of computation points spaced throughout the network. The mobile receiver then interpolates the corrections from the closest computation points to calculate the exact correction for its particular location. As stated above, the methodology can be used for both code and carrier-phase measurements. When applying to carrier-phase measurements, the double difference integer ambiguities between the reference receivers must be calculated and accounted for in the measurement double differences. It is important to recognize that the network RTK method generates corrections for every raw measurement, as opposed to double differenced measurements. In order to perform double differencing of the corrected measurements, the corrections would first be applied to the individual measurements, and then the measurements would be double differenced. This is useful from an operational point of view because there are no assumptions about which base satellite should be used and any double difference combination can be generated. COMPARISON BETWEEN SEPTEMBER 1997 AND SEPTEMBER 1998 Previous results [2] showed that the network RTK approach is able to significantly reduce errors associated with atmosphere and orbit. The data used for this evaluation was collected in September 1997. The results are based on a 24-hour data set that was collected from the five of the six permanent reference stations shown in Figure 1 plus some additional temporary stations. The Olso station was not used because of data collection problems. The temporary stations were placed in such a way as to densify coverage in the middle of the reference station network. To further the evaluation, a second 24hour data set from September 1998 was analysed and is presented here. There were no temporary stations added to the network for this test. Since both data sets from were collected at the same time of year it is expected (but not assumed) that the tropospheric conditions are similar. The same is not expected for the ionosphere however. Figure 3 (adapted from [4]) shows the sunspot numbers for solar cycles 21 and 22 plus the predicted sunspot numbers for the first part of solar cycle 23. As indicated in the figure the solar cycle was near a low in September 1997 whereas it has significantly increased in September 1998. The effect this might have on the network RTK approach is of particular interest.

Sept 98

The correlated error function plots the variances of the errors as function of baseline length. As the baseline length increases so does the error variance. This indicates how much the errors decorrelate with baseline length. The results show that the difference between 1997 and 1998 is small. Therefore the increase in solar activity did not cause signigicant spatial decorrelation due to the ionosphere.

Sept 97

L1 Mapping function 8

Figure 3:

7

Solar Cycles 21,and 22 Plus 23 Predicted

6 Mapping function

L1 correlated error function

Variance of the correlated errors (L1 cycles2)

0.25

0.2

5 4 3 2

Sept 98 Sept 97

0.15 1

0.1

0 10

Sept 98

20

30

40 50 60 70 Elevation of lower satellite (deg)

80

90

Sept 97

Figure 6:

0.05

Mapping Function for L1 Carrier Phase Observables

0 0

Figure 4:

100

200

300 Distance(km)

400

500

600

WL Mapping function 8

Correlated Error Function for L1 Carrier Phase Observables

7 6 Mapping function

WL correlated error function

Variance of the correlated errors (WL cycles2)

0.018 0.016 0.014 0.012

5 4 3 2

0.01

Sept 98 Sept 97

1

0.008 0.006

0 10

Sept 98

0.004

Sept 97

Figure 7:

0.002

20

30

40 50 60 70 Elevation of lower satellite (deg)

80

90

Mapping Function for Wide Lane Carrier Phase Observables

0 0

Figure 5:

100

200

300 Distance(km)

400

500

600

Correlated Error Function for Wide Lane Carrier Phase Observables

Figures 4 and 5 show the correlated error function plots for the L1 and wide lane (WL) carrier phase observables respectively. The results are given for both the 1997 and 1998 data sets.

Figures 6 and 7 show the L1 and WL mapping functions for the September 1997 and September 1998 data sets respectively. A mapping function is calculated from the data and it is plotted as a function of the satellite elevation angle. The value of the mapping function is the ratio of the satellite measurement error at a give elevation angle to the measurement error for a satellite at the zenith. The mapping function value at 90 degrees elevation angle is always 1.

As can be seen from the results there is a marked increase in the mapping function from 1997 to 1998. This indicates the ionospheric error has grown in size. The next step in the analysis is the calculation of the double difference (DD) misclosure errors for uncorrected and corrected measurements. The misclosure error is the residual difference between the calculated DD measurements (from the known coordinates and carrier phase ambiguities) and the observed measurements. This was already done for the 1997 data and needs to be carried out for the 1998 data. For this analysis one of the reference stations is left out of the network correction calculations. The reference station then acts as a rover receiver. Figure 9:

Figure 8:

Alesund to Trondheim Baseline

In the first case presented, Ales is the reference station that has been removed from the computation of the network RTK corrections. It is represented as a square in Figure 8. To calculate the measurement misclosures the closest reference station in the network is used as this baseline would be used in a single reference station approach. Tron at a distance of 232 km is the closest reference station to Ales. It should be noted here that using the closest reference station for DD only impacts the calculation of measurement misclosures in the uncorrected case. When the measurements are corrected any of the reference stations in the network could be used and similar results would be produced.

Uncorrected Wide Lane Doubl e Difference Misclosures for Ales to Tron Baseline

Figure 10: Corrected Wide Lane Double Difference Misclosures for Ales to Tron Baseline Figure 9 shows the WL DD misclosures for uncorrected measurements and similarly Figure 10 shows the WL DD misclosures for corrected measurements. The uncorrected data shows significantly larger misclosures. Also the diurnal effects of the ionosphere can be seen as the size of the misclosures increases. This trend is not seen in the misclosures for the corrected data indicating that the network RTK algorithms adequately model these effects. It should be noted that the data gaps apparent in the plots was caused by a data collection problem and is not a problem with the method. In a similar manner Berg is the reference station that has been removed from the computation of the network RTK corrections. It is represented as a square in Figure 11.

The closest reference station is Stav at a distance of 143 km.

Figure 13: Corrected Wide Lane Double Difference Misclosures for Berg to Stav Baseline

Figure 11: Stavanger to Bergen Baseline As before Figure 12 shows the WL DD misclosures for uncorrected measurements and similarly Figure 13 shows the WL DD misclosures for corrected measurements.

The results for four baselines from September 1998 are compiled in Table 1. Listed are the RMS error misclosures for L1 code, L1 carrier phase, and WL carrier phase observables for the corrected and uncorrected (raw) cases. The ‘Test Network’ column indicates which of the reference stations was left out of the network correction calculations and used as the rover receiver. The number beside the name indicates the distance in kilometres to the nearest reference station. The results show a 25 to 50 percent reduction in errors for L1 carrier phase and WL observations. The L1 code results do not show as significant of improvement. This is because multipath is a more dominant error source in code measurements and it is usually not correlated between reference stations.

Figure 12: Uncorrected Wide Lane Double Difference Misclosures for Berg to Stav Baseline Difference between the corrected and uncorrected cases is less significant than in the previous case. This most likely is due to the fact that the nearest reference station is much closer. Still the diurnal effect is visible and there is an marked decrease in the size of the misclosures.

To further analyse the results, Table 2 contains results from the September 1997 data collection campaign [1]. Although the 1997 reference station network was denser we see similar results to 1998 for L1 carrier phase and WL carrier phase measurements. The effect of the ionosphere does not appear to be significant. The L1 code results for 1997 and 1998 do not compare as well. This is probably due the fact that in 1997 many of the GPS receivers did not have choke ring antennas and therefore the overall error is larger. The results so far have shown the validity of the network RTK method. They have been derived from postprocessed data. The next section begins to deal with some of the real-time implementation considerations.

Table 1:

Double Difference RMS error comparison between raw and corrected data for L1 code, L1 phase and Wide Lane phase measurements

Test Network

BERG-143 KRIS-170 ALES-232 OSLO-232 Table 2:

L1 Code (m)

L1 Phase (cycles)

Raw

Corr.

Imprv

Raw

Corr.

Imprv

Raw

Corr.

Imprv

0.40 0.34 0.57 0.36

0.35 0.29 0.36 0.31

13% 14% 37% 16%

0.387 0.525 0.612 0.619

0.201 0.403 0.379 0.369

48% 23% 38% 40%

0.108 0.124 0.171 0.171

0.064 0.092 0.077 0.114

41% 26% 55% 33%

Table with results for September 97 data obtained from reference 2

Test Network

ARER-0 GEIR-29 ARER-67 STAV-143 GEIR-164 GEIR-223s ALES-242

L1 Code (m)

L1 Phase (cycles)

WL Phase (cycles)

Raw

Corr.

Imprv

Raw

Corr.

Imprv

Raw

Corr.

Imprv

1.09 0.92 1.34 1.17 1.15 0.97 1.96

0.89 0.61 0.90 0.86 0.62 0.66 1.89

18% 34% 33% 26% 46% 32% 4%

0.081 0.180 0.301 0.455 0.560 0.707 0.794

0.090 0.154 0.226 0.260 0.297 0.332 0.461

-10% 15% 25% 43% 47% 53% 42%

0.041 0.053 0.096 0.135 0.165 0.190 0.236

0.041 0.048 0.077 0.081 0.088 0.095 0.134

0% 9% 20% 40% 47% 50% 43%

IMPLEMENTATION CONSIDERATIONS Figure 14 shows the major components of DeciPos. The data from the reference stations is transmitted to the control centre. The network RTK corrections are computed and they are, along with raw GPS reference station data, broadcast to the user. The data from only one reference station needs to be broadcast. Calculation of corrections

Data Broadcast RTCM and Network RTK Data User Data Receiver

Reference Stations

Figure 14:

WL Phase (cycles)

DeciPos Approach Block Diagram

The SATREF® system has high speed lines connecting the control centre to the reference stations and the control centre has large computers capable of computing the network corrections quickly. It is expected that the computations will be made within 1 to 2 seconds.

The data broadcast is much more limited. The bandwidth available is in the range of 2400 to 4800 baud. Since the size of the correction data is expected to be quite large this could cause a problem for getting the data to the user in a timely manor. The GPS raw data has the highest priority and should be received by the user within 5 seconds. It is expected that the correction data is more stable and can be sent out with the remaining data bandwidth on channel after the GPS raw data has been sent. The only question is is how sensitive the correction is to latency. To test this the September 98 data was re-processed with this in mind. A fixed delay was applied to the correction data and the DD misclosures were recalculated. That is, reference station data for a given epoch was corrected using network correction data that was computed at fixed interval of time in the past. This is meant to simulate a real situation where the correction data is received at the rover receiver with higher latency and a lower update rate then the GPS raw data. Table 3 shows the results when a 30 second delay is applied to the correction data. When comparing with Table 1 virtually no increase in the L1 carrier phase and WL carrier phase DD RMS error misclosures occurs. The L1 code shows degradation but this is not surpising

because, as explained in the previous section, the multipath errors dominate the results. Table 4 shows the results when a 600 second delay is applied to the correction data. At this point we start to see an increase in the misclosures due to latency in the correction data.

Table 3:

Double Difference RMS error comparison between raw and corrected data with latency of 30 seconds for L1 code, L1 phase and Wide Lane phase measurements

Test Network

BERG-143 KRIS-170 ALES-232 OSLO-232 Table 4:

The results show that the correction data is very stable for the September 1998 data set. This indicates that correction data latency may not be the limiting factor for the data broadcast and that the time to the first position fix from a cold start may be a more important factor.

L1 Code (m)

L1 Phase (cycles)

Raw

Corr.

Imprv

Raw

Corr.

Imprv

Raw

Corr.

Imprv

0.40 0.34 0.57 0.36

0.43 0.38 0.66 0.39

-8% -11% -15% -8%

0.387 0.525 0.612 0.618

0.201 0.403 0.380 0.367

48% 23% 38% 41%

0.108 0.124 0.171 0.171

0.064 0.092 0.078 0.114

41% 26% 54% 33%

Double Difference RMS error comparison between raw and corrected data with latency of 600 seconds for L1 code, L1 phase and Wide Lane phase measurements

Test Network

BERG-143 KRIS-170 ALES-232 OSLO-232

L1 Code (m)

L1 Phase (cycles)

WL Phase (cycles)

Raw

Corr.

Imprv

Raw

Corr.

Imprv

Raw

Corr.

Imprv

0.39 0.33 0.56 0.35

0.43 0.38 0.69 0.39

-10% -14% -25% -10%

0.383 0.526 0.610 0.596

0.232 0.415 0.416 0.373

39% 21% 32% 37%

0.107 0.125 0.170 0.166

0.072 0.095 0.092 0.115

33% 25% 46% 31%

CONCLUSIONS The September 1997 and 1998 tests show consistent results. The increase in ionospheric activity that was detected had little impact on results. This may not be the case as the ionospheric activity increases to a maximum in 2000 in which case more reference stations may be required. The carrier phase corrections showed high stability over time. This allows for some flexibility in the implementation. The validity of the network RTK approach is proven but many implementation aspects need to be resolved.

[2]

Raquet, J., Lachapelle, G., Melgård, T., Test of a 400 km x 600 km Network of Reference Receiver for Precise Kinematic Carrier-Phase Positioning in Norway. In Proceedings of the 11th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS-98). Nashville, Tennessee, Sept. 1998.

[3]

Raquet, J., Lachapelle, G., and Fortes, L.P., Use of a Covariance Analysis 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 (ION GPS98). Nashville, Tennessee, Sept. 1998.

[4]

Klobuchar, J.A.; Doherty, P.H.; El-Arini, B. Potential Ionospheric Limitations to the GPS Wide-Area Augmentation System. Navigation, Vol. 42, No. 2, pp. 353-370.

REFERENCES [1]

WL Phase (cycles)

Raquet, J, Development of a Method for Kinematic GPS Carrier-Phase Ambiguity Resolution Using Multiple Reference Receivers, Ph.D. dissertation, UCGE Report Number 20116, The University of Calgary, May 1998.