Testing of a Multi-Reference GPS Station Network for ... - CiteSeerX

Testing a Multi-Reference GPS Station Network for OTF Positioning in Brazil L. P. Fortes, M. E. Elizabeth Cannon, G. Lachapelle Geomatics Engineering, University of Calgary

BIOGRAPHIES Luiz Paulo Fortes holds an M.Sc. in Computer Science applied to Geomatics and is currently a Ph.D. student at the University of Calgary. He has been working the last 18 years for IBGE Department of Geodesy (the “Geodetic Survey” of Brazil) where he was responsible for the Research and Analysis division most of the time and as the head of the department in the last two years before enrolling in the Ph.D. program. Bolsista da CAPES – Brasília/Brasil. 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. 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. ABSTRACT Differential GPS has the capability to provide cm-level positioning accuracy, as long as the carrier phase ambiguities are resolved on-the-fly (OTF) to integer values. Existing methods are based on the use of a single fixed reference station located in the vicinity of the rover. The maximum distance allowed between the reference station and user is generally limited to within 50 km due to effects from the atmosphere and orbit. The number of reference stations can be increased to extend the coverage. However, the installation and maintenance of

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such stations and their data transmission links is operationally complex and expensive. The optimal use of existing stations is therefore of utmost importance to maximize cost effectiveness. A novel and unique method developed at the University of Calgary uses all available reference stations to generate regional code and carrier phase corrections, which can be transmitted to the user in order to resolve integer ambiguities OTF over the region. One of the major advantages of this method is to increase the coverage within which successful OTF ambiguity resolution is possible. The Brazilian Network for Continuous Monitoring of GPS (RBMC) is an active geodetic reference network functioning in Brazil since 1997. As the distances between the established stations are too long for carrier-phase positioning, a 5-day densification campaign was carried out in August 1999 covering a 700x700-kilometer region. The generated data was used to test the feasibility of the multi-reference station approach in a region strongly affected by the ionosphere, under the equatorial anomaly. During the campaign, a solar eclipse occurred. Despite the fact that the zone of totality was mainly seen over Europe and Asia, this event added an interesting feature to the collected data. Results and analysis using the regional code and carrier phase corrections are presented and compared to the single reference receiver case to demonstrate the improvement achieved by this method under the conditions pointed out. INTRODUCTION Real time kinematic GPS positioning is able to provide cm-level positioning accuracy, as long as the carrier phase ambiguities are resolved on-the-fly (OTF) to integer values. Existing methods are based on differential positioning using a single fixed reference station located in the vicinity of the rover. The maximum distance allowed between the reference station and user is

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generally limited to within 50 km due to effects from the atmosphere and orbit. A novel and unique method developed at the University of Calgary uses all available reference stations to generate regional code and carrier phase corrections, which can be transmitted to the user in order to resolve integer ambiguities OTF over the region. One of the major advantages of this method is to increase the coverage under which successful OTF ambiguity resolution is possible, decreasing the number of reference stations that would be needed using the standard single reference station approach and, consequently, maximizing cost effectiveness. The Brazilian Network for Continuous Monitoring of GPS (RBMC) [Fortes et al., 1998] is an active geodetic network, established in Brazil to support 3-D postprocessing positioning. Considering the dimensions of the country and the network’s national coverage, the interstation spacing ranges from 400 to more than 1000 km, supporting mainly static carrier-phase applications as well as differential code positioning (Figure 1). All collected data contribute to the International GPS Service [IGS Central Bureau, http://igscb.jpl.nasa.gov] densification network in South America, and two stations (BRAZ and FORT) belong to the IGS global network. This existing infrastructure has enormous potential to contribute to the establishment of RTK services. As the baselines are too long for carrier-phase RTK positioning, a 5-day densification campaign was carried out from August 11 to 15, 1999 in Southeastern Brazil, in order to assess the feasibility of the multi-reference station network method developed at the University of Calgary in a region very much affected by the ionosphere. MULTI-REFERENCE STATION APPROACH The multi-reference station approach was proposed by Raquet [1998], in order to model errors that affect GPS differential code and carrier-phase kinematic positioning applications [Raquet and Lachapelle, 2000; Townsend et al., 1999]. The principle of the method is that as long as the carrier-phase observable errors are corrected (or minimized), it is possible to resolve integer ambiguities over longer distances, which increases the achievable accuracy of the user. The equations used to compute the corrections to the carrier-phase observables are as follows: −1 T δˆl r = Cδlr , δl B (B Cδl BT ) (BΦ − λ∆∇N)

(1)

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

(2)

Figure 1: The Brazilian network for Continuous Monitoring of GPS (RBMC). BRAZ and FORT belong to the IGS global network. The low density in Northwest, around MANA, is explained by the presence of the Amazon jungle. It will be densified there with additional six stations in near future. The rectangle shows the region where the densification campaign was carried out in August 1999. δlr

are the corrections to carrier-phase observables collected at the rover receiver, in meters, δl are the corrections to carrier-phase observables collected at the reference stations, in meters, Φ are the measurement-minus-range carrierphase observables ( Φ = Φ − ρ ), in meters, assuming that the reference station coordinates are known in order to compute the geometric range ρ, ∆∇N are the double difference integer ambiguities between the reference stations (assumed to be known), λ is the carrier-phase wavelength, in meters, B is the double difference matrix ( B = ∂∆∇ Φ / ∂Φ ) (made up of the values +1, -1 and 0), Cδl is the covariance matrix of the carrier-phase observables collected at the reference stations, and Cδlr , δl is the cross-covariance matrix between the carrier-phase observables collected at the rover receiver and at the reference stations.

where,

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The above equations can be derived using the principle of least squares prediction (collocation), as shown by Fortes [1998].

method (this is actually a requirement of least squares prediction). The procedure used to determine the integer ambiguities and the covariance matrix is described in the next sections.

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Through equations (1) and (2), it can be seen that the double difference integer ambiguities between the reference stations must be known, along with precise coordinates for the reference stations. The covariance matrices Cδl and Cδlr , δl are also required to apply the

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Since the RBMC network inter-station spacing is too large for carrier-phase RTK positioning, code and carrierphase data were acquired from ten temporary stations, in addition to four stations belonging to the RBMC network, namely BRAZ, PARA, UEPP and VICO, during August 11 to 15, 1999. Except for the receiver located at UEPP, which collected data at a 15-second data rate, all the others collected data every 5 seconds. The observed elevation mask was set to 5°. Figure 2 shows the stations occupied during the campaign as well as the receiver used at each one. Due to logistical problems, some stations did not function during the whole duration of the campaign. Therefore August 11 and 13 data were selected for processing and analysis, corresponding to days when most of the stations tracked the GPS satellites during the entire 24-hour period. August 11 had an additional feature, as it was the day when a solar eclipse occurred. Precise coordinates of the reference stations were computed using Bernese GPS Software Version 4.2 [Rothacher and Mervart, 1996]. Data collected in each selected day were reduced using IGS final precise orbits. All processing was carried out decimated to 15-second intervals, with a 15° elevation cutoff angle. The agreement between the daily solutions was at the millimeter level. Afterwards, the normal equations for the two-day solutions were combined to generate the final adjusted coordinates. The coordinates of BRAZ, CACH, PARA, UEPP and VICO, also part of the SIRGAS continental network [IBGE, 1997] were constrained to 0.0001m, in order to tie the results to this reference system. As previously mentioned, it is necessary to know the double difference integer ambiguities between reference stations in order to apply equations (1) and (2). This step was carried out in the scope of the coordinate determination described in the previous paragraph.

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Figure 2: Stations occupied during the RBMC densification campaign, held from August 11 to 15, 1999. Stations represented as a square belong to the RBMC national structure. Stations in black (9) were occupied with Trimble 4000SSi receivers; in grey (4), with Ashtech Z-XII receivers; and in white (1) with Javad Legacy receiver

Operationally, this would be done in real-time as per Sun et al. [1999] and Lachapelle et al. [2000], using network geometric constraints. Almost all L1 and L2 ambiguities between the various reference stations were successfully resolved to integers using the Quasi-Ionospheric Free (QIF) strategy [Rothacher and Mervard, 1996]. The ones that could not be reliably fixed to integers correspond to periods when the ambiguities were only valid for a short time (less than an hour), due to unreconstructed cycleslips. One interesting aspect of the data set was the large number of losses of L2 tracking in many stations. This can be explained by problems some receivers experienced in maintaining satellite tracking under active ionospheric conditions. This region is affected by the equatorial anomaly, where the incidence of scintillation (amplitude fading or enhancement and phase fluctuation [Wanninger, 1993]), due to small-scale irregularities in the electron content of ionosphere, is frequent. The closer to solar maximum, the more frequent scintillation occurs, with peak activity at the equinoxes. The receiver performance depends very much on the technology implemented for L2 tracking, with codeless receivers performing worse than semi-codeless ones, as the first technique implies a 13dB loss when compared with the second one [Woo, 1999]. Table 1 shows the number of unpaired (L1 without L2) single difference observations for some baselines for different types of receivers, obtained by Bernese in the pre-processing. Notably, the correlation with receiver technology is evident, despite some differences that

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Table 1: Unpaired single difference observations for 24-hour sessions. The total number of observations (at 15 sec.) per session is about 30000 Number of GPS L2 Unpaired Baseline Receivers Tracking Single Diff. used Technique Obs. Agua – Sjrp SemiAsthech Z-XII 5 on Aug 11 codeless Agua – Sjrp SemiAsthech Z-XII 7 on Aug 13 codeless Botu – Regi Trimble Codeless 1394 4000SSi on Aug 11 Braz - Chua Trimble Codeless 1645 4000SSi on Aug 11 Braz - Chua Trimble Codeless 1573 4000SSi on Aug 13 Cach – Limo Ashtech Z-XII Semion Aug 11 codeless and 973 Trimble and 4000SSi codeless Cach – Limo Ashtech Z-XII Semion Aug 13 codeless and 994 Trimble and 4000SSi codeless Chua – Fran Trimble Codeless 2841 4000SSi on Aug 11 Chua – Fran Trimble Codeless 2826 4000SSi on Aug 13 Fran – Limo Trimble Codeless 2018 4000SSi on Aug 11 Fran – Limo Trimble Codeless 2039 4000SSi on Aug 13 Jagu – Lond Javad Legacy ? and on Aug 13 Semi142 Ashtech Z-XII codeless

happen due to the specific location of each site. These results match the ones shown by Skone and deJong [1999]. The covariance matrices Cδl and

Cδl r ,δl have to be known

in order to compute the corrections using equations (1) and (2). Each element of these matrices can be calculated based on the knowledge of mathematical functions that map how the correlated errors (atmospheric delays and satellite position errors) behave over the region covered by the network and their dependency on the satellite elevation. In addition, it is necessary to know the variance of the uncorrelated errors (multipath effects and receiver noise) for each station in the network. Thus, elements of the covariance matrices can be properly estimated by combining the correlated and uncorrelated variances by a

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covariance function, according to the procedure described in detail in Raquet [1998] and Raquet et al. [1998a]. In the present test, the covariance functions described in Fortes et al. [2000] were used. Despite the fact that those covariance functions were derived using data collected by a network located in the St Lawrence region, Canada, the conditions were similar, with an active ionosphere in both cases. Fortes [1999] showed that the impact of using different covariance functions in the correction computation is not critical. To confirm that, new covariance functions were calculated using the data collected in the present research, which increased the percentage improvement by only 2% in the observation domain. Therefore the former covariance functions were used in all tests herein. The Solar Eclipse

The Solar eclipse occurred on August 11, 1999, between 09:00 to 13:00 UT (06:00 to 10:00, local time in the test region). Despite the fact that the zone of totality was not seen over all the test area in Brazil, it is interesting to check if it had any influence on GPS differential positioning. Double difference residuals were computed using the known coordinates and ambiguities for several baselines using different types of observables: L1 and L2 code, L1 and L2 carrier-phase, wide lane ( φ WL = φ L1 − φ L 2 , where φ is the corresponding carrierphase in cycles), ionospheric-free ( φ IF = φ L1 − (f 2 / f1 )φ L2 , where f1 and f2 are the GPS L1 and L2 frequencies) and ionospheric signal in L1 (geometric-free scaled to L1, i.e,

IS L1 =

f 22

[λ1φ1 − λ 2 φ 2 ] , where λ1 and λ 2 are the f 12 − f 22 L1 and L2 wavelengths, respectively). Figure 3 shows the RMS values of the double difference residuals for each kind of observable mentioned above, for the entire 24-hour period, for 24 baselines observed on August 11, as a function of baseline length. The two graphs on the top correspond to L1 code (DD C1) and L2 code (DD P2), and it can be seen that the code noise dominates this observable, as a correlation with distance is not seen (only for L2 code, as the ionospheric error is greater for this frequency). For all other observables, the correlation with distance is evident, mainly due to the ionosphere, except in the ionospheric-free observable case, as the remaining residuals are due to tropospheric plus orbit errors (the graph for this observable is shown twice, one following the same scale as the others, for comparison purposes, and another one with a greater scale in the vertical axis, to show that the correlation with distance is still present). Figure 4 shows the same type of graphs, for 35 baselines observed on August 13. A direct

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comparison of results in both figures shows a slightly larger spatial gradient of the ionospheric residual errors (DD ISL1) on August 13, in addition to a higher noise (see DD IF on the right). In order to confirm that the quieter behavior of the ionosphere on August 11 is justified by the solar eclipse, data collected on a third day, August 14, 1999, was processed in the same way. Figure 5 shows the corresponding results for 30 baselines. It can be seen that the level of the ionosphere was as high as in the second day, with observations even noisier.

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Improvement by the Multi-Reference Station Approach Over Standard OTF

Results of the comparison between a single station and multi-reference station approaches were computed for the observation, position and ambiguity domains. The

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Figures 6 and 7 show the same results for one specific baseline (AGUA to SJRP, 146 km), for August 11 and 13, respectively. Comparing both figures, it can be seen that the double difference ionospheric signal residuals after sunset for the eclipse day are not as high as for the second day (due to a reduced secondary peak in the total electron content that normally occurs around 22:00 local time under the equatorial anomaly region). Analyzing these figures, maximum differential ionospheric effects up to 13 ppm and 17 ppm, respectively for August 11 and 13, can be deduced.

DD P2 RMS (m)

Figure 4: Double difference residual RMS values for each kind of observable, for 35 baselines observed on August 13, 1999, as a function of baseline length DD C1 RMS (m)

Figure 3: Double difference residual RMS values for each kind of observable, for 24 baselines observed on August 11, 1999, as a function of baseline length

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Figure 5: Double difference residual RMS values for each kind of observable, for 30 baselines observed on August 14, 1999, as a function of baseline length

objective was to assess how much improvement the multireference station approach developed at the University of

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Figure 6: Double difference residual RMS values for each kind of observable for AGUA to SJRP baseline (146 km), for August 11, 1999 (Eclipse day)

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Calgary gives over standard OTF processing, which uses only one reference station.

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In all these tests, three scenarios were used. In each scenario, one specific station was removed from the reference network in order to play the role of a rover (user) receiver. These three scenarios for August 13, 1999, are shown in Figure 8, each one corresponding to different baseline distances to the closest reference station in the network. In the first one, LIMO is the rover, at 122 km from FRAN, the closest reference station. In the second one, SJRP is the rover, at 146 km from AGUA. In

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Figure 7: Double difference residual RMS values for each kind of observable for AGUA to SJRP baseline (146 km), for August 13, 1999

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Figure 8: The three scenarios used in the tests (for August 13, 1999). The square represents the station working as a rover

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Table 2: Raw and corrected double difference residual RMS values and respective improvement for FRAN to LIMO, AGUA to SJRP, and REGI to BOTU baselines for August 11, 13, 1999 Baseline Length L1 (m) WL (m) (km) Raw Corr. Improv. Raw Corr. Improv. FRAN - LIMO 122 Aug 11 0.191 0.116 39% 0.258 0.170 34% Aug 13 0.327 0.181 45% 0.418 0.250 40% AGUA - SJRP 146 Aug 11 0.284 0.119 58% 0.364 0.159 56% Aug 13 0.350 0.138 61% 0.440 0.186 58% REGI - BOTU 193 Aug 11 0.239 0.128 47% 0.312 0.180 42% Aug 13 0.407 0.162 60% 0.516 0.199 61%

the third one, BOTU is the rover, at 193 km from REGI. The scenarios used for August 11, 1999, are basically the same, except JAGU, PARA and UEPP were not included, since they did not collect data for 24 hours on that day. In each scenario, the rover station is assumed to have unknown coordinates. Corrections generated using equation (2) were then used to correct the raw observations of the closest reference stations, while corrections using equation (1) were computed for the “rover” positions. BRAZ and VICO, belonging to the national RBMC structure, were not included in the reference network for correction computations in any scenario because they are located too far from the other stations. In the observation domain, the single reference station (raw) L1 and WL double difference residuals were compared with those generated after applying the corrections. The root mean square (RMS) of the raw and corrected double differences residuals for each scenario described was computed, as well as the percentage improvement for August 11 and 13. The results are shown in Table 2. The improvement reached up to 61%, which is at the same level as the ones reported in other studies applying the same method to networks in different parts of the world [Townsend et al., 1999; Fortes et al., 2000]. However, the absolute values of the raw double difference carrier-phase misclosures were very high in this project due to a very active ionosphere. Even with corrected observations, RMS values of 0.18 m in L1 and 0.25 m in WL still remain, which are too large for ambiguity resolution. This will be addressed again later, when the results in the ambiguity domain are presented. It should be noticed that the residuals obtained using raw (and corrected) observations are systematically higher in the second day, confirming that the ionosphere was more active on that day.

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Figure 9 shows raw and corrected L1 and WL double difference carrier-phase residuals for the AGUA to SJRP baseline for August 13, 1999. It can be seen that the method did an effective job correcting the observations, even those related to very large residuals. However, some double difference residuals with absolute values up to 1 m still remain. The isolated residuals greater than 1 m in the corrected observation graphs are being investigated, but it seems that during these epochs the corresponding remote satellite (normally at low elevation) was not observed by a significant number of reference stations in the network. 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

Figure 9: Raw and corrected L1 and WL double difference carrier-phase residuals for AGUA to SJRP baseline (146 km) for August 13, 1999

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Table 3: Raw and corrected position difference RMS values and respective improvement for August 11 and 13, 1999 FRAN → LIMO (122 km), August 11, 1999 Coord. Component L1 (m) WL (m) IF (m) Raw Corr. Improv. Raw Corr. Improv. Raw Corr. Improv. Latitude 0.20 0.10 50% 0.27 0.14 48% 0.02 0.02 0% Longitude 0.13 0.08 38% 0.16 0.11 31% 0.02 0.02 0% Ellipsoidal Height 0.39 0.26 33% 0.50 0.36 28% 0.06 0.07 -17% AGUA → SJRP (146 km), August 11, 1999 Coord. Component L1 (m) WL (m) IF (m) Raw Corr. Improv. Raw Corr. Improv. Raw Corr. Improv. Latitude 0.25 0.09 64% 0.31 0.11 65% 0.02 0.01 50% Longitude 0.19 0.11 42% 0.23 0.14 39% 0.02 0.01 50% Ellipsoidal Height 0.50 0.25 50% 0.65 0.35 46% 0.06 0.06 0% REGI → BOTU (193 km), August 11, 1999 Coord. Component L1 (m) WL (m) IF (m) Raw Corr. Improv. Raw Corr. Improv. Raw Corr. Improv. Latitude 0.26 0.11 58% 0.33 0.15 55% 0.03 0.02 33% Longitude 0.19 0.11 42% 0.24 0.14 42% 0.02 0.01 50% Ellipsoidal Height 0.47 0.28 40% 0.63 0.44 30% 0.10 0.08 20% FRAN → LIMO (122 km), August 13, 1999 Coord. Component L1 (m) WL (m) IF (m) Raw Corr. Improv. Raw Corr. Improv. Raw Corr. Improv. Latitude 0.33 0.13 61% 0.42 0.17 60% 0.03 0.02 33% Longitude 0.28 0.19 32% 0.35 0.27 23% 0.03 0.02 33% Ellipsoidal Height 0.64 0.42 34% 0.70 0.55 21% 0.05 0.06 -20% AGUA → SJRP (146 km), August 13, 1999 Coord. Component L1 (m) WL (m) IF (m) Raw Corr. Improv. Raw Corr. Improv. Raw Corr. Improv. Latitude 0.27 0.11 59% 0.37 0.16 57% 0.03 0.02 33% Longitude 0.32 0.10 69% 0.39 0.16 59% 0.03 0.02 33% Ellipsoidal Height 0.69 0.36 48% 0.72 0.51 29% 0.05 0.05 0% REGI → BOTU (193 km), August 13, 1999 Coord. Component L1 (m) WL (m) IF (m) Raw Corr. Improv. Raw Corr. Improv. Raw Corr. Improv. Latitude 0.37 0.13 65% 0.45 0.16 64% 0.04 0.02 50% Longitude 0.34 0.15 56% 0.39 0.19 51% 0.05 0.03 40% Ellipsoidal Height 1.07 0.49 54% 1.27 0.59 54% 0.15 0.09 40%

process. Raw and corrected 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, it was modified to read ambiguities from a file instead of trying to resolve them. For each scenario, coordinates of the rover, computed by FLYKIN using raw and corrected L1 and WL observations for August 11 and 13, were compared with the known values. The RMS values of the differences are shown in Table 3. A third solution is also included, using the ionospheric-free (IF) linear combination, which removes the first-order effect of the ionosphere. The ambiguities in this case are not integer numbers, but were computed from the known integer L1 and L2 ones using the formula ∆∇N IF = ∆∇N L1 − (f 2 / f 1)∆∇N L 2 , where ∆∇N is the usual notation for double difference ambiguities. It is important to note that, even with known

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ambiguities and raw observations, the RMS of the solution in height is as large as 1.07 m for L1 and 1.27m for WL. Despite the fact that the method brought improvements up to 69% for L1 and WL observables, the residuals using raw observations were too high to be fully corrected by the current error modeling implemented in the method. The percentage improvements for the IF solution are lower than the ones for the other two observables, and even negative in some cases, corresponding to differences between raw and corrected RMS at the level of the carrier-phase noise. The raw RMS in the IF case, encompassing mainly troposphere and orbit errors, were already very small, except for the REGI to BOTU baseline, which has a significant height difference between both stations (700 m), contributing to a higher residual tropospheric delay.

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Table 4: Ambiguity domain improvement for AGUA to SJRP, FRAN to LIMO, and REGI to BOTU baselines for August 11 and 13, 1999 Baseline Length % of corrected fixes of Mean time(sec.)/number of % of WL ambiguities reliably (Km) WL ambiguities epochs to correctly fix converted to L1 WL ambiguities Single Multi Single Multi Single Multi Ref. St. Ref. St. Ref. St. Ref. St. Ref. St. Ref. St. FRAN - LIMO 122 August 11 60% 65% 302 / 20 273 / 18 9% 12% August 13 53% 66% 352 / 23 194 / 13 5% 11% AGUA - SJRP 146 August 11 47% 63% 264 / 18 160 / 11 4% 6% August 13 48% 49% 357 / 24 314 / 21 7% 6% REGI - BOTU 193 August 11 64% 59% 305 / 20 260 / 17 8% 15% August 13 51% 58% 392 / 26 334 / 22 5% 13%

For the ambiguity domain test, the baselines in each of the three scenarios were processed using FLYKIN Suite [GEOsurv, 1999], using raw and corrected observations. This software can perform a L1 or WL ambiguity search, trying to convert the WL ambiguities to L1 in the second option. Considering the relatively long baselines in the network, in addition to an active ionosphere, this test was restricted to the second option. In order to generate statistics to actually measure the improvement in the ambiguity domain, it was necessary to force FLYKIN Suite to re-start the WL ambiguity search at fixed time intervals, to generate enough samples for each session. Thus almost every twenty minutes a new ambiguity set was searched. Sometimes twenty minutes was not enough to fix the corresponding ambiguities, so FLYKIN Suite was left running for an extra 20-minute interval. This procedure generated about 72 samples for each 24-hour session per baseline. The ambiguities computed by FLYKIN Suite were then compared with the ones solved by the batch Bernese solution. Table 4 shows the results in terms of percentage of corrected fixes, mean time to fix ambiguities and percentage of L1 ambiguities reliably converted to L1. It can be seen that, using the multi-reference approach, improvements in all three types of comparisons were achieved. However, the percentage of success in fixing WL ambiguities was never greater than 65%, even using corrected data, which means that, despite the fact that the method has largely reduced the errors present in the observations (mainly ionosphere), the remaining ones still impacted the ambiguity resolution process. This also shows the limit of the multi-reference station approach under non-linear ionospheric conditions. In such a case, a denser network is needed. One alternative to be used is to determine the rover position using a float solution, which means that the ambiguities are solved as real numbers instead of trying to

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fix them as integers. Fortes et al. [2000] found a general degradation of only 5 to 7% when using float ambiguities in another test network. Similar analyses will be done using the Brazilian data set, including the case when the ambiguities can not be fixed to integers in the network. CONCLUSIONS AND FUTURE WORK

The results of the test with the Brazilian network demonstrated the improvement brought by the multireference station approach over the single-reference station case in all of the observation, position and ambiguity domains. The test was conducted under high ionospheric activity (up to 17 ppm), which was expected considering the location of the network, under the equatorial anomaly, and the proximity to the solar maximum. The occurrence of a solar eclipse in the first day of the campaign seemed to have reduced the effect of the ionosphere on the data, mainly after local sunset. Based on the results, an optimization of the method, in terms of modeling separately each error affecting GPS positioning (basically ionosphere, troposphere and orbit), is envisaged, in order to try to improve even more the method effectiveness. ACKNOWLEDGEMENTS

The authors would like to express their gratitude to IBGE Department of Geodesy, Brazil, for conducting the field densification campaign and for releasing all the data used in this research. The authors also acknowledge Dr. Susan Skone, from the Department of Geomatics Engineering, the University of Calgary, for her comments.

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ION GPS-2000 / Salt Lake City / September 19—22, 2000

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