Integration of Regional GPS Network to ITRF Using

Integration of Regional GPS Network to ITRF Using Precise Point Positioning J. F. G. Monico, J. A. S. Perez Department of Cartography, Faculty of Science and Technology – FCT/UNESPPaulista State University, Rua Roberto Simonsen, 305, 19060-900 - Presidente Prudente, SP, Brazil Abstract. GPS precise point positioning (PPP) can provide high precision 3-D coordinates. Combined pseudorange and carrier phase observables, precise ephemeris and satellite clock corrections, together to data from dual frequency receivers, are the key factors for providing such levels of precision (few centimeters). In general, results obtained from PPP are referenced to an arbitrary reference frame, realized from a previous free network adjustment, in which satellite state vectors, station coordinates and other biases are estimated together. In other to obtain consistent results, the coordinates have to be transformed to the relevant reference frame and the appropriate daily transformation parameters must be available. Furthermore, the coordinates have to be mapped to a chosen reference epoch. If a velocity field is not available, an appropriated model, such as NNR-NUVEL-1A, has to be used The quality of the results provided by this approach was evaluated using data from the Brazilian Network for Continuous Monitoring of the Global Positioning System (RBMC), which was processed using Gipsy-Oasis II software. The results obtained were compared to SIRGAS 1995.4 and ITRF2000, and showed precision better than 2cm. A description of the basic fundamentals of the PPP approach and its application in the integration of regional GPS networks with ITRF is the main purpose of this paper.

1 Introduction The term ‘GPS point positioning’ commonly refers to the method in which only pseudorange measurements derived from C/A code, together with information about the satellite positions and clock errors derived from the broadcast ephemeris, are used to compute receiver coordinates. In this case, instantaneous positioning provides horizontal and height precision of the order of 10 and 14 m, respectively, at 95% confidence. If carrier phase

observables are also available, they may be included in the processing. However, such procedure is not a common practice. The main errors affecting this method are related to the broadcast ephemeris (satellite positions and clock errors), ionosphere and troposphere refraction and multipath (Monico, 2000). For applications not requiring real time solutions, it is possible to make use of the IGS (International GPS Service) precise ephemeris and satellite clock corrections, both of which have a precision of a few centimeters (http://www.igscb.jpl.nasa.gov). These products can be used in the processing of pseudorange and/or carrier phase observations, either for single or dual frequency receivers. The procedure by which pseudoranges from single or dual frequency receivers are used to compute receiver coordinates has been used for some time by the Canadian Active Control System of the Natural Resources Canada (NRCAn). Results have shown 3-D precision of the order of 1m, using only one epoch of measurements (Héroux and Kouba, 1995). Using a combination of carrier phase and pseudorange observables collected by dual frequency receivers, also together to IGS products, the precision of point positioning can be at the same level as a solution in which several receivers have their data processed as a global network. The procedure involves, in a first step, the analysis of data of a globally distributed subset of receivers to determine transmitter parameters, which will be used, in a second step, for the analysis of the remaining receivers data, involving one receiver at a time (Zumberge et. al., 1997). The second step of this procedure is referred to as precise point positioning (PPP). The main aim of this paper is to evaluate the quality resulting from the integration of regional GPS stations into the ITRF (International Terrestrial Reference Frame) using PPP. Firstly, the fundamental concepts of PPP will be presented. It will be followed by an experiment, which was carried out using a sample of data from the Brazilian continuous GPS network (RBMC),

which was established in Brazil by IBGE (Brazilian Institute of Geography and Statistics) (Fortes, 1997). The software used was GIPSYOASIS II (GOA-II), developed by JPL (Jet Propulsion Laboratory).

2 Fundamentals of Precise Point Positioning (PPP) Consider a receiver A collecting pseudorange observables from all visible satellites. Each collected observable generates an observation equation, which will compose the system of equations. The linearized observation equation is given by (Blewitt, 1989; Monico, 2000):

∆PD Aj = a Aj ∆X A + b Aj ∆YA + c Aj ∆Z A + c (dt A − dt j ) + I Aj + T Aj + εPj

(1)

where ∆PDA is the difference between the observed pseudorange from station A to satellite j j ( PD A ) and the pseudorange computed as a j function of the approximate parameters ( ρA 0 ). j j j The coefficients a A , b A e c A are the components of the design A matrix (Gemael 1994). c is the speed of light in the vacuum. Equation 1 has 4 unknowns; 3 corrections to the approximate coordinates of the station (∆XA , ∆YA , ∆ZA) and the receiver clock error (dt A ) Therefore, at least 4 satellites have to be observed in order to obtain an instantaneous position. The satellite clock error (dt j ) can be computed from the broadcast ephemeris. Atmospheric refraction j j (ionosphere( I A ) and troposphere ( TA )) can be reduced using appropriate models or be neglected. j The term ε A accounts for code noise measurement and unmodeled errors, such as satellite and receiver hardware delays, related to pseudorange ( C/A code for example) Using the precise ephemeris and the satellite clock errors provided by IGS instead of those computed from the broadcast ephemeris, better results can be obtained. IGS provides three kinds of orbits and corrections to satellite clocks (http://www.igscb.jpl.nasa.gov): - IGS, one day orbits resulting from a combinations of all orbits produced by the IGS analysis centers, available with a latency of 13 days; - IGR, one day orbits resulting from a combinations of all rapid orbits produced by j

the IGS analysis centers, available with a latency of 17 hours; - IGU, the Ultra Rapid orbit combinations are generated twice each day (at 0300 and 1500 UT) and contain 48 hour spans of orbits; the first 27 are based on observations and the second 21 are a predicted orbit. Concerning the accuracy of the satellite positions, it is stated that IGS orbits is better than 0.05m for IGS type, 0.05 m for IGR and approximately 0.25 m for IGU (http://www.igscb.jpl.nasa.gov). The satellite clock corrections for IGS products provide precision at the centimeter level. This product provides satellite positions and clock corrections with sampling interval of 15 minutes. Such interval is appropriated for realizing satellite orbit interpolation, but not for the clock corrections. Aiming to reduce this degradation, the Geodetic Survey Division (GSD), from Natural Resources Canada (NRCan) started to generate, in addition to the quarter-hourly satellite orbits and clock corrections, a set of satellite clock corrections every 30 seconds, using data from CACS (Canadian Active Control System) (Héroux and Kouba, 1995). Similar work has been developed by JPL. They have produced satellite orbits and clock corrections in the SP3 format (Spofford and Remondi, 1996) with a 30 second interval. Single epoch C/A code point positioning using satellite clock corrections and precise ephemeris can provide sub-metric precision (Camargo, 1999). For users having dual frequency receivers, Eq. 1 can also be written for pseudorange on L2. Additionally, carrier phase observables may be included in the processing. The carrier phase linearized equations are given as (Blewitt, 1989; Monico 2000):

λ1 ∆φAj 1 = a Aj ∆X A + b Aj ∆Y A + c Aj ∆Z A + + c( dt A − dt j ) − I Aj + T Aj + N Aj1 + εφj1 λ2 ∆φAj 2 = a Aj ∆X A + b Aj ∆Y A + c Aj ∆Z A +

(2)

+ c( dt A − dt j ) − I Aj + TAj + N Aj 2 + εφj 2 These equations have, in addition to the elements already presented in Eq. 1, the following terms: - ∆φj A 1 and ∆φj A 2 refer to the difference between the observed and computed carrier phase as function of the approximate parameters, for L1 and L2 , respectively;

- λ1 and λ2 are the wavelengths for the L1 and L2 carriers respectively; j - I A is the ionosphere refraction for the L2 carrier; j j - N A 1 and N A 2 are the ambiguities on L1 and L2 respectively; and j j - εφ 1 e εφ 2 account for data noise in the measurements and other unmodelled errors. The two carriers can be combined in order to reduce the error due to ionosphere refraction. Similar procedures can be applied to the pseudorange observations. Using one of the several models for the troposphere, together with some parameterization technique, it is possible to reduce troposphere refraction effects. More details on PPP can be found in Zumberge et al. (1997). They demonstrated that this method can provide horizontal precision of few millimeters, whilst vertical precision is a little worse, at the level of few centimeters. In this case, the processing software operated in static PPP mode, using 24 hours of data with 30-second interval. In order to reduce temporal correlation, the processing interval was 5 minutes.

3 The Integration to ITRF Using PPP The adjustment of GPS data using PPP provides coordinates related to the frame of the satellite orbits and clock corrections used. The satellite orbits and clock corrections may be produced in a free adjustment, where station coordinates and other bias parameters were also estimated together (Blewitt et al., 1992), or in an adjustment using fiducial stations (Ffoulkes-Jones, 1990). Some characteristics of each approach can be found in Monico et al. (1997). In the free adjustment, the solution will be in a poorly defined reference frame, but immune to fiducial error. In order to make the free frame compatible to the desired ITRF, some of the globally distributed stations with available ITRF coordinates are used to estimate the similarity transformation parameters between the free frame and ITRF. These transformation parameters are available to the users in order to apply the transformation in the PPP results and make them compatible to the corresponding ITRF. The corrections and models used in the PPP should follow the IERS standards (McCarthy, 1996).

4 Experiment: Data Description, Software Used and Applied Strategy

4.1 Data Involved in the Experiment In order to evaluate the PPP performance, a series of experiments were undertaken. The GPS data were made available by IBGE. These data were collected by the RBMC, comprising at the time of the experiment of 10 stations (see Fig. 1).

Fig. 1: Distribution of the RBMC stations.

Table 2 shows the stations with data involved in the processing. As one can see, for some stations data were not available, due to problems at the station during this period. Although a more representative set of data could be used, only 3 weeks of data were used. Such data set may provide enough information for reaching the aim of this paper. Table 2: Data used in the processing Day of Year (1998) Stations

91

BOMJ

XX

92

93

94

95

96

97

121 122 123 124 125 126 127 152 153 154 155 156 157 158

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

BRAZ

XX

XX

XX

XX

XX

XX

CUIB

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

FORT

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

IMPZ

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

MANA

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

PARA

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

UEPP

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

VICO

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

XX

4.2 Software Used in the Processing The data in Table 2 were processed using the GIPSY-OASIS II (GOA-II) software running in a Sun Ultra 1 platform with SunOS 5.5.1 operation system. This software allows PPP, in addition numerous other options, which are summarized in Webb and Zumberge (1997). As stated previously, dual frequency data should be available for PPP, allowing for reduction of ionosphere effects using the ionospheric-free combination. One can use the IGS precise or broadcast ephemerides, as well as the ephemeris provided by the IGS analysis

4.3 Strategy Applied in the PPP Parameters Estimation In PPP parameter estimation, the ionospheric free (L3) observables were used, either for carrier phase or pseudorange measurements. In order to avoid correlation between observation epochs, a 5-minute data interval was used in the processing. The elevation mask adopted was 15°. For tropospheric modeling, the Neill mapping function was used, and the zenithal troposphere residuals were modeled using a random walk process (Bierman, 1977), with rate of change of the process noise covariance given by 2cm/(1h)1/2 . The receiver clock errors estimated in the processing were related to FORT station standard oscillator. The orbits, satellite clock corrections and Earth Orientation Parameters (EOP) used were those produced by JPL, and available via anonymous ftp at . They were produced in a free adjustment. Therefore, a set of transformation parameters was also used, in order to transform from the free frame, provided by the satellite orbits, to ITRF. For this specific case, ITRF96 was used.

5 Analysis Of The Results In general, the analysis of precision and accuracy of geodetic positioning is based in three different procedures: Formal standard deviation, based in the geometry (A matrix) and the covariance matrix of the observations (precision); Repeatability of the results (a more realist measure of precision) and; Comparison with other techniques of better quality (accuracy). The formal standard deviation is obtained from the covariance matrix of the estimated parameters, which normally provides over-optimistic values for the quality of the parameters. Figure 2 shows the results.

Standard deviation (mm)

2

1.5 E 1

N h

0.5

0 B O M J

B R A Z

CUIB

F O R T

IMPZ

M A N A

P A R A

U E P P

V I C O

Stations

Fig. 2: Coordinates standard deviation of the stations.

Station BRAZ presents the worst results. This was the station with the least quantity of data (see Table 1). One can also observe, as expected, that the precision of the height component is worse than the horizontal components. Figure 3 also illustrates the formal precision, but for baseline components. They are slightly worse than those shown in Fig. 2, because each baseline has two stations involved, resulting in propagation of errors. It is important to note that there is no precision deterioration as function of baseline length. It is due to the fact that in PPP approach the correlation between stations coordinates are not taken into account.

Standard deviation (mm)

centers, like JPL. As the IGS precise ephemeris provide clock corrections every other 15 minutes, only observations collected very close to these epochs would be used in the processing, reducing the number of observations. Using the ephemeris provided by JPL, appropriated for being used with GOA-II in the PPP mode, almost all observations can be used in the processing.

2.5 2 1.5 1

E N h

0.5 0 0

1000

2000

3000

Baseline length (km)

Fig. 3: Standard deviation of the baseline components.

The daily repeatability (Rep) provides a more realistic measurement of the coordinate quality, as well as of the baselines. It is given by the expression (Blewitt, 1989):

 n n ( Ri − Rˆ )2  ∑ 2 Re p =  n − 1 i =1 σi  

   n 1  ∑ 2   i =1 σi 

1

2

(3)

In this expression, n is the number of days involved in the processing, Ri and σ i are the coordinate with the respective standard deviation for each coordinate component of the i-ésimo day,

and R$ is the weighted average of the considered coordinate component. The repeatability values are illustrates in the Figure 4. As before, the h component presents the worst results. In this case, the component h of station MANA, located at Amazon region provided the worst results at all. Considering that this station is located in a region with high humidity, such result may be due to the troposphere refraction, not completely modeled by the applied model. More research has to be carried out on this topic.

Repeatability (mm)

20

15 E 10

N h

5

for performing such tests: SIRGAS 1995.4 realization (IBGE, 1997) and ITRF2000 (http://lareg.ensg.ign.fr/ITRF/ITRF2000). Considering 1998.4 as the reference epoch for analysis, discrepancies were computed between the different solutions. The SIRGAS 1995.4 coordinates were mapped to 1998,4 using the NNR NUVELA-1 model (McCarthy, 1996). The ITRF2000 coordinates were mapped to the reference epoch using the ITRF2000 velocities and the precision of each coordinate was propagated to a local coordinate system. Figure 6 shows the precision of the ITRF2000 Brazilian stations at epoch 1998.4. As the correlations between Cartesian coordinates were not available in the ITRF solution, they were neglected. This should be the reason why the precision of the component h is at the same level of E.

0 CUIB

FORT

IMPZ

MANA

PARA

UEPP

VICO

Stations

Fig. 4: Repeatability of the station coordinates.

Repeatability (mm)

Figure 5 shows the repeatability as function of the baseline components, for the local coordinates E, N and h. For the h component, one can observe that there is a relation between baseline lengths. This may be contrasted with figure 3. A linear regression provides a precision of the order of 6 mm + 4ppb (part per billions). 30 25 20 15 10 5 0

E N h

0

1000

2000

3000

Baseline length (km)

ITRF2000 precision (mm)

BRAZ

60 50 40 30 20 10 0

E N h BOMJ

BRAZ

CUIB

FORT

IMPZ

MANA

PARA

UEPP

VICO

Stations

Fig. 6: Precision of the Brazilian ITRF2000 Stations.

Figures 7 and 8 show the discrepancies between PPP and ITRF2000 and SIRGAS 1995.4 solutions respectively, both at epoch 1998.4. Discrepancies (mm)

BOMJ

40 20

E

0

N h

-20 -40

BOMJ

BRAZ

CUIB

FORT

IMPZ

MANA

PARA

UEPP

VICO

Stations

Fig. 5: Repeatability of the baseline components. Fig. 7: Discrepancies to ITRF2000 coordinates1998.4.

From Figures 3 and 5 one can conclude that the repeatability is of the order of 10 times higher than the formal precision. The same conclusion can be obtained by analyzing Figures 2 and 3. Therefore, the values shown in Figure 4 provide a more realistic evaluation of the quality of the stations coordinates. Concerning the comparison with other techniques or processing, in order to evaluate the accuracy of the PPP, two solutions were available

From Figure 7 one can observe that for most of the stations coordinates the discrepancies are better than the precision provided by ITRF2000 solution (see Fig. 6). The worst results are related to station IMPZ, which also presents the worst precision in ITRF2000. The comparison with SIRGAS 1995.4 also shows very reasonable results. The values shown in Figure 4 are a good

indication of the precision of the stations coordinates presented in this paper.

Discrepancies (mm)

40 20

E

0

N h

-20 -40

BOMJ

BRAZ

CUIB

FORT

IMPZ

MANA

PARA

UEPP

than the formal precision. Comparison with SIRGAS 1995.4 and ITRF2000, both at the reference epoch 1998.4, showed that the accuracy is in the same level of the estimated precision (repeatability). It is of the order of 2cm. The results obtained from the experiment carried out showed that the PPP is a good tool for providing connection of a regional GPS network to the ITRF, if centimetre accuracy is required.

VICO

Stations

7 Acknowledgments Fig. 8: Discrepancies to SIRGAS coordinates at 1998.4.

Considering that in a local coordinate system the correlation between the components of the coordinates of one ITRF has to be neglected, another comparison was performed, but using the geocentric Cartesian coordinates. Figure 9 shows the discrepancies between both solutions. Again, the PPP solution agrees quite well with the ITRF2000 solution. The higher discrepancy is also related to the station IMPZ, which also provided the worst precision in the ITRF2000 (54, 59 and 14 mm for X, Y and Z respectively).

Discrepancies (mm)

40 20

X

0

Y Z

-20 -40

BOMJ

BRAZ

CUIB

FORT

IMPZ

MANA

PARA

UEPP

VICO

Stations

Fig. 9: Discrepancies to ITRF2000 coordinates at 1998.4.

From what was shown, one can conclude that PPP provides good accuracy for the purpose of connecting regional GPS network to ITRF. A limitation, as stated by Zumberge et al. (1997), is that no correlation is provided between sites, independently of the receiver location. Therefore, for using the covariance matrix, additional investigation is required.

6 Final Comments and Conclusions The basic fundamentals of PPP were presented as well as the results of an experiment carried out with GPS data from Brazilian RBMC stations. The results were analysed in terms of formal precision, repeatability and accuracy. The daily repeatability was of the order of 10 times higher

The financial support was provided by FAPESP (grant 95/08775-1) and CNPq (grant 523448/953). IBGE provided the data.

8 References Bierman G. J. (1977). Factorization Method for Discrete Sequential Estimation, Academic, San Diego, 233 p. Blewitt G., M. B. Heflin, F. H. Webb, U. J. Lindqwister; R. P. Malla (1992). Global Coordinates with Centimeter Accuracy in the ITRF Using GPS, Geophysical Research Letters, Vol. 19, No. 9, pp.853-856. Blewitt G. (1989). Carrier Phase Ambiguity Resolution for the Global Posistioning System Applied to Geodetic Baselines up to 2000 km, Journal of Geophysical Research, Vol. 94. NO. B8, 10.187-10.203. Ffoulkes-Jones G.H. (1990). High Precision GPS by Fiducial Techniques, Nottingham, PhD Thesis, University of Nottingham. Fortes L. P. S. (1997). Operacionalização da Rede Brasileira de Monitoramento Contínuo do Sistema GPS (RBMC), Tese de Mestrado, IME, 152 p. Gemael C. (1994). Introdução ao Ajustamento de Observações: Aplicações Geodésicas, Curitiba, PR., Editora da UFPR, 319p. Héroux P. and J. Kouba (1995). GPS Precise Point Positioning with a Difference, http://www.geod.emr.ca/docs/PDF, 12p. IBGE, Departamento de Geodésia (1997) SIRGAS Final Report , Rio de Janeiro, 99 p. Mccarthy D. D. (1996). IERS Conventions (1996), IERS Technical Note 21, Central Bureau of IERSObservatoire de Paris, 95 p. Monico J. F. G. (2000). Posicionamento Pelo NAVSTARGPS: Descrição, Fundamentos e Aplicações, Editora Unesp, 287 p. Monico J. F. G., E. S. FONSECA, D. BLITZKOW (1997). The Non-Fiducial Approach Applied to GPS Networks, In: Proc. of IAG Scientific Assembly 97, RJ, p. 149-154. Zumberge J. F., M. B. Heflin, D. C. Jefferson, M. M. Watkins and F. H. Webb (1997) Precise Point Positioning for the efficient and robust analysis of GPS data from large networks, Journal of Geophysical Research, VOL. 102, NO. B3, 5005-5017. Webb F. H. and J. F. Zumberge (1997). An Introduction to GIPSY/OASIS-II, Jet Propulsion Laboratory, JPL D11088, Pasadena CA.