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УДК 629.783:528
ЭФФЕКТИВНОСТЬ СПУТНИКОВЫХ ДАННЫХ НА КОНЕЧНЫХ ПУНКТАХ IGS ДЛЯ КИНЕМАТИЧЕСКИХ РЕШЕНИЙ PPP С ИСПОЛЬЗОВАНИЕМ ПРОГРАММНОГО ОБЕСПЕЧЕНИЯ BERNESE И ОНЛАЙН-СЕРВИСА CSRS-PPP
Ашраф Абдаллах
Университет Штутгарта, Институт инженерной геодезии, Германия, Stuttgart, D-70174, Ge-schwister-Scholl-Str. 24D, магистр, тел. +49 (0711) 6858-4051, факс: +49 (0711) 6858-4044, e-mail: ashraf.abdallah@ingeo.uni-stuttgart.de
Фолькер Швигер
Университет Штутгарта, Институт инженерной геодезии, Германия, Stuttgart, D-70174, Ge-schwister-Scholl-Str. 24D, доктор наук, профессор, директор, тел. +49 (0711) 6858-4044, факс: +49 (0711) 6858-4044, e-mail: volker.schwieger@ingeo.uni-stuttgart.de
Кинематическая оценка PPP - это одна из самых больших проблем получения высокой точности позиционирования, сдвиг временной шкалы навигационных спутников играет важную роль в оценке PPP, особенно в кинематическом режиме. В статье анализируется влияние сдвигов временной шкалы навигационных спутников на кинематическое решение PPP. В исследованиях использованы два инструментария для обработки: программное обеспечение Bernese GNSS и онлайн-сервис CSRS-PPP. Для оценки рассматривались временные шкалы навигационных спутников IGS со сдвигом 30 секунд. В данном исследовании проводились наблюдения и обработка трех кинематических траекторий на реке Рейн в районе г. Дуйсбург (Германия). Данные обрабатывались с интервалом 5 секунд. Кинематические решения PPP сравнивались с решением по двойным разностям, полученным программным обеспечением Bernese GNSS.
Программное обеспечение Bernese GNSS выдает два решения по умолчанию - среднее SD для трех траекторий - 9 см в плане и 18 см по высоте. Адаптированное программное обеспечения Bernese дает лучшее решение по средним SD - 7 см в плане и 12 см по высоте. Выполнен последующий анализ результатов по данным из онлайн-сервиса CSRS-PPP. Сервис поставляет среднее SD 6 см по восточному направлению, северному и по высоте. Результаты обработки данных позволяют оценить кинематическое решение PPP посредством программного обеспечения Bernese GNSS и онлайн-сервиса CSRS-PPP. CSRS-PPP улучшает точность в плане на 33 % по сравнению с точностью, полученной из решения по умолчанию с помощью программного обеспечения Bernese, и по высоте более чем на 67 %.
Ключевые слова: точные эфемериды от IGS, кинематические GPS-PPP, программное обеспечение Bernese GNSS, онлайн-сервис CSRS-PPP.
PERFORMANCE OF IGS FINAL SATELLITE DATA FOR KINEMATIC PPP SOLUTIONS
USING BERNESE SOFTWARE AND CSRS-PPP ONLINE SERVICE
Ashraf Abdallah
University of Stuttgart, Institute of Engineering Geodesy, Germany, Stuttgart, D-70174, Geschwi ster-Scholl. - Str. 24D, M. Sc., tel. +49 (0711) 6858-4051, fax: +49 (0711) 6858-4044, e-mail: ashraf.abdallah@ingeo.uni-stuttgart.de
Volker Schwieger
University of Stuttgart, Institute of Engineering Geodesy, Germany, Stuttgart, D-70174, Geschwister-Scholl.-Str. 24D, Dr.-Ing., Professor, Director of the Institute of Engineering Geodesy, tel. +49 (0711) 6858-4041, fax: +49 (0711) 6858-4044, e-mail: volker.schwieger@ingeo.uni-stuttgart.de
The kinematic PPP estimation is one of the greatest challenges to obtain high accuracy for positioning. The satellite clock interval plays a major effect on the PPP estimation, especially in the kinematic mode. This paper analyses the impact of the interval of satellite clocks on the kinematic PPP solution. Two processing tools have been used in this study: Bernese GNSS software and the CSRS-PPP online service. IGS satellite clocks with an interval of 30 seconds have been considered for the estimation. In this research study, three kinematic trajectories, which were observed on the Rhine River, Duisburg, Germany have been processed. The processed data have an interval of 5 seconds. The kinematic PPP solutions are compared to the double-difference solution of Bernese GNSS software.
Bernese GNSS software provides two solutions; the default solution shows for the three trajectories a mean SD of 9 cm in the horizontal components and 18 cm in the height plan. The adapted solution of Bernese software delivers a better solution with a mean SD of 7 cm in the horizontal components and 12 cm in the height plan. Further analysis results from CSRS-PPP online service are introduced in this research. It delivers a mean SD of 6 cm in East, North, and height. The results provide insights for the PPP kinematic solution using Bernese GNSS software and CSRS-PPP online service. CSRS-PPP achieves more than 33 % improvement in the horizontal accuracy than that obtained from the default solution of Bernese software; it achieves in height, more than 67 %.
Key words: IGS Final Ephemeris, kinematic GPS-PPP, Bernese GNSS software, CSRS-PPP online service.
1. INTRODUCTION
Over the last two decades, the precise point positioning (PPP) technique, which uses only a single receiver has gained an increase of interest. To obtain the centimeter accuracy level, a dual frequency GNSS instrument is required (Gao, 2006). Zumberge et al. (1997a) have been through the group of the Jet Propulsion Laboratory (JPL) administrated the most efficient method for the PPP estimation for GPS data. Zumberge et al. (1997b) introduced the PPP estimation using precise satellite clock data with 30 second interval.
As seen in Equation (1), the true geometric range r between the receiver coordinates xR, yR, zR and satellite coordinates xs, ys, zs is a function of the time difference between the transmitted GNSS signal from the satellite ts and the received signal from the reciever tR. This time is multiplied by the speed of light in vacumm c. The satellite clock bias ds is adjusted using of the precise clock ephermeris. The receiver clock bias 3R is estimated during the estimation (Hoffmann-Wellenhof, et al., 2000). The pseudo-range p in metre is caculated regarding Equations 2.a, b, and c (Kaplan & Hegarty, 2006). Ip symbol mentions to the ionospheric delay in metre; Tp denotes to the tropospheric delay in metre. sp and sp refer to the un-modelled errors e.g. the solid earth tides, pole tides, ocean and atmospheric loading, and the random noice ef-
fects (Mirsa & Enge, 2012). In case of the carrier phase measurements, the range between the satellite and the receiver could be measured by the total numbers of full cycles plus the fractional cycle at the receiver. These numbers of cycles are multiplied by the carrier wavelength (A). The carrier phase measurement in metre (A.<P) can be presented as in following Equation (3) (Mirsa & Enge, 2012).
r = c(tR -ts) = c-At = J(xs - xR)2 + (ys - yR)2 + (zs - zR)2, (1)
p = c ((tR + 5R) - (tS + 5s)) + Ip + Tp + £p, (2.a)
p = c(tR - tS) + c(5R - 5s)) + Ip + Tp + £p, (2.b)
p = r + C(8R - 8s)) + Ip + Tp + £p, (2.c)
№ = r + c (ÔR- 0s) -I0 + Tcp + AN + s0, (3)
The precise satellite orbits and clocks may be provided from the International GNSS Service (IGS). The final ephemeris is obtained with a time latency of 12-18 days after the observation day with an orbit accuracy about 2.5 cm and an interval of 15 min. The clocks are avilable with two intervals: 5 min and 30 sec with an accuracy around, 0.075 ns. The IGS satellite orbit and clock data can be obtained from the FTP server under (ftp://igscb.jpl.nasa.gov/pub/product/wwww/) (IGS-FTP, 2015). Further satelllite orbits are available from the Centre of Orbit Determenation in Europa (CODE) (CODE, 2015). The satellite orbit data have an interval of 15 minutes, and the clock data from CODE are presented with two intervals: 30 and 5 seconds. These kind of satellite data can be downloaded from the FTP server under (ftp: //ftp. unibe. ch/aiub/CODE/yyyy/).
Typically, the concept of the PPP solution for the dual frequancy measurement data is based on the ionosphere-free linear combination. This linear combination includes the carrier phase (O) and code data (p), see Equation (4) and (5) (Mirsa & Enge, 2012):
0IF = W-K)®11 = 2.5460L1 - 1.546^2, (4)
PiF =772-T^Pli -772-T^PL2 = 2.546pLi - 1.546pL2 (5)
fii p__fi2
(fL{ - fu2) (fll - fh2) where
&IF & pIP ionosphere-free linear combination for carrier phase and code data, fL1 & fL2 GPS frequencies of the L1 and L2 signals, </)L1 & (f>L2 carrier phase for the signals Lj & L2, pL1&pL2 code data for the signals Lj& L2.
The ionosphere-free linear combination removes the first order of the ionospheric error. Therefore, higher order ionospheric terms are recommended for more accurate solution (Keder, et al., 2003) & (Bassiri & Hajj, 1993). The troposphere zenith delay consists of two parts: dry (hydrostatic) and wet zenith delay. The dry part can be
modelled, and it represents around 90% of the total delay (Hoffmann-Wellenhof, et al., 2000). The wet part depends on the water vapour along the signal path. This part is unpredectable and varies quickly (Mirsa & Enge, 2012). By considereing the arbitrary zenith angle of the signal, the troposphere delay is functionaly estimated related to the elevation angle using the mapping function for dry and wet parts and the elevation angle (Böhm, et al., 2006a) & (Hoffmann-Wellenhof, et al., 2000). More information about the tropospheric delay can be found in Saastamoinen (1973), Hopfield (1969), Marini (1972), Niell (1996), Böhm, et al., (2006.a), and Böhm, et al., (2006.b).
This paper invistigates the performance of the IGS satellite clocks with an interval of 30 seconds on the PPP kinematic solution. Two processing tools are used in this research study: (i) Bernese GNSS software, which uses the linear interpolation between the two known neighbor clocks (Dach, et al., 2007) and (ii) CSRS-PPP online service, which uses the linear interpolation process as well. Moreover, as a contact with Tetreault(2015), ' The standard deviations of the interpolated clocks are adjusted to take into account the behavior of the respective satellite clocks"The reference solution in this research is the double-difference solution from Bernese GNSS software. Three trajectories have been observed on the Rhine River, Duisburg, Germany as part of the project "HydrOs - Integrated Hydrographical Positioning System".
The investigation of the effect of satellite clocks interval is a major area of interest within the field of the kinematic PPP solution. Previous study from Fei et al. (2010) has documented the effect of different satellite clock products on the kinematic PPP solution. One day of the static IGS station, ALGO, with an interval of 1 second has been processed using IGS satellite clocks with an interval of 30 seconds. The estimated RMS was in 5 cm in the East and North and 11 cm in the height direction. The clocks are linearly interpolated and the PPP solution is estimated using the TriP software, which is delivered by Wuhan University, China. To determine the effects of satellite clock interval for the kinematic PPP solution using CSRS-PPP online service, Abdallah & Schwieger (2014) have reported the accuracy of kinematic data with an interval of 1 second. The estimated RMS is 5 cm in the horizontal direction and in 10 cm in the height direction.
Regarding the solution using Bernese, Abdallah & Schwieger (2015) have presented the accuracy of the Bernese GNSS software for two trajectories of our study. The used satellite clocks were from CODE with an interval of 5 seconds. This means, in this case, that the measurement sample matches the interval of satellite clocks. The reported SD of the absolute errors for the first trajectory was 6 cm, 2.1 cm, and 6.8 cm in East, North and height directions respectively. Moreover, the second trajectory showed 1.7 cm in East, 2.6 cm in North, and 4.9 cm in height.
2. GNSS SOLUTIONS
The PPP solution in this study has been obtained using Bernese GNSS software V. 5.2 and the CSRS-PPP online service. The solution methodology using the two processing tools is explained in the next points.
2.1 Bernese GNSS Software
Using Bernese GNSS software V. 5.2, the GNSS data can be processed in post processing in static and kinematic mode. This software was developed at the Astronomical Institute of the University of Bern (AIUB), Switzerland. The software is widely used to solve geodetic networks. It deals with the GNSS measurement data for double-difference (Differential GNSS estimation), and zero-difference (PPP solution estimation) (Dach, et al., 2007). The software has a windows user interface for easly usage during the processing. Figure 1 depicts the processing schedual using Bernese software. The processing steps can be concluded as follow:
1. Download the related orbits from IGS ftp server for the satellite orbit and clock data (IGS-FTP, 2015).
2. The orbit tools consist of three programs:
o POLUPD program: convert the Earth orientation parameters to Bernese format,
o PRETAB program: convert the satellite data a tabulate orbit file, o ORBGEN program: generate the standard orbit format to Bernese software.
3. Pre-processing tools for RINEX files, which contain of three programs: o RNXGRA program: check the overview of the RINEX data,
o RNXSMT program: this program aims to clean the RINEX observation data. The outliers and cycle slips are screened. Later, the cycle slips are corrected,
o RXOBV3 program: this program is used to transform the RINEX observation file into Bernese binary format.
4. Clock Synchronization for the receiver clock using the dual code combination; these clocks are stored into the observation files. This step is carried out through program (CODSPP). Moreover, an a priori kinematic file is created also to be inserted to the final solution.
5. The parameter estimation of the zero-difference solution (PPP solution) is estimated using the main program of GPSEST program. In this case, the orbit data, observation data after receiver clock synchronization, and the a priori kinematic file are inserted into the estimation. Two loops from GPSEST program are carried inside the software to get the final solution:
I. The first solution is aimed to generate a residual file for data based on the L3 linear combination. The satellite residuals for each epoch are written as elevation dependent weighting of the observations. The residuals are screened. The default considered values to be screened is 6 mm for the phase residuals and 60 cm for the code residuals. The bad observation data are marked and written to the observation files,
II. The second solution is based on the cleaned observation.
6. In case of double-difference solution (the right box in the flow chart in Figure (1)):
o The base line form is created using SNGDIF program.
Figure 1: General processing schedule for Bernese GNSS software
o Regarding the main estimation for double-difference solution, four loops GPSEST program and other sub- programs are considered.
I. The first loop aims to screen the satellite residuals using float solution of ionosphere-free linear combination L3,
II. The second loop aims to estimate the tropospheric delay using float solution L3,
III. The estimated tropospheric delay parameters are inserted to the third loop to estimate the ambiguity for L& L2,
IV. The final solution is accomplished through the forth loop by inserting the estimated ambiguity. The kinematic PPP estimation (Epoch-wise solution) is activated in this final loop.
7. The final estimated output is the epoch-wise kinematic file for double-difference or PPP solution.
2.2 CSRS-PPP Online Service
The Canadian Spatial Reference System (CSRS) is an online service for the PPP solution for static and kinematic RINEX measurement data. This service is provided by the National Resource of Canada (NRC). CSRS-PPP online service is one of the most
famous services. The access of the service is available for registered users under (CSRS-PPP, 2015). The user uploads the RINEX file to the website, and he obtains the solution details via e-mail. As seen in Figure (2), the user may select the type of processing, and the datum. Finally, the RINEX file is selected to be uploaded.
Figure 2: CSRS-PPP online service technique (CSRS-PPP, 2015) 3. KINEMATIC PPP SOLUTION AND ANALYSIS PROCEDURE
As seen in Table 1, the reference system for the two processing tools is ITRF2008 (International Terrestrial Reference Frame) (ITRF, 2015). The estimated PPP coordinates from Bernese GNSS software have XYZ format; later, they are transformed to Ellipsoidal/UTM system; On the other hand, CSRS-PPP provides Ellipsoidal/UTM system. The IGS final products are used for the two processing techniques with satellite orbit of 15 minutes interval and clock of 30 seconds interval. The satellite and receiver antenna phase variation are based on IGS-ANTEX format (NGS, 2014). The troposphere estimation is a little bit different; the estimation using Bernese software is estimated based on the Global mapping Function (GMF) model, which is the meteorological data is base on the Global Pressure and Temperature (GPT) model. On the other side, the hydro-static troposphere delay is modelled in CSRS-PPP using Davis model based on GPT model. The wet part is modelled using Hopfield model based on GPT and the mapping function is GMF. The ionosphere delay is eliminated mainly using the linear ionospheric free combination, and the second order is considered also for the two solutions. Only GPS measurement data are processed with an interval of 5 seconds and an elevation angle of 10°.
Table 1: Processing parameters
ID Bernese GNSS software CSRS-PPP online service
Reference System ITRF2008
Coordinate format XYZ XYZ/Ellipsoidal/UTM
Satellite Orbit and clock ephemeris IGS final (Orbit: 15 min interval & clock: 30 sec interval)
Satellite phase center offsets IGS ANTEX
Receiver phase center offsets IGS ANTEX
Tropospheric model GMF (GPT) Dry :Davis (GPT)
Wet: Hopfield model (GPT)
GMF
Linear ionospheric free combination
Ionospheric model
second order parameters
GNSS System GPS
Observation data Both phase and code
Elevation cut-off angle 10°
Sampling rate 5 second
As shown in Figure 3, mainly the double-difference solution from Bernese GNSS software have been considered as the reference solution for the obtained PPP solutions from Bernese software and CSRS-PPP online service. In this contest, the error between the refernce coordinates M and the PPP solution M' are estimated as to be in Equation (6). i refers to the number of epochs, and j mentions to the East, North, and ellipsoidal height. The root mean square error (RMS), which refers to the error relative to the know coordinates estimated regarding to Equation (7); n refers to the total number of epochs. Furthermore, the standard deviation a is calculated as shown in Equation (8) relative to the mean error value ^ (Mikhail, 1976). The kinematic measurements have been twice processed using Bernese software: © the default solution with the default solution; © the adapted solution, which means, deactivate the screening of the residuals in the GPSEST process.
8Uj = M — M'
RMS = 2 A 1 r M2
G = A 1 n — 1 Y (su v)
(6)
(7)
Figure 3: Processing scheme
4. EXPERIMENTAL WORK
In order to identify the accuracy of kinematic PPP solution that obtained from Bernese GNSS software and CSRS-PPP, three kinematic trajectories have been surveyed from Duisburg harbor, Rhine River, Duisburg, Germany with a total length around 51 km. These data are observed as a part of 'HydrOs - Integrated Hydrographical Positioning System' project (Beitenfeld, et al., 2014). An antenna of LEIAX1203+GNS S and a receiver LEICA GX1230+GNSS are located on the surveying vessel (Mercator) to collect the GNSS data. Figure 4 presents the surveying vessel and the GNSS antenna over it. Figure 5 shows the layout of the first trajectory; other trajectories are in the same location. Some details about the three trajectories are reported in Table 2. The data have been observed during two days; the start and end time are listed, as well.
Table 2: Details of the observation data
ID Country/ Year/ DOY Start time End time Interval Trajectory Length [km]
City hh mm ss hh mm ss ss
1 Germa- 2014/126 07 40 00 10 10 05 05 10.70
2 ny/ 2014/126 10 17 05 14 15 00 05 19.40
3 Duisburg 2014/127 06 14 20 11 34 30 05 21.00
Figure 4: Observation vessel for the measurement data Mercator observation vessel (left figure); GPS antenna over the vessel (right figure)
Photo by: Annette Scheider (IIGS)
Figure 5: Layout of the first trajectory (DOY: 2014/126) © Google earth (Image: 30.06.2015)
5. RESULTS AND DISCUSSION
As previously described, the RINEX measurement data have been processed using Bernese GNSS software and CSRS-PPP online service. To begin this process, the data of three kinematic trajectories are differenced with a virtual station from SAPOS (SAtelliten POSitionierungsdienst der deutschen Landesvermessung). This SAPOS station was provided from SAPOS-NRW team (SAPOS-NRW, 2014). SAPOS is a CORS (Continuously Operating Reference Station) service, which is collecting the GNSS data around Germany (SAPOS, 2014). The PPP estimation using Bernese
GNSS software is carried through an automatic script (Bernese Protocol Engine (BPE)).
5.1 Bernese GNSS software solution
To distinguish between the two solutions, Figure 6a - f presents the PPP solution errors for the three trajectories using Bernese GNSS software. The left part of these plots shows the errors in the East, North, and height plans. The horizontal axis refers to the GPS time week second and the vertical axis mentions the error value in meter. The right part of these plots provides the error plots in two planes: East-North, and East-Height planes. Figure 6a - b shows the PPP error for the default and adapted solution for the first trajectory. The solution faces some loss of lock during the measuring; therefore, some epochs have not been resolved; the un-resolved epochs are marked with two dashed lines. The default solution in East and North show errors up to 25 cm and other epochs report more than this value. Otherwise, the results obtained in the height direction show higher PPP errors. This error reaches to up to 50 cm. On the other hand, the adapted solution shows a smoother solution than that reported from the default solution. Table 3 summarizes the statistical analysis for the Bernese PPP estimation; the default solution for the first trajectory shows a RMS of one decimeter in the horizontal and 18 cm in height. The adapted solution shows a little improvement in the horizontal plan; otherwise, an obvious improvement in the height plan, which reports one decimeter.
Regarding the second trajectory, Figure 6c - d shows the PPP errors; the default solution reportes in the horizontal direction up to more than 25 cm. In height direction, the solution shows errors more than half meter and increased up to 1 m in some epochs. The adapted solution shows a smooth PPP solution, which decreases the error's ranges. As given in table 3, the solution is closed to the first trajectory. The third trajectory shows a better solution than that obtained from the previous trajectories; the possible explanation is due to the lower number of cycle slips and higher convergence time. The solution shows errors up to more than 50 cm, and 1 m for the horizontal and height directions, respectivelly; see Figure 6e - f. The statistical results for this trajectory that reported in table 3, shows a RMS for the default solution of 7 cm for horizontal plan and double decimeter for height. The adapted solution delivers a RMS of 5 cm in horizontal plan and 15 cm in height plan.
Error plot for the first trajectory BERNESE-Default Error in East 4 North or East a Height
Error plot for the first trajectory BERNESE-Adapted
Error in East & North or East & Height
2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2 09
GPS time week second . „
x 10
Error plot for the second trajectory BERNESE-Default
2.1 2.12 2.14 2.16 2.18 2,2 2.22 GPS time week second
Error plot for the second trajectory BERNESE-Adapted
2 1 2.12 2.14 2.16 2.18 2,2 2.22 GPS time week second
Error plot for the third trajectory BERNESE-Default
2 82 2.84 2
2 88 2.9 2.92 2.94 2.96 2.98 3 GPS time week second ,
1£
Error plot for the third trajectory BERNESE-Adapted
B 0.5
c 0
o
Ü -0.5
-1.5
f
♦ 9 t • East • North • Height
2.82 2.84 2.86 2.88 2.9 2,92 2.94 2.96 2.98 3 GPS time week second „ ,
E 1.5
JZ CD I
I 0-5
o £ 0
T
(■> -0.5
e
p
LU ■1.5
-1 5 Error in
1 -0.5 0 0 5 1 1.5 Error in East (m)
East 8. North or East & Height
._. 1.5
-C en
X 0.5
o 0
o z -0.5
tC
p
LU -1.5
-1.5
-1 -0 5 0 0.5 1 1.5 Error in East (m)
Error in East & North or East & Height
._. 1.5
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X 0.5
o 0
o z -0.5
tC
p
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-1.5 -1 -0 5 0 0.5 1 1.5 Error in East (m)
Error in East S North or East & Height
1.5
■
-C en
CD X 0.5
o 0
o z -0.5
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Error in East & North or East & Height
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CT 1
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o 0
: ■
o -0.5
O
ID -1.5
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Figure 6: PPP solution form Bernese GNSS software Table 3: Statistical results from Bernese GNSS software
TRAJ1 TRAJ2 TRAJ3
East North height East North height East North height
Default-Solution RMS [m] 0.104 0.120 0.178 0.10 0.11 0.186 0.078 0.072 0.203
a [m] 0.103 0.119 0.164 0.087 0.089 0.186 0.078 0.07 0.184
Adapted-Solution RMS [m] 0.081 0.104 0.010 0.10 0.09 0.113 0.050 0.052 0.149
a [m] 0.081 0.096 0.096 0.068 0.075 0.107 0.050 0.052 0.144
5.2 CSRS-PPP Online Service solution
Interesting results are obtained from the PPP solution from the online service of CSRS-PPP. Figure 7a shows the PPP solution for the first trajectory. The trajectory faces loss of lock as to be seen in the dashed lines. The solution is deviated after these un-resolved epochs. Possible explanation of this deviation is to be due to the shifted in the ambiguity resolution after the loss of lock. The errors display up to more than 25 cm in East-North and up to more than 50 cm in the height direction. Figure 7b - c refer to the errors for the second and third trajectories; the solution shows a significant improved accuracy. The results obtained from the analysis indicate up to more than 10 cm in the horizontal direction and up to more than 25 cm in the height direction.
Table 4: Statistical results from CSRS-PPP online service
TRAJ1 TRAJ2 TRAJ3
East North height East North height East North height
RMS [m] 0.182 0.114 0.068 0.082 0.082 0.087 0.023 0.026 0.041
a[m] 0.098 0.104 0.063 0.066 0.072 0.087 0.022 0.022 0.033
Error plot for the first trajectory CSRS-PPP
Error in East & North or East & Height
b
2.04 2.05 2.06 GPS time week ficconri
Error ptot for the second trajectory CSRS-PPP
Cast
o North
* MeigW
2.16 2.1S 2.2 GPS time week second
Error plot for the second trajectory CSRS-PPP
; 0.5 0' -05 -1
-1.5
2.32 2.S4 2.B6
2 00 2.3 2.32 2.34 GPS rime week second
2.24 x 10s
Cast
O North
• HeigM
3
x 10s
E 1
Î 0.5
I 0
1 -0.5
c
I
w -1.5
-1.5 -1 -0.5 0 0.5 1 1.5 Error in East (rn)
Error in East&North or East&Height ■ 1.5
1
0 5 0
-0 5 -1 -1.5
1 5 -1 -0 5 0 0.5 1 Error in East in;
Error in East & North or East 5. Height 1.5.....
1
0 5 0
-0 5 -1 -1.5
-1 5 -1 -0.5 0 0.5 1 1.5 Error in East (m)
c
Figure 7: PPP solution form CSRS-PPP online service
The statistical results for the solution from CSRS-PPP online service are set out in Table 4. The first trajectory shows the highest error due to the loss of lock during the
measurement. The solution has a higher RMS in the East & North directions than the one obtained in the height direction. The second trajectory indicates a RMS in East, North in 8 cm and around 9 cm in the height. The third trajectory shows the best solution, where it reports couple cm in the horizontal and 4 cm in height.
5.3 Discussions
As previously mentioned, the two processing tools have the same IGS satellite orbits data with a clock interval of 30 seconds. Nevertheless, there are differences in estimation process and tropospheric delay modelling between those two methodologies. In this current study, two solutions have been estimated using Bernese GNSS software. As to be seen in Figure 8, the study found that the SDmean from the default solution delivered 9 cm for East and North plans. Moreover, obtained one for height is 18 cm level. The adapted solution from Bernese GNSS solution showed SDmean of 7 cm in East and North plans; for height, it achieved SDmean of 12 cm. The most interesting finding was that, the CSRS-PPP provided a better solution, especially in height direction, than that achieved from Bernese GNSS software. The online service showed 6 cm in all plans.
By comparing the current results to the previous ones of Abdallah & Schwieger (2015), Bernese GNSS software provided with CODE satellite clocks of 5 seconds a better solution than that obtained from IGS satellite clocks with 30 seconds. Abdallah & Schwieger (2015) have been reported that the mean SD with 5 seconds clocks was 4 cm, 2.40, and 5.9 cm in the East, North, and height, respectively. The comparison of results with those from Abdallah & Schwieger (2015) study confirms that, Bernese GNSS software provides with CODE orbit data with clock interval of 5 seconds a better solution in horizontal plan than that obtained from CSRS-PPP online service. In height plan, the two solutions delivered almost the same accuracy.
0,20 0,18 0,16 0,14
JS 0,12
Q
0,10
§
e0,08 0,06 0,04 0,02 0,00
H Bernese_Default QBernese_Adapted □CSRS-PPP
0,18
0,07
vvvv ♦♦♦♦♦♦♦♦♦
♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦♦♦
East North Height
Figure 8: Mean SD for Bernese GNSS and CSRS-PPP online service
6. CONCLUSION
This research establishes a framework for the exploration of the effect of the satellite clock interval on the PPP kinematic measurements using Bernese GNSS software and the CSRS-PPP online service. Moreover, this study enhances our understanding of one of the parameters, which are affecting the kinematic PPP estimation. Three kinematic trajectories have been measured for two days on the Rhine River, Duisburg, Germany. In this study, the double-difference solution from Bernese GNSS software has been considered as the reference solution. The used satellite clocks in this study were IGS with an interval of 30 s. The results indicate that the achieved mean SD from the default solution of Bernese GNSS software were 9 cm in the two horizontal components and 18 cm for height. The processing has been extended to adapt the Bernese solution by deactivating of satellite residual screening. This adapted solution from Bernese delivered a better solution than that achieved from the default solution. The horizontal components showed mean SD of 7 cm; in height, the solution showed mean SD of 12 cm. Other side, the CSRS-PPP online service showed a better solution with 6 cm for all plans.
In a comparison with the previous study of Abdallah & Schwieger (2015), Bernese GNSS software using CODE orbit data with 5 seconds satellite clocks delivered the best solution. Moreover, the CSRS-PPP online service comes in the second time regarding the estimated accuracy. Finally, the solution using Bernese software with IGS satellite clocks with an interval of 30 seconds comes later in the accuracy level, even with the adapted solution. Therefore, this study recommends the using of the Bernese GNSS software with CODE satellite clocks with 5 seconds for the kinematic application with high rate observation interval. Otherwise, it is best to use the CSRS-PPP online service to obtain an acceptable PPP accuracy for the kinematic measurements.
ACKNOWLEDGEMENTS
The authors would like to thank Ms. Annette Scheider for receiving the GNSS measurements through the HydrOs project. Special thanks go to our partners from the BfG Mr. Harry Wirth and Mr. Marc Breitenfeld. Further thanks also for Mr. Bernhard Galitzki form SAPOS-NRW for providing us with the reference station. Further thanks for Mr. Pierre Tetreault in the Natural Resources Canada for the kindly contacts regarding the CSRS-PPP online service. The authors would like to thank the Egyptian higher education ministry and the German Academic Exchange Service (DAAD) in Germany for the funding of the PhD research.
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© Ashraf Abdallah, Volker Schwieger, 2016
