Reliability of CSRS-PPP for Validating the Egyptian Geodetic Cors Networks

The global navigation satellite system (GNSS) techniques are effective for monitoring landslides and earth movement in high-rise and coastal regions. The GNSS techniques support construction activities against earthquake effects, leading to an early warning for the catastrophic crisis and risk management. The US National Oceanic and Atmospheric Administration’s (NOAA’s) national geodetic survey (NGS) introduced the concept of continuously operating reference stations (CORS) two decades ago. This system is designed to provide users with the geodetic latitude, longitude, height, orthometric height, geopotential, acceleration of gravity, and vertical deflection at any point in the USA (Snay & Soler 2008).

The international GNSS service (IGS) provides a worldwide collection of CORS network stations. Walpersdorf et al. (2007) reported that the IGS stations in Africa have many characteristics. The network is mainly situated in a coastal area with long baselines, and this location affects the accuracy of network precision. In addition, the network is very active with ionosphere activities.

Egypt is rapidly undertaking many infrastructure projects such as highways, railway projects, and the construction of many new cities. One of the main obstacles in obtaining reliable continuous GNSS solutions is the lack of coverage for IGS stations. Consequently, the Egyptian Surveying Authority (ESA) established the first permanent Egyptian CORS network in January 2012. The network consisted of 40 stations covering mainly the Nile valley and its delta (Figure 1). Furthermore, according to the ESA (2012), the network was adjusted relative to the International Terrestrial Reference Frame (ITRF) system at the epoch October 23, 2011 (ITRF 2020). Moreover, the ESA older national passive GNSS reference network, called the high-accuracy reference network (HARN) (Figure 1), established in 1995, was referenced to the ITRF1994 (epoch 1996).

Figure 1.

Zumberge et al. (1997) introduced the precise point positioning (PPP) estimation model two decades ago. The PPP technique that requires just one GNSS receiver faces many error sources, and these errors need to be modeled or eliminated. Four types of errors are considered: satellite-dependent, receiver-dependent, atmospheric (troposphere and ionosphere), and geophysical errors, including solid earth tides, polar tides, ocean tidal loading, and atmospheric tidal loading. Several software packages and online services provide the PPP solution (Table 1).

Researchers have recently shown increasing interest in evaluating the PPP accuracy of CORS network in Africa. Abdallah (2015) investigated different static PPP solutions for four CORS in Germany and found that solutions reached centimeter-level accuracy using the static technique for a convergence time of 24 h. This result matched the one obtained by Ayhan and Almuslmani (2021). In addition, Abdallah and Schwieger (2016) introduced a study of the PPP solution for the IGS-CORS in Africa. They concluded that the PPP solution obtained using (Canadian Spatial Reference System) CSRS-PPP online service produced three-dimensional (3D) root mean square error (RMSE) between 4 and 6 mm. Similar results based on GNSS datasets in Egypt were reported by El Shouny and Miky (2019) and El Manaily et al. (2017). Rabah et al. (2016) proposed the utilization of PPP for geodetic datum maintenance and update in Egypt. Jamieson and Gillins (2018) determined the accuracy of static PPP solution for a static campaign, which consisted of six stations with 10 h of observation data. The study showed less than 1 and 1.5 cm accuracies for the horizontal and vertical directions, respectively. To evaluate the accuracy of the new Nigerian GNSS network (NIGNET), Isioye et al. (2019) studied different PPP online services with different observation durations (1, 2, and 6 h, and up to 24 h). The study used free online PPP services (e.g., GNSS Analysis and Positioning Software (GAPS-PPP) and magicGNSS). They found that the online GNSS PPP processing services can provide users with reliable results. Further, the results showed that the 24-h observation files produced results with a millimeter to centimeter level of accuracy by processing with magicGNSS and GAPS-PPP services.

This study aims to contribute to this growing area of research by exploring the accuracy of static PPP solutions for the Egyptian permeant CORS (ESA-CORS). The observation data of ESA-CORS are accessible only for the ESA and unavailable for users. Therefore, this paper assesses the significance and reliability of using CSRS-PPP as a solution to obtain a geodetic coordinate, such as a static PPP solution. The overall structure of the study comprises five sections, including this introductory section. Section 2 begins by laying out the theoretical approach of PPP solution and explaining the processing parameters using CSRS-PPP online service. Section 3 discusses the dataset and evaluation methodology. Section 4 presents the analysis and discusses the results obtained. Finally, the conclusion provides a summary of our findings.

As shown in equations (1)–(4), the PPP position is determined based on the processing of the following ionosphere-free combination of the undifferenced code (ρRIFS), and phase (ΦRIFS) of multi-constellation GNSS observations (Hofmann-Wellenhof, Lichtenegger & Wasle 2008; and Misra & Enge 2012). The first order of the ionospheric delay is eliminated for dual-frequency receivers using the ionospheric-free linear combination (IF). This combination does not eliminate the full ionosphere refractions. The higher order that ranges from sub-millimeters to several centimeters is considered for highly accurate applications such as surveying CORS coordinates (Kedar et al. 2003). 1 ρ=r+c(δR−δS)+Δiono+Δtrop+Δsol+Δpol+Δocn+Δatm+Δmul+∈p 2 λΦ=r+c(δR−δS)−+Δtrop+λN+Δsol+Δpol+Δocn+Δatm+Δmul+Δpcv+λw+∈Φ $$\matrix{ {\lambda \Phi = r + c({\delta ^R} - {\delta ^S}) - + {\Delta _{{\rm{trop}}}} + \lambda {\rm{N + }}{\Delta _{{\rm{sol}}}} + {\Delta _{{\rm{pol}}}} + {\Delta _{{\rm{ocn}}}} + {\Delta _{{\rm{atm}}}} + {\Delta _{{\rm{mul}}}} + } \hfill \cr {{\Delta _{{\rm{pcv}}}} + \lambda {\rm{w + }}{ \in _\Phi }} \hfill \cr } $$ 3 ρRIFs=fl12ρl1−fl22ρl2(fl12−fl22)=2.546ρl1−1.546ρl2 4 ΦRIFs=fl12Φl1−fl22Φl2(fl12−fl22)=2.546Φl1−1.546Φl2 where:

Δ_iono is the ionospheric delay,

The tropsphereic zenith delay (Δ_trop) consi sts of dry and wet components. The dry component (zenith hydrostatic delay) is about 90% of the delay; this part can be modeled using mathematical models. The wet component (zenith wet delay) is unpredictable; it depends on water vapor and is typically less than 30 cm (Hofmann-Wellenhof, Lichtenegger & Wasle 2008; Bar-Sever, Kroger & Borjesson 1998). The total tropospheric zenith delay is expressed in equation (5). Due to the consideration of the arbitrary zenith angle of the signal, the estimation of the delay is expressed in the function of the elevation angle of the satellite E. Equation (6) estimates the tropospheric delay relating to the mapping function for the dry m_h and wet parts m_w (Misra & Enge 2012). 5 Δtrop=Tzh+Tzw 6 Δtrop(E)=Tzh⋅mh(E)+Tzw⋅mw(E) $${\Delta _{{\rm{trop}}}}\left( E \right) = T_z^h \cdot {m_h}(E) + T_z^w \cdot {m_w}(E)$$

Table 2 presents the processing parameters of CSRS-PPP software. The reference system for the software is based on ITRF 2014 (epoch 2019 according to measurement date); the obtained coordinates have Cartesians XYZ format and Ellipsoidal/(Universal Transverse Mercator) UTM system. The IGS final ephemerides are used during processing with a satellite orbit of a 15-min interval and a satellite clock of a 30-s interval. The ionospheric delay is eliminated for dual-frequency data using the ionospheric-free linear combination, and the second-order errors are equally considered. For single-frequency data, the ionospheric delay is modeled using the final global ionospheric maps (GIM) from IGS. Regarding the tropospheric delay, the processing tool that is based on the global pressure and temperature (GPT) model uses the Davis model for the hydrostatic delay. For the wet part, the processing mechanism uses the Hopfield model that is based on the GPT model. In addition, the Vienna mapping function (VMF1) is utilized (Boehm, Werl & Schuh 2006). The satellite and receiver antenna phase variations are based on the IGS-ANTEX (NGS 2021) format (CSRS-PPP 2021). Furthermore, the PPP-based coordinates in ITRF 2014 (epoch 2019) were compared with the recent network adjustment in the same frame and epoch.

Overall, 32 ESA-CORS were analyzed for three consecutive days (DOY: 201–203/2019) with an observation interval of 30 s (Figure 2a) using CSRS-PPP online service (see Table 2). For global impact, six IGS-CORS were also processed for the same observation days (Figure 2b); these stations are surrounding Egypt. The complete list of processed stations is presented in Table 3. The height of ESA-CORS varied between 30 and 149 m. Moreover, the height of IGS-CORS (shadowed stations in Table 3) varied between 31 and 886 m. Figure 2a shows the ESA-CORS and Figure 2b shows the IGS-CORS.

Figure 2.

To obtain the reference solution of ESA-CORS, Trimble Business Center (TBC) V 5.0 was used to process our geodetic network. The final precise satellite orbits “.SP3” and the satellite clock corrections “.clk” were downloaded from the IGS website and included in data processing. To achieve such a high-precision GNSS solution, ionospheric and tropospheric delays as well as ocean tide loading were considered. The processing strategy consisted of two steps: firstly, six ESA-CORS (ADFO, ALEX, CARO, MOUS, QANT, and SUZE) were first processed with six tied IGS-CORS (YKRO, DYNG, NICO, NKLG, NOT1, and RAMO). The reference solution for IGS-stations was obtained from http://sopac-old.ucsd.edu/sector.shtml. These ESA-CORS were selected to cover the marginal borders of the permanent stations. In the second step, a local constrained network solution was solved depending on the previous six ESA-CORS that were solved from the global network. The overall local network consisted of 32 ESA-CORS. Figure 3 shows the network solution procedure.

Figure 3.

As shown in equation (7), the evaluation methodology is presented using estimation of the error values δ_i,j between the reference coordinates m and the PPP solution m′. i refers to the number of epochs, and j refers to the east, north, and ellipsoidal height. For statistical evaluation in each direction, the RMSE, which refers to the error relative to the reference coordinates, is estimated using equation (8); n refers to the total number of epochs. In addition, the standard deviation (SD), which refers to the mean value for each direction μ, is calculated using equation (9) (Mikhail 1976). Finally, the confidence level of 95% is calculated for the SD values (SD_95%) (see Figure 4). 7 δi,j=m−m′ 8 RMSE=1n∑i=1n(δi,j)22 9 SD=1n−1∑i=1n(δi,j−μ)22 $${\rm{SD}} = \root 2 \of {{1 \over {n - 1}}\mathop \sum \limits_{i = 1}^n {{({\delta _{i,j}} - \mu )}^2}} $$

Figure 4.

To assess the results, the consistency of results obtained from each case study should be evaluated separately.

a)

ESA-CORS

In Figure 5, the accuracy obtained in east, north, and height directions for DOY 201–202 and 203/2019 is presented. Furthermore, Table 4 shows the estimated statistics for all stations for the three consecutive days and the mean values. This table also shows the calculated values of maximum, mean, minimum error values, RMSE, and SD. SD95% is estimated by excluding the outliers.

Figure 5.

Table 4.

Statistics of static-PPP solution for ESA-CORS in millimeters

	DOY201			DOY202			DOY203			Overall mean values
	E	N	h	E	N	h	E	N	h	E	N	h
Max.	20.0	15.0	44.0	10.0	15.0	48.0	9.0	10.0	48.0	13.0	13.3	46.7
μ	6.5	4.2	18.5	6.0	4.6	17.4	4.3	4.2	17.6	5.6	4.3	17.8
Min.	0.0	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.3	0.3	0.0
RMSE	7.7	5.6	22.3	6.4	5.8	22.7	4.8	5.0	22.2	6.3	5.5	22.4
SD	4.2	3.8	12.8	2.3	3.6	14.8	2.1	3.8	13.7	2.9	3.7	13.8
SD95%	2.1	1.8	5.8	2.0	1.8	6.3	1.9	1.8	7.0	2.0	1.8	6.4

For DOY 201, the horizontal components showed an error of up to 20 mm with an average value of 4–6 mm using an RMSE of 6–7 mm (SD = 4 mm). Only ADWH, BADR, QANA, ADFO, and WAKF stations showed an error between 1 and 1.5 cm. It is clear from the result obtained that the error presented a value of up to 44 mm (μ = 18.5 mm) in the height direction with an RMSE of 22 mm (SD = 13 mm). From this data, we can determine the greatest height errors among the stations BADR, BLTM, ISNA, LXOR, MNSH, MOUS, QANA, RSHD, THAT, TSHT, and WAKF. No significant differences were found between DOY201 and DOY202 for horizontal direction; in the height direction, the component showed an error of up to 48 mm (μ = 17.4 mm). As shown in Table 4, the results indicated that the RMSE was 22.7 mm (SD = 14.8 mm). The themes from Figure 5 show that the extreme height errors were identified from the stations BLTM, ISAN, LXOR, MNSH, MOUS, QANA, THAT, TSHT, and WAKF.

The error for DOY203 was up to 10 mm (μ = 4 mm) for horizontal direction and up to 48 mm (μ = 17.6 mm) for height direction (Table 4). The estimated RMSE was 5 mm (SD = 2–4 mm) and 22 mm (13.7 mm) for horizontal and height directions, respectively. The stations that reported high errors in the height direction matched the ones reported for DOY202. The average errors of all days were up to 13 mm for horizontal (μ = 4–6 mm) and up to 47 mm (μ was circa 8 mm) for height direction. The obtained RMSE values were 6 mm (SD = 3–4 mm) for horizontal and 22 mm (SD was about 14 mm) for height direction. For a confidence level of 95%, the overall SD_95% was 2 mm for horizontal and 6–7 mm for height direction.

Three stations continuously lacked observation data for 1 day or three successive days (Table 5). In addition to the tabulated stations, other stations also had some losses in the observation data for various epochs. These continuous lacks or small losses affected the quality of PPP solutions. ADFO station lacked data for 4 h at the beginning of DOY 201, and the data also had some other losses (see Figure 6). However, some high errors were reported in the north direction. ADWH station lacked observation data for 1 h on DOY 201, which yielded a high error in the east direction. Furthermore, ASHM and AYAT stations had continuous observation data that reflected the high error in height direction for DOY 201. BADR station had an extreme lack of observation data for DOY 201, which led to high errors. For stations BLTM, DMNH, KBER, QANA, and TSHT, the continuous lack of observation data decreased PPP accuracy in the height direction. Several issues were identified for ISNA, LXOR, MNSH, MOUS, MTMR, RSHD, SMLT, and THAT stations; the solution reported a high error for height direction due to several data losses during the convergence time for the 3 days. Finally, WAKF station had a high error for the height direction for DOY 202/203. The possible reason for the losses is bad Global System for Mobile Communications (GSM) transfer for the observation data to the center in Cairo, especially for the stations in Upper Egypt (e.g., WAKF, ISNA, LXOR, and MNSH).

Table 5.

Statistics of continuous lack of observation data for ESA-CORS

Station ID	DOY 201	DOY 202	DOY 203	Station ID	DOY 201	DOY 202	DOY 203
ADFO	4 h	-	-	QANA	9 h	9 h	9 h
ADWH	1 h	-	-	QANT	1 h	-	-
BLTM	6 h	12 h	8 h	RMDN	3 h	-	-
DMNH	13 h	6 h	5 h	THAT	1 h	-	-
ISNA	2 h	-	-	TSHT	8 h	-	-
KBER	16 h	16 h	16 h	WAKF	22 h	-	-
MNSH	1 h	-	-

Figure 6.

b)

IGS-CORS

Figure 7 presents the PPP errors in the east, north, and height directions; in addition, Table 6 shows the detailed statistics of the PPP solution (max., min., average, RMS, SD, and SD_95%). For DOY201, the horizontal error showed up to 3 mm (μ = 1.7 mm). Further analysis showed that the obtained RMSE was 1.7 mm (SD = 1.2 mm). For the height direction, the component presented an error of up to 8 mm (μ = 3.3 mm). As shown in Table 6, the obtained RMSE was 4.5 mm with an SD of 3.3 mm. Regarding DOY202, the component showed an error of up to 2 mm for horizontal (μ = 1.0–1.2 mm) and up to 13 mm (μ = 5.5 mm) for height directions. It is clear from this table that the RMSE had values of 1.3–1.5 mm (SD was circa 1 mm) and 6.7 mm (SD was circa 4 mm).

Figure 7.

Table 6.

Statistics of static-PPP solution for IGS-CORS in millimeters

	DOY201			DOY202			DOY203			Mean
	E	N	h	E	N	h	E	N	h	E	N	h
Max.	3.0	3.0	8.0	2.0	2.0	12.0	4.0	2.0	5.0	3.0	2.3	8.3
μ	1.3	1.2	3.3	1.0	1.3	5.5	1.2	1.2	3.0	1.2	1.2	3.9
Min.	0.0	0.0	0.0	0.0	0.0	1.0	0.0	1.0	2.0	0.0	0.3	1.0
RMSE	1.7	1.6	4.5	1.3	1.5	6.7	1.8	1.2	3.2	1.6	1.4	4.8
SD	1.2	1.2	3.3	0.9	0.8	4.2	1.5	1.2	1.3	1.2	1.1	2.9
SD95%	1.0	0.8	1.0	0.9	0.8	1.0	0.5	0.8	1.3	0.8	0.8	1.1

Finally, from Table 6, the error obtained in DOY203 for the east direction was up to 4 mm (μ = 1.2 mm) with an RMSE of 1.8 mm (SD = 1.5 mm). For north direction, the obtained error was up to 2 mm (μ = 1.2 mm) with an RMSE of 1.2 mm (SD = 1.2 mm). According to these data, we can infer that the error in height was between 2 and 5 mm (μ = 3 mm) with an RMSE of 3.2 mm (SD = 1.3 mm). In summary, these results show that the horizontal error was up to 3 mm (μ = 1.2 mm) with an RMSE value of about 1.5 mm (SD was circa 1.2 mm). Further, the height error was up to 8 mm with an RMSE of 5 mm (SD was about 3 mm). This study shows that SD95% was less than 1 mm for horizontal and 1.2 mm for height directions after eliminating the outliers. Finally, Figure 8 presents the epoch-wise analysis for the stations; it is clear that IGS stations had continuous observation data.

Figure 8.

Establishing GNSS CORS in Egypt is considered one of the main means to provide precise positioning and navigation for all development applications. This study provided a framework for investigating the accuracy of 32 ESA-CORS in addition to six IGS-CORS. Three consecutive observation days were analyzed using CSRS-PPP’s free PPP online service.

The overall PPP solution for ESA-CORS showed up to 13 mm errors with a mean value μ of 4–6 mm in the horizontal direction. The results indicated that the RMSE value was 6 mm (SD = 3–4 mm). The solution had up to 47 mm (μ was circa 18 mm) error for height direction with an RMSE value of 22 mm (SD was circa 14 mm). By excluding the outliers, the current study found that SD_95% was 2 mm for east and north directions and 6–7 mm for height direction. The extreme height errors seen in stations BLTM, ISAN, LXOR, MNSH, MOUS, QANA, THAT, TSHT, and WAKF are explained by the loss of the observation data due to data transmission via GSM from the receiver onsite to the center of Cairo. These results matched similar regional results obtained by Abdallah (2015), Abdallah and Schwieger (2016), and Jamieson and Gillins (2018) in east, north, and height directions.

Regarding the PPP solution for six IGS-CORS, this study has shown that the errors for East and North were up to 3 mm with a mean value of 1.2 mm (RMSE was circa 1.5 mm). In the height direction, the PPP solution was up to 8 mm (μ was circa 4 mm) with an RMSE of 5 mm. This study shows that the SD95% value was less than 1 mm for horizontal and 1.2 mm for height direction. This accuracy delivered by IGS-CORS is two times better for horizontal and four times better for height direction than the one obtained from ESA-CORS.