Ultra-Low-Cost Real-Time Precise Point Positioning Using Different Streams for Precise Positioning and Precipitable Water Vapor Retrieval Estimates

Abstract

This article aims to examine the real-time precise point positioning (PPP) solution’s accuracy utilizing the low-cost dual-frequency multi-constellation U-blox ZED-F9P module and real-time GNSS orbit and clock products from five analysis centers, including Bundesamt für Kartographie und Geodäsie (BKG), Centre National d’Etudes Spatiales (CNES), International GNSS Service (IGS), Geo Forschungs Zentrum (GFZ), and GNSS research center of Wuhan University (WHU). Three-hour static quad-constellation GNSS measurements are collected from ZED-F9P modules and geodetic grade Trimble R4s receivers over a reference station in Aswan City, Egypt, for a period of three consecutive days. Since a multi-GNSS PPP processing model is applied in the majority of the previous studies, this study employs the single-constellation GNSS PPP solution to process the acquired datasets. Different single-constellation GNSS PPP scenarios are adopted, namely, GPS PPP, GLONASS PPP, Galileo PPP, and BeiDou PPP models. The obtained PPP solutions from the low-cost module are validated for the positioning and precipitable water vapor (PWV) domains. To provide a reference positioning solution, the post-processed dual-frequency geodetic-grade GNSS PPP solution is applied; additionally, as the station under investigation is not a part of the IGS reference station network, a new technique is proposed to estimate reference PWV values. The findings reveal that the GPS and Galileo 3D position’s accuracy is within the decimeter level, while it is within the meter level for both the GLONASS and BeiDou models. Additionally, millimeter-level PWV precision is obtained from the four PPP models.

1. Introduction

Presently, the precise point positioning (PPP) technique is frequently applied for accurate navigation, position, atmospheric sounding, and space weather applications. PPP can be performed in a post-processing method by using accurate satellite orbit and clock products available from the international global navigation satellite systems (GNSS) service (IGS). To address the demands of instantaneous applications (e.g., positioning, atmospheric monitoring, hazard prediction), IGS released the real-time service (RTS), which is attainable from a number of analysis centers, for example, Bundesamt für Kartographie und Geodäsie (BKG), Centre National d’Etudes Spatiales (CNES), Geo Forschungs Zentrum (GFZ), IGS, GNSS Research Center of Wuhan University (WHU), Natural Resources Canada (NRCan), and European Space Agency (ESA). The RTS products contain corrections of multi-GNSS orbits and clocks, as well as code and phase biases through the Radio Technical Commission for Maritime Services (RCTM) and IGS State Space Representation (SSR) formats.

Numerous researchers have lately studied the quad-GNSS real-time products’ performance in various applications [1,2,3,4,5,6,7]. For example, the precision of products from 10 analysis centers has been explored for kinematic PPP applications [1]. It has been shown that the CNES, WHU, and GFZ products offered stable quad-constellation kinematic PPP solutions with three-dimensional accuracy within the centimeter level. Li et al. [3] examined the GPS, BeiDou, and Galileo real-time PPP solutions’ accuracy in both static and kinematic domains using smart phones. Their obtained results indicated that the positioning accuracy was within the decimeter and meter levels for both static and kinematic modes, respectively.

More recently, several manufactures have made low-cost dual-frequency quad-constellation GNSS devices, for instance, the U-blox ZED-F9P device. Various quad-constellation GNSS measurements can be tracked by the ZED-F9P module, including GPS L1 C/A and L2C, GLONASS G1 and G2, Galileo E1 and E5b, and BeiDou B1 and B2; furthermore, it can be operated in differential, PPP, real-time kinematic (RTK), and RTK-PPP modes. With the ability to collect dual-frequency GNSS observations, the ionosphere-free linear combination can be formed, which mitigates the ionospheric error; therefore, accurate positioning estimates become more feasible. The ZED-F9P device has been evaluated in many applications in the post-processed mode, such as precise point positioning [8,9,10,11,12,13,14,15,16] and surveying applications [17,18,19,20]. For example, Robustell et al. [11] investigated performance of the ZED-F9P GNSS module in PPP-RTK mode in ambiguity resolution and positioning accuracy domains, and their results indicated that centimeter-level positioning accuracy was obtained from the static PPP-RTK solution; moreover, Hamza et al. [17] explored the accuracy of the ZED-F9P device along with low-cost and geodetic-grade antennas in both open-sky and urban areas. It has been found that the low-cost receiver achieved horizontal and vertical accuracies of less than 10 mm and 15 mm, respectively, using relative positioning mode in urban areas, while it has been enhanced to 5 mm in horizontal and vertical directions in open-sky areas.

Furthermore, the affordable ZED-F9P module can be utilized in both tropospheric and ionospheric estimation applications [21,22,23,24,25]. For instance, Kashcheyev et al. [25] established a network consisted of 15 low-cost receivers to monitor the ionosphere and its behavior over Canada. The estimated total electron contents (TECs) from the network were compared with the geodetic-based TEC; their results showed that the TEC values had good agreement with those obtained through the geodetic receivers; the ZED-F9P receiver is also investigated in deformation monitoring applications [26,27,28,29,30,31,32,33]. As an example, Oku Topal et al. [28] assessed the low-cost ZED-F9P GNSS receiver along with two different types of affordable antennas in horizontal displacement estimation using different static observation periods. It was found that the low-cost system can be used effectively in structural health monitoring applications.

The main innovation point of our paper is to explore the positioning accuracy of real-time single-constellation PPP solutions (i.e., GPS, GLONASS, Galileo, and BeiDou PPP) with a ZED-F9P device utilizing satellite orbit and clock corrections from BKG, CNES, IGS, GFZ, and WHU instantaneous data streams, which has not been addressed yet in previous studies; additionally, our proposed real-time PPP scenarios are validated in the troposphere precipitable water vapor (PWV) domain. Since the examined station does not belong to the IGS stations, a new method is developed to create PWV reference values; then, these reference values are used in PWV validation.

In our research, the real-time PPP algorithm is elaborated in Section 2; thereafter, the PWV estimation method is discussed in Section 3, and the data processing scheme is presented in Section 4. Additionally, the obtained results are analyzed and interpreted in Section 5; after that, the findings are summarized in Section 6, and the conclusion is finally drawn in Section 7.

2. Real-Time Precise Point Positioning Algorithm

The ionosphere-free real-time precise point positioning mathematical model for both code- and carrier-phase GNSS observations is applied through the following formula [34]:

$$P_{IF}={\rho }_r^s+c\left({dt}_r{-dt}^s\right)+T_r^s+c\left(\mathsf{\Delta }{B}_r-{\mathsf{\Delta }B}^s\right)+{\epsilon }_{P,IF}$$

(1)

$${\Phi }_{IF}={\rho }_r^s+c\left({dt}_r{-dt}^s\right)+T_r^s+c\left({\mathsf{\Delta }\delta }_r-\mathsf{\Delta }{\delta }^s\right)+\overline{\lambda N_r^s}+{\epsilon }_{\Phi ,IF}$$

(2)

where $P_{IF }$ and ${\Phi }_{IF}$ are the dual-frequency code- and carrier-phase ionosphere-free linear combinations, respectively; the GPS, GLONASS, Galileo, and BeiDou satellite systems are referred by $s$; $r$ denotes to the receiver; the range between satellite and receiver is ${\rho }_r^s$; the speed of light in a vacuum is $c$; ${dt}_r$ and ${dt}^s$ are receiver and satellite clock errors, respectively; $T_r^s$ indicates the tropospheric delay; $\mathsf{\Delta }{B}_r$ and ${\mathsf{\Delta }B}^s$ are the receiver and satellite ionosphere-free differential code bias (DCB), respectively; ${\mathsf{\Delta }\delta }_r$ and $\mathsf{\Delta }{\delta }^s$ are the receiver and satellite ionosphere-free differential phase bias (DPB); $\lambda$ is the carrier phase’s wavelength; $\overline{N_r^s}$ is the ionosphere-free carrier-phase ambiguity term; ${\epsilon }_{P,IF}$ and ${\epsilon }_{\Phi ,IF}$ are the residual errors of both the code and carrier phase, respectively.

For the real-time PPP method, the DCB is included in receiver and satellite clocks as described below:

$$P_{IF}={\rho }_r^s+c\left({dt}_r+{\mathsf{\Delta }B}_r\right)-c\left({dt}^s+{\mathsf{\Delta }B}^s\right)+T_r^s+{\epsilon }_{P,3}$$

(3)

$${\Phi }_{IF}={\rho }_r^s+c\left({dt}_r+{\mathsf{\Delta }B}_r\right)-c\left({dt}^s+{\mathsf{\Delta }B}^s\right)+T_r^s+\left(\overline{\lambda N_r^s}+D_r-D^s\right)+{\epsilon }_{\Phi ,IF}$$

(4)

where $D_r$ and $D^s$ are the difference between the DCB and DPB for the receiver and satellite, respectively. After applying the satellite and clock corrections, the real-time PPP model can be rewritten for both code and phase measurements as given below:

$$P_{IF}={\rho }_r^s+c{dt}_r^{~}-c{dt}_{cor}^s+T_r^s+{\epsilon }_{P,3}$$

(5)

$${\Phi }_{IF}={\rho }_r^s+c{dt}_r^{~}-c{dt}_{cor}^s+T_r^s+\widetilde{N_r^s}+{\epsilon }_{\Phi ,IF}$$

(6)

where ${dt}_r^{~}$ represents the receiver DCB plus receiver clock parameter; ${dt}_{cor}^s$ denotes to the corrected satellite clock parameter; $\widetilde{N_r^s}$ is the ambiguity parameter. The tropospheric delay parameter ($T_r^s$) in Equations (5) and (6) is broken down into hydrostatic and wet tropospheric parts. The hydrostatic tropospheric error parameter can be estimated using the Saastamoinen model [35], while the wet tropospheric error parameter is computed as an unknown term; thus, the unknown parameter vector ($\mathit{X}$) can be mathematically represented as given below:

$$\mathit{X}={\left[\begin{array}{ccc}∆x& ∆y& \begin{array}{cc}∆z& \begin{array}{cc}c{dt}_r^{~}& zwd \begin{array}{ccc}{\tilde{N}}^{s=1}& \cdots & {\tilde{N}}^{s=n}\end{array}\end{array}\end{array}\end{array}\right]}^T$$

(7)

where $zwd$ points to tropospheric zenith wet delay; $n$ is the number of tracked GNSS satellites.

3. Real-Time PWV Estimation

Precipitable water vapor is the total amount of water vapor in an air column. The PWV is determined based on the zenith tropospheric delay using the following formula [34]:

$$PWV={10}^6{\left[{ \rho }_w{R}_w\left({\displaystyle \frac{k_3}{T_m}}+k_2^{\prime }\right)\right]}^{-1}\times Z_w$$

(8)

where ${ \rho }_w$ refers to the liquid water density (${\rho }_w$ = 997 kg/m³); $R_w$ indicates to the water vapor’s gas constant ($R_w$ = 461.525 J/K.kg); $k_3$ is the troposphere refractivity coefficient ($k_3$ = 3754.63 K²/Pa); $T_m$ denotes the weighted mean temperature (K), which is calculated based on surface temperature ($T_s$) at the reference station ($T_m=70.2+T_s \left[34\right]$); $k_2^{\prime }$ is also a tropospheric refraction coefficient and it is determined using the following equation:

$$k_2^{\prime }=k_2-\left(k_1{\displaystyle \frac{M_w}{M_d}}\right)$$

(9)

where $k_1$ and $k_2$ are equal to 0.776890 K/Pa and 0.712952 K/Pa, respectively; the wet air’s molar mass $M_w$ = 15.9994 g/mol; $M_d$ represents the dry air’s molar mass ($M_d$ = 8.9644 g/mol).

4. Real-Time Multi-GNSS Dataset Processing

To investigate the ZED-F9P’s accuracy, dual-frequency quad-constellation GNSS datasets were collected over a reference station in Aswan city, Egypt (Figure 1) spanning three consecutive days (i.e., Day of year (DOY) = 225, 226, and 227 in 2023). The setup of the ZED-F9P module over the examined station is illustrated in Figure 2. The observation time window is three hours with a 30 s interval.

To provide a reference solution, GNSS measurements were collected using the geodetic-grade Trimble R4s receiver over the same examined point, also with an observation interval of 30 s; thereafter, the collected observations were processed using the GNSS PPP technique by employing the final precise GNSS orbit and clock products.

Net_Diff GNSS version 1.13 software [36] has been utilized to process the ZED-F9P datasets in real-time PPP mode. Various instantaneous PPP solutions have been adopted, namely, GPS PPP, GLONASS PPP, Galileo PPP, and BeiDou PPP. For our proposed RT-PPP models, the hydrostatic error has been determined using the Saastamoinen tropospheric model; moreover, dry and wet Vienna mapping functions have been applied [37]. A Kalman filter has been adopted for parameter estimation. To model the observations stochastically, the elevation-dependent plus the signal-to-noise ratio (SNR) model has been employed. For static data processing, a 30 s time interval has been used.

Furthermore, to mitigate the GNSS orbit and clock errors, the broadcasted navigation message from the ZED-F9P module has been used; additionally, the satellite orbit and clock corrections available from multiple data streams, namely, BKG, CNES, IGS, GFZ, and WHU, have been employed. In our paper, the SSRA has been utilized, including corrections to GNSS orbits and clocks in the SSR format every 5 s using BKG version 2.13.1 software [38].

Table 1. Summary of the adopted PPP solutions.

Receiver Type	ZED-F9P				Trimble R4s
PPP solution	GPS	GLONASS	Galileo	BeiDou	GPS
Frequency	L1/L2	G1/G2	E1/E5b	B1/B2	L1/L2
Data streams	BKG	BKG	BKG	IGS	Final NRCan
	CNE	CNE	CNE	GFZ
	IGS	IGS	IGS	WHU
	GFZ	GFZ	GFZ
	WHU	WHU	WHU

outlines parameters for each adopted precise point positioning solution.

Another objective of our paper was to examine the obtained real-time PWV’s accuracy through the ZED-F9P module. It should be mentioned that to provide reference PWV values, our examined station has neither IGS Zenith tropospheric delay (ZTD) product file nor radiosonde measurements; hence, to achieve this, GNSS measurements have been simultaneously acquired from the two receivers (Figure 3). As presented in Figure 3, the reference station was occupied by the low-cost module, while another point, about 1-m distant, was occupied by the geodetic-grade receiver. For the ZED-F9P datasets, the acquired datasets were processed in the real-time PPP domain; on the other hand, the Trimble R4s datasets have been processed in post-processed PPP mode to supply reference PWV values. For the PWV calculation, the surface temperature (T_s) has been estimated through the GPT2w model [39] because our selected station was not equipped with metrological sensors.

To investigate the number of tracked satellites and the position dilution of precision (PDOP) over our reference station, their values have been computed over the three days and are depicted in Figure 4. It can be noticed that there are more GPS tracked satellites than other systems, while the GLONASS system has the lowest number of tracked satellites. It is also noticed that the GPS PDOP values are better than the other PDOP values; in addition, the PDOP values of both the GLONASS and BeiDou systems are larger than those of the GPS and Galileo systems over the three days.

5. Analysis of Results

In our research, the ZED-F9P four-system GNSS observations are processed in instantaneous PPP mode, applying the obtained corrections to satellite orbits and clocks through BKG, CNES, IGS, GFZ, and WHU analysis centers. Various single-constellation dual-frequency PPP solutions are adopted, including GPS-PPP, GLONASS-PPP, Galileo-PPP, and BeiDou-PPP solutions; moreover, the acquired datasets from the Trimble R4s receiver are processed in post-processed PPP mode utilizing the traditional dual-frequency GPS-PPP processing model. Thereafter, the resulting coordinates from the ZED-F9P’s PPP models are validated with those estimated from the geodetic-grade GPS-PPP solution; our obtained results are validated in static positioning and PWV applications.

5.1. Static Application Validation

The positioning errors of the four real-time precise point positioning solutions are computed in the east, north, and height directions. The proposed PPP models are compared with the station’s coordinates computed from the geodetic-grade post-processed GPS PPP model. Figure 5 illustrates the three-hour positioning errors of GPS, GLONASS, Galileo, and BeiDou PPP solutions, respectively, on DOY 225 as an example. As previously mentioned in Table 1, only GFZ, IGS, and WHU analysis centers offer BeiDou orbit and clock corrections.

For the GPS PPP model, it is obvious that the obtained positioning accuracy through the five products is within the decimeter level with superiority of BKG, CNE, and WHU products; furthermore, CNE and WHU products accelerate the convergence time compared with the other products, and there are some clear gaps in the obtained solutions from the IGS products. This is due to interruption in the real-time data streams. It is also found that the GLONASS PPP solution’s accuracy is within the sub-meter level in the north and height components, but not in the east component. This is attributed to the GLONASS orbit and clock products’ accuracy attainable from the five centers and the GLONASS satellite configuration; on the other hand, by using the five products, real-time Galileo PPP solutions achieve decimeter position accuracy in three directions. Moreover, acceleration in the Galileo PPP’s convergence time is achieved in the three components. An exception is the height component obtained from GFZ and WHU products.

For the BeiDou RT-PPP solutions, the positioning errors are within the decimeter level for GFZ products; however, the positioning errors are increased to the meter level and sub-meter level for the IGS and WHU products, respectively. This is because the ZED-F9P module collects only BeiDou-2 satellite signals, which are noisier than the BeiDou-3 satellite signals; in addition, the GFZ BeiDou orbit and clock products’ accuracies are better than those of their counterparts from IGS and WHU analysis centers.

For additional assessment of the PPP processing models’ accuracy, the root mean square error (RMSE) for the positioning errors over the three examined days are calculated and given in Figure 6. Obviously, the RMSEs for the GPS PPP processing model by utilizing the five products types are within the centimeter-to-decimeter level in both the east and north directions, while it is within a few decimeters in the up direction; in contrast, the positioning error of the GLONASS PPP is increased to the meter level in the east component on the first two days and the few-decimeter level on the third day. For the north and up components, the positioning errors are within the few-decimeter level. An exception is the meter-scale error in the up-component on DOY 225, which is derived from WHU orbit and clock products. This may be due to GLONASS satellite configuration and the accuracy of WHU products. The real-time Galileo PPP’s accuracy ranges are 0.080–0.452, 0.039–0.531, and 0.122–0.756 m in the east, north, and up directions, respectively. On DOY 227, the results obtained through WHU products are an exception, particularly in the east and up positions; additionally, the up positioning accuracy is estimated from the GFZ products. This might be attributed to the accuracy of the products on this day; on contrary, the BeiDou PPP’s accuracy ranges from the sub-meter to the meter level with observed improvements for GFZ products on DOY 225; moreover, it is obvious that the WHU products are better than the other products on the three examined days.

To further examine the real-time PPP solutions’ accuracy, the RMSE values for the 3D position errors are calculated at 30, 60, 120, and 180 min intervals (Figure 7). It should be clarified that after the 3 h data set processing, the three-dimensional position errors at 30, 60, 120, and 180 min are computed for each day, and then the RMSE values over the three days are computed. As given in Figure 7, the 3D position errors decreased as the observation widow increased, with obvious impacts in the GLONASS, Galileo, and BeiDou models; furthermore, GPS real-time PPP is superior to the GLONASS, Galileo, and BeiDou solutions, with RMSE values less than 0.4 m for all products. On the other hand, the 3D errors are less than 2.0 m for both the GLONASS and Galileo solutions and 2.5 m for the BeiDou solution. For the GPS processing model, BKG, CNE, and WHU products are better than GFZ and IGS products over the four time windows; also, the obtained GLONASS solutions obtained through BKG products are better than those of the other products. Additionally, improvements in the 3D positioning accuracies are obtained with time window increments for CNE, GFZ, IGS, and WHU products. For Galileo 3D RMSEs, similar results are achieved for BKG, CNE, and IGS products, and the attained 3D RMSE values from WHU products obviously decrease with observation time window increment. The GFZ’s 3D RMSE values are an exception. Furthermore, WHU products clearly outperform GFZ and IGS products for real-time BeiDou solutions.

The three-dimensional positioning accuracy is examined further by calculating the cumulative distribution function (CDF) of the 3D position errors (Figure 8). It can be noticed that for GPS PPP models, about 90% of the 3D position errors are equal to or less than 0.5 m utilizing the five products, with superiority to WHU products; in contrast, 90% of the three-dimensional position are less than 2 m for GLONASS PPP processing model. An exception is the obtained 3D position from WHU products; additionally, about 90% of the Galileo PPP errors are smaller than 1 m for BKG, CNE, and IGS products, and less than 1.5 m for GFZ and WHU products. The significant superiority of the BeiDou 3D accuracy utilizing WHU products compared with GFZ and IGS products is clear.

5.2. Real-Time PWV Determination Validation

To explore the precision of the ZED-F9P device in tropospheric applications, GNSS observations are collected simultaneously from both the device and the geodetic-grade receiver over the three previously selected days. The ZED-F9P’s observations are processed in real-time PPP mode utilizing BKG, CNE, GFZ, IGS, and WHU products, while the post-processed PPP mode is utilized for the Trimble R4s observations; thereafter, the ZTD is calculated as a by-product from the proposed PPP solutions. The estimated ZTDs from real-time GPS, GLONASS, Galileo, and BeiDou PPP solutions are referenced to the geodetic-grade PPP extracted ZTD values. The estimated ZTDs from the GPS, GLONASS, Galileo, and BeiDou PPP models are depicted in Figure 9, compared with the obtained ZTD values through geodetic-grade solutions over DOY 225 as an example. It is seen that the extracted real-time ZTDs from both the GPS and BeiDou solutions utilizing the five products are close enough to the extracted geodetic-grade ZTD with slight fluctuations in the first 40 min. This is due to the PPP solution’s convergence time, and thereby the ZTD values; however, the obtained real-time ZTDs through GLONASS PPP solutions have large discrepancies with respect to the extracted geodetic-grade ZTD; also, the computed real-time ZTDs from BeiDou solutions have small discrepancies compared with to the extracted geodetic-grade ZTD. This is attributed to the accuracy of the real-time GLONASS and BeiDou PPP solutions.

The performance of the ZED-F9P module in atmospheric sounding applications is further examined through the computation of the real-time precipitable water vapor. The estimated real-time PWV from the four proposed PPP processing solutions are validated with the estimated PWV from the geodetic-grade PPP solution. Figure 10 represents the PWV’s time series derived from ZED-F9P PPP and geodetic-grade PPP solutions. It is clear that the derived PWVs from the GPS PPP models are more precise than the others; furthermore, the calculated real-time PWVs from the Galileo PPP models relatively agree with geodetic-grade PWVs. An exception is the IGS-extracted PWVs. Similarly to ZTD, both the GLONASS-based and BeiDou-based PWVs have differences in comparison with the geodetic-grade PWVs.

To further analyze the PWV’s precision on daily basis, the standard deviation (STD) for the differences between the PWVs and the derived geodetic-grade PWVs are calculated and given in Figure 11. It is shown that the STD values are smaller than 4 mm and 10 mm for GPS and the other solutions, respectively; also, it is seen that the STD values on the third day are greater than on the other two days for all solutions. This may be due to variations in water vapor because of surface temperature increment on that day.

Furthermore, the WHU-derived GPS PWV values are more precise than the other products over the three days. For GLONASS-derived PWVs, there are variations in STD values over the three days for each product, with minor changes for BKG and CNE products. This might be attributed to the daily GLONASS product’s accuracy for each analysis center; on contrary, the STD values are quite small over the first two days, with large differences in the third day for Galileo-derived PWVs. Additionally, the IGS-derived PWVs have greater STDs than the other products. The variability in the BeiDou-derived PWV precision is obvious, particularly on DOY 226 and 227; in addition, WHU products offer more precise PWV values compared with GFZ and IGS products.

Furthermore, the CDF of the PWV differences is determined (Figure 12). As shown in Figure 12, about 90% of the obtained real-time PWV’s precision through GPS solutions is less 10 mm; also, the calculated PWVs by utilizing WHU and BKG products outperform the other products. For the precisions of the GLONASS-derived real-time PWVs, however, 90% of their values are less than 20 mm, outperforming BKG products; moreover, 90% of the errors in real-time PWVs resulting from Galileo processing models are less than 15 mm, with superior to GFZ and WHU products. For the BeiDou solutions, about 90% of the PWV errors range from 15 mm to 20 mm for GFZ and WHU products, respectively, with an exception for IGS products.

6. Discussion

At present, the cost-effective dual-frequency multi-GNSS modules are widely utilized in precise navigation and positioning applications; in addition, there are a number of precise multi-GNSS satellite orbit and clock products which improve the multi-GNSS RT-PPP accuracy. Examples for these products include BKG, CNE, GFZ, IGS, and WHU products; as a result, in our study, we propose an ultra-low-cost real-time multi-GNSS PPP solution employing the ZED-F9P device and the five aforementioned products. Our proposed PPP solutions are validated for positioning and tropospheric applications. To provide a reference solution, the geodetic-grade Trimble R4s receiver post-processed PPP is employed.

Table 2. Three-dimensional position statistics for the static PPP solutions (in meters).

Product	GPS-PPP		GLONASS-PPP		Galileo-PPP		BeiDou-PPP
	Mean	RMSE	Mean	RMSE	Mean	RMSE	Mean	RMSE
BKG	0.168	0.253	1.031	1.123	0.318	0.419	--	--
CNE	0.155	0.225	1.135	1.302	0.303	0.496	--	--
GFZ	0.249	0.319	1.247	1.488	0.625	0.854	1.486	2.151
IGS	0.248	0.307	1.167	1.298	0.279	0.451	2.235	2.804
WHU	0.120	0.164	1.416	1.603	0.466	0.980	0.858	1.402

summarizes the statistical metrics of the 3D positioning, such as mean and RMSE, to analyze the achieved positioning accuracy. As can be seen, few-decimeter 3D positioning accuracies can be attained through the GPS PPP model using the five products; moreover, the Galileo 3D position is better than those of GLONASS and BeiDou, with an RMSE value less than 0.5 m. An exception is GFZ and WHU products. GLONASS 3D positioning errors are large because of the satellites’ configuration and the products’ accuracy. For the BeiDou solution, the three-dimensional errors are at the meter level, with slight improvements for WHU products. This is due that the ZED-F9P collects only BeiDou signals, as well as the available product’s accuracy. For comparison between products, WHU provides more accurate GPS and BeiDou solutions than the other products, while BKG offers the accurate GLONASS and Galileo solutions.

Furthermore, to explore the extracted PWV’s precision, the statistical measures for the PWV differences over the three investigated days are determined.

Table 3. Real-time PWV statistics derived from PPP solutions (in mm).

Product	GPS-PPP		GLONASS-PPP		Galileo-PPP		BeiDou-PPP
	Mean	RMSE	Mean	RMSE	Mean	RMSE	Mean	RMSE
BKG	0.30	3.53	3.30	8.72	3.63	7.87	--	--
CNE	1.53	3.47	1.11	9.24	3.57	7.60	--	--
GFZ	3.55	3.38	3.10	9.95	3.52	3.98	5.75	9.45
IGS	3.27	2.83	4.18	9.80	2.43	9.34	6.26	11.40
WHU	1.75	2.78	3.86	10.32	2.74	5.37	3.42	10.90

lists the mean and STD values. It can be said that the WHU-derived GPS PWVs are more precise than those of the other products, with an STD less than 2.78 mm; in addition, IGS products offer precise PWV values, taking into account that IGS streams have some discontinuities on the three days. The STD values for the obtained GLONASS PWVs are large in comparison with the other solutions, with superiority to BKG products. For the real-time PWV obtained through Galileo solutions, both GFZ and WHU products supply precise PWVs with respect to the others, with superiority to GFZ products, and the precision of the GFZ-acquired BeiDou PWVs are better than those of IGS and WHU products, with STD value less than 9.45 mm.

Based on the obtained findings from both static and PWV validations, the following points can be concluded:

• Decimeter- to meter-level 3D positioning accuracy and few-millimeter PWV precision can be achieved utilizing the ZED-F9P receiver in the real-time domain using the BKG, CNE, GFZ, IGS, and WHU products;
• The real-time GPS PPP processing model outperforms the Galileo, GLONASS, and BeiDou real-time PPP processing models for both 3D positioning and PWV results;
• The Galileo solution outperforms the GLONASS and BeiDou PPP solutions in the 3D position and PWV domains;
• The products’ accuracy has a significant impact on both GLONASS and BeiDou PPP accuracies, as well as the satellite geometry;
• The GPS PPP solution using WHU products outperforms the other products, with 0.164 m 3D position accuracy and 2.73 mm PWV precision;
• BKG GLONASS products provide better GLONASS PPP solution than other products, with 1.123 m 3D position accuracy and 8.72 mm PWV precision;
• For the Galileo PPP solution, BKG provides 3D positioning accuracy superiority compared to the others, with a 0.419 m RMSE value; however, both GFZ and WHU have superior PWV precision compared to other products, with 3.98 mm and 5.37 mm STD values;
• Both GFZ and WHU products offer better BeiDou PPP solutions in comparison with IGS products, with 2.151 m and 1.402 m 3D position accuracy, respectively, and 9.45 and 10.90 mm PWV precision, respectively.
• For future work, using different types of low-cost antennas will be investigated.

7. Conclusions

In our paper, the accuracy of instantaneous PPP employing a low-cost dual-frequency multi-constellation U-blox ZED-F9P receiver in precise positioning and tropospheric applications is investigated. Three-hour multi-GNSS static datasets over a reference station in Egypt spanning a period of three successive days were collected. The acquired datasets were processed by applying four real-time PPP models, which were GPS, GLONASS, Galileo, and BeiDou PPP. To adopt the real-time PPP mode, GNSS orbit and clock corrections products from five analysis centers were utilized, including BKG, CNE, GFZ, IGS, and WHU products. Our proposed solutions were explored in the static positioning and PWV domains. GNSS observations were acquired from the geodetic-grade Trimble R4s receiver and then processed in post-processed PPP mode to provide positioning and PWV reference solutions. The results demonstrated that decimeter-level 3D positional accuracy can be achieved by employing GPS and Galileo PPP solutions with significant superiority to the GPS PPP solution, while the 3D position of both the GLONASS and BeiDou solutions can reach the meter level. The GPS PPP’s positioning accuracy ranged from 0.164 to 0.319 m, with WHU outperforming the other products, whereas the positioning accuracy of the Galileo PPP solution varied from 0.419 to 0.980 m, with superiority to BKG products. The BKG products showed the best performance for GLONASS scenarios compared with the other products, with 1.123 m 3D positioning accuracy; however, the WHU-based BeiDou PPP solution was better than the other solutions, with 1.402 m positioning accuracy. For the PWV domain, millimeter-level precision was attained using the four PPP models; moreover, WHU introduced more precise GPS-based PWV estimation than the others, with 2.78 mm precision. For GLONASS-derived PWV, an 8.72 mm PWV precision was attained utilizing BKG, which outperformed other products; on other hand, GFZ showed better precision than other products, with STD values of 3.98 mm and 9.45 mm for Galileo and BeiDou solutions, respectively. Consequently, the ultra-low-cost ZED-F9P module can be used in real-time atmospheric sounding applications.