An Evaluation of Static Affordable Smartphone Positioning Performance Leveraging GPS/Galileo Measurements with Instantaneous CNES and Final IGS Products

Abstract

This research examines the performance of the affordable Xiaomi 11T smartphone in static positioning mode. Static Global Navigation Satellite System (GNSS) measurements are acquired over a two-hour period with a known reference point, spanning three consecutive days. The acquired data are processed, employing both real-time and post-processing Precise Point Positioning (PPP) solutions using GPS-only, Galileo-only, and the combined GPS/Galileo datasets. To correct the satellite and clock errors, the instantaneous Centre National d’Études Spatiales (CNES), the final Le Groupe de Recherche de Géodésie Spatiale (GRG), GeoForschungsZentrum (GFZ), and Wuhan University (WUM) products were applied. The results demonstrate that sub-30 cm positioning accuracy is achieved in the horizontal direction using real-time and final products. Additionally, sub-50 cm positioning accuracy is attained in the vertical direction for the real-time and post-processed solutions. Furthermore, the real-time products achieved three-dimensional (3D) position accuracies of 40 cm, 29 cm, and 20 cm using GPS-only, Galileo-only, and the combined GPS/Galileo observations, respectively. The final products achieved 3D position accuracies of 24 cm, 26 cm, and 28 cm using GPS-only, Galileo-only, and the combined GPS/Galileo measurements, respectively. The attained positioning accuracy can be used in some land use and urban planning applications.

1. Introduction

Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) are now the most widely utilized high-precision Global Navigation Satellite System (GNSS) positioning techniques. RTK approach relies on reference stations, referred to as base stations, in conjunction with robust communication networks, while the PPP technique utilizes a single GNSS receiver [1,2]. On the other hand, a significant limitation of the PPP approach is its prolonged convergence time, which presents a challenge for real-time applications [3]. With the accelerated advancements in GNSS technology, the current constellations comprise over 100 GNSS satellites, including GPS, GLONASS, Galileo, and BeiDou satellite systems [4]. The integration of these multi-GNSS satellites significantly contributes to reducing convergence time, and it enables users to achieve centimeter-level accuracy within ten minutes of convergence time [5,6]. Furthermore, it aids in enhancing the GNSS raw data from low-cost receivers, which are often prone to data losses [7]. To achieve a high level of accuracy, PPP depends on the International GNSS Service (IGS), which provides a variety of products to mitigate GNSS-based errors. These products include GNSS satellite ephemerides, Earth rotation parameters, satellite clock corrections, zenith tropospheric path delay estimates, and Global Ionosphere Maps (GIM). Moreover, they are available from various Analysis Centers (ACs), such as the Center for Orbit Determination in Europe (CODE), the European Space Operations Center (ESA), the GeoForschungsZentrum (GFZ), Le Groupe de Recherche de Géodésie Spatiale (GRG), Wuhan University (WUM) [8,9,10], and the Centre National d’Etudes Spatiales (CNES), archived real-time products [11]. Since ionospheric delay is a crucial issue for single-frequency PPP users, they have to utilize the Klobuchar, NeQuick, or IGS-GIM models [12,13,14] to account for the ionospheric error. Dual-frequency users can take advantage of the ionospheric dispersive nature by employing the Ionosphere-Free Precise Point Positioning (IF-PPP) method, which effectively mitigates approximately 99% of the ionospheric delay [15]. Furthermore, the undifferenced Uncombined Precise Point Positioning (UPPP) method that estimates the ionospheric delay as an unknown parameter can enhance both positional accuracy and convergence time [16].

At present, significant breakthroughs in affordable smartphone-based GNSS precise positioning are fulfilled with the launch of the Xiaomi Mi8, which is equipped with the Broadcom BCM4775 chipset because it supports multi-frequency and multi-GNSS systems [17]. Also, it demonstrated Root Mean Square Error (RMSE) of 4.14 m in horizontal, when utilizing single-frequency multi-GNSS data in conjunction with Single Point Positioning (SPP) approach [18]. Moreover, the results showed that decimeter- and meter-level horizontal positioning accuracy can be attained in static and kinematic modes, respectively, using the PPP technique [19]. Following the launch of the Mi8, several smartphone modules are released, such as Huawei Mate 40 and P40, Samsung Galaxy S20, and Google Pixel 4 [20,21,22], which pave the way for low-cost and highly precise GNSS positioning applications. Unlike the geodetic receiver, the carrier-to-noise ratio (C/N0) for the smartphone is low [23]; as a result, the observed datasets are lost, and then the positioning accuracy is degraded. For this reason, a number of researchers suggest applying the weighting model based on the C/N0 rather than the model based on the elevation angle for stochastic model estimation [24,25,26].

In this research, the real-time and post-processing GNSS positioning performance of the Xiaomi 11T module for static applications is evaluated. This Xiaomi 11T module has many GNSS features, such as supporting multi-frequency multi-constellation GNSS (i.e., GPS L₁/L₅, Galileo E₁/E_5a, GLONASS G₁, and BeiDou B₁ [27]. The ionosphere-free PPP approach is applied for both instant and post-processed scenarios. Our paper is organized as follows: First, the ionosphere-free PPP mathematical model is introduced. Subsequently, the GNSS data collection and processing methodology are presented, along with an evaluation of the quantity and quality of the collected data. The processing results and their analysis are presented and discussed in Section 4. Finally, the conclusion is drawn in the final section.

2. Ionosphere-Free PPP Processing Model

The dual-frequency GNSS ionosphere-free PPP processing scenario can be expressed mathematically as follows [28]:

$$P_{IF}^s={\rho }_r^s+c(d{t}_r+b_{r,\mathrm{ }IF})-cd{t}_{corr}^s+T_r^s+{\epsilon }_p^s$$

(1)

$${\mathsf{\Phi }}_{IF}^s={\rho }_r^s+c\left(d{t}_r+b_{r,\mathrm{ }IF}\right)-cd{t}_{corr}^s+T_r^s+{\widetilde{N_{IF}}}^s+{\epsilon }_{\mathsf{\Phi }}^s$$

(2)

where $P_{IF}$ and ${\mathsf{\Phi }}_{IF}$ represent ionosphere-free code and phase combinations, respectively; ${\rho }_r^s$ is the satellite receiver geometric range; ${dt}_r$ denote to receiver clock errors; $b_{r,IF}$ is the receiver ionosphere-free differential code bias; $d{t}_{corr}^s$ is the corrected satellite clock parameter after applying the archived real-time and post-processing products; $T_r^s$ refers to the tropospheric delay; ${\epsilon }_{(p_i,{\mathsf{\Phi }}_i)}$ denote multipath and noisy measurements for code and phase measurements, accordingly; $\widetilde{N_{IF}}$ refers to the real-value ambiguity parameter, including both code and carrier phase biases, which can be expressed as follows:

$${\widetilde{N_{IF}}}^s={\displaystyle \frac{f_1^2{\lambda }_1{N}_1-f_2^2{\lambda }_2{N}_2}{f_1^2-f_2^2}}+[(b_{r,\mathrm{ }IF}+{\delta }_{r,\mathrm{ }IF})-(b_{IF}^s+{\delta }_{IF}^s)]$$

(3)

where $f_1$ and $f_2$ are the frequencies of $L_1$ and $L_2$, respectively; ${\lambda }_1$ and ${\lambda }_2$ are the wavelength of $L_1$ and $L_2$, respectively; $N_1$ and $N_2$ are the carrier-phase ambiguity parameters on $L_1$ and $L_2$, respectively; $b_{IF}^s$ is the satellite ionosphere-free differential code bias; ${\delta }_{r,IF}$ and ${\delta }_{IF}^s$ are the receiver and satellite ionosphere-free carrier phase biases, respectively. It is well known that the receiver differential code bias is lumped in the receiver clock parameter (i.e., $c{dt}_r^{~}=c(d{t}_r+b_{r,IF})$); thus, the vector of the estimated parameters ($\overrightarrow{X_{PPP}}$) takes the following mathematical expression:

$$\overrightarrow{X_{PPP}}=\left[X,\mathrm{ }\mathrm{ }Y,\mathrm{ }\mathrm{ }Z,\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }c{dt}_r^{~},\mathrm{ }\mathrm{ }{T}_w,\mathrm{ }\mathrm{ }{\widetilde{N_{IF}}}^s\right]$$

(4)

where $X$, $Y$, and $Z$ denote the receiver position; $T_w$ indicates the wet tropospheric delay.

3. GNSS Data Collection and Processing Methodology

For data collection, two hours of GPS/Galileo observations with a 30 s interval are collected using the Xiaomi 11T module over a base point located in Aswan, Egypt, on Days of Year (DOY) 70, 71, and 72 (Figure 1). Thereafter, the acquired datasets from the smartphone are converted into RINEX format using the Geo++RINEX mobile (Version 2.1.6) application [29]. The reference point was established using 4.5 h of raw GPS data collected from a geodetic receiver (i.e., Trimble R4S), which was subsequently processed through the CSRS-PPP online service using the final precise products [30]. The characteristics of the smartphone GNSS datasets are outlined in

Table 1. The attributes of Xiaomi 11T GPS/Galileo raw data.

System	Frequency	Observations
		Code	Carrier	Doppler	Signal Strength
GPS	L1	C1C	L1C	D1C	S1C
	L5	C5Q	L5Q	D5Q	S5Q
Galileo	E1	C1C	L1C	D1C	S1C
	E5a	C5Q	L5Q	D5Q	S5Q

.

The quantity check is applied to our acquired dataset by computing the percentage of GNSS measurements to the total number of epochs. For this purpose, the open-source RINEX SCAN GNSS (Version 1.0.0) software [31] was utilized, which supports multi-GNSS system data quantity through a user-friendly graphical interface (GUI).

Table 2. GPS and Galileo measurements availability on DOY 71.

PRN	C1C %	L1C %	C5Q %	L5Q %	PRN	C1C %	L1C %	C5Q %	L5Q %
G32	100	98.6	100	100	E34	100	99.9	100	18.7
G27	100	100	100	100	E30	100	99.6	100	99.4
G26	100	100	100	100	E27	100	100	100	100
G23	100	100	100	100	E26	100	98.9	100	95.5
G18	100	100	100	100	E21	100	100	100	100
G10	100	100	100	100	E15	100	100	100	100
G08	100	99.6	100	97.3	E13	100	100	100	100
E03	100	99.7	100	99.9	E08	100	99.9	100	99.9
E01	100	71.8	100	87.5	E07	100	100	100	99.9

summarizes the quantity check outputs for GPS/Galileo measurements on DOY 71. Galileo signals experience greater data losses compared to those of GPS, particularly in carrier phase measurements.

The datasets are processed using the open-source Net-Diff GNSS (Version 1.14) software, which is capable of processing GNSS data through PPP approaches, as well as data processing and output analysis [32,33]. Given that just 17 GPS satellites transmit the L₅ signal, it is expected that the total number of processed GPS satellites may not be enough for the PPP solution [34]; therefore, a pre-mission plan was employed using the Trimble GNSS online service [35]. As illustrated in Figure 2, the number of processed satellites for GPS-only (G), Galileo-only (E), and combined GPS/Galileo (GE) varies depending on the type of products used, even for the same PPP solution, which affects the Position Dilution of Precision (PDOP) factor.

To assess the quality of the collected raw GNSS data, the average C/N0 was calculated for both GPS and Galileo satellites (Figure 3). It can be seen that the average C/N0 values of the GPS L₁ and Galileo E₁ are superior to that of the GPS L₅ and Galileo E_5a with the exception for satellites E19 on DOY 70 as well as satellite E05 on DOY 72, also it is obvious that the average C/N0 values for all GPS satellites are superior to those of Galileo satellites.

The computed C/N0 values were further analyzed using the epoch-by-epoch domain, which is illustrated in Figure 4 and Figure 5. It can be seen that there are some obvious fluctuations in the C/N0 values for the GPS L₅ and Galileo E_5a signals over the three examined days; on the contrary, the C/N0 values for the GPS L₁ and Galileo E₁ signals are stable. An exception with L₁ and E₁ signals transmitted by satellites on DOY 71 and 72.

Based on data quality analysis, the acquired smartphone-GNSS raw measurements are processed in the PPP approach in three different scenarios, including GPS-only (G), Galileo-only (E), and combined GPS/Galileo (GE) in real-time and post-processing. For real-time solutions, the archived real-time CNES products are utilized [36], while the final IGS products from GFZ, GRG, and WUM analysis centers are employed [37] for post-processing solutions. Additionally, based on the aforementioned C/N0 analysis, both the satellite elevation-dependent and the signal-noise-ratio GNSS weighting model are employed for weighting analysis, which follows the equation:

$$\sigma ={\displaystyle \frac{1}{\sqrt{\mathit{sin}E}}}+\left(a+b·{10}^{(-{\displaystyle \frac{1}{2}}·{\displaystyle \frac{\mathrm{C}/\mathrm{N}0}{10}})}\right)$$

(5)

where $\sigma$ represent signal uncertainty; a and b are coefficients estimated from filter residuals, E is the elevation angle of the satellite above the horizon, and C/N0 is the carrier-to-noise density ratio, in dB-Hz (signal quality metric).

Table 3. The PPP processing parameters using the Net-Diff GNSS software.

Parameter	Solution
	Real-Time	Final
Ephemeris and Clock	CNES	GFZ–GRG–WUM
Ionosphere	Ionosphere free Combination
Troposphere	Saastamoinen
Systems	GPS–Galileo–The combined GPS/Galileo
Frequencies	GPS: L1L5–Galileo: E1E5a
Observation Type	Code measurements + Carrier phase measurements
Interval	30 s
Elevation	5°
Ambiguity	FLOAT
Stochastic model	ELE1 + C/N0
Estimation parameter	Kalman Filter

summarizes the ionosphere-free PPP parameters using the Net-Diff GNSS software.

4. Results and Analysis

The positioning errors for the proposed PPP solutions are given in Figure 6. It is shown that the real-time processing scenario can be converged to meter-level for Galileo-only observations or sub-40 cm-level for GPS-only and the combined GPS/Galileo observations in horizontal directions after approximately 30 min. As observation time increased, the horizontal position accuracy for the Galileo-only PPP solution improved to sub-meter levels, reaching sub-50 cm after approximately 1.5 h, while the GPS-only and the combined GPS/Galileo PPP solutions achieved positioning accuracy less than 30 cm. For the vertical components, the processing results demonstrate positioning accuracy within 1 m after 30 min for Galileo-only PPP solution and within 40 cm after 30 min for GPS-only and the combined GPS/Galileo PPP solutions.

For the post-processing solutions, both the horizontal and the vertical positioning errors after 30 min are within 50 cm for the Galileo-only PPP solution and less than 30 cm levels using GPS-only and the combined GPS/Galileo PPP processing scenarios.

To further study the Xiaomi 11T GNSS positioning performance, the positioning errors for horizontal and vertical components after 30 min, 60 min, and 120 min were computed for each IF-PPP solution as illustrated in Figure 7.

By the 30 min mark of observation, the GPS-only IF-PPP solution achieved horizontal positioning accuracies better than 35 cm and 20 cm when using real-time and final correction products, respectively. By the 60 min mark, all horizontal positioning errors using the GPS-only IF-PPP solution were within 29 cm. Furthermore, by the 120 min mark, horizontal positioning accuracy improved to better than 20 cm when using CNES products and 28 cm with final IGS products. The vertical positioning accuracies of the GPS-only IF-PPP solution at 30 min of observation were approximately better than 47 cm and 53 cm when using real-time and final correction products, respectively. By the 60 min and 120 min marks, the vertical accuracies improved to better than 30 cm for all correction products.

The Galileo-only IF-PPP solution achieved horizontal positioning accuracies better than 25 cm using real-time CNES products by the 30 min mark and better than 45 cm using final IGS products by the 60 min mark. By the 120 min mark, horizontal accuracies improved to better than 25 cm with real-time products and 15 cm with final products. Regarding the vertical directions, the Galileo-only IF-PPP solution achieved accuracy better than 35 cm across all analyzed time marks and correction products. The final IGS products demonstrated a superior performance at the 30 and 60 min marks, with vertical accuracies better than 10 cm.

The combined GPS/Galileo IF-PPP solution demonstrated a horizontal accuracy of approximately better than 30 cm across all analyzed time marks and products. However, it can be noticed that CNES products achieved better than 20 cm by 30 min time marks. Regarding the vertical accuracy using the combined GPS/Galileo IF-PPP solution, approximately 30 cm accuracy was achieved using CNES across all analyzed time marks, while better than 25 cm was achieved using final IGS products across all analyzed time marks. Similarly to the Galileo-only solution, the combined GPS/Galileo IF-PPP solution vertical accuracy was better than 15 cm for 30 and 60 min time marks using final products.

An analysis of the positioning error accuracy across different time windows indicates that the positioning performance remains generally stable, with minor fluctuations in accuracy over time. Notably, real-time CNES products and single-constellation solutions occasionally demonstrated slightly improved performance at certain time intervals. This trend is particularly evident in the Galileo-only IF-PPP solution, where the vertical component showed enhanced accuracy at specific time marks compared with other IF-PPP solutions.

Figure 7. The positioning errors in horizontal (Left) and vertical (Right) direction for different time windows on DOY 71.

Figure 7. The positioning errors in horizontal (Left) and vertical (Right) direction for different time windows on DOY 71.

The aforementioned outputs of error time series and positioning errors at different time windows clearly demonstrate some fluctuations and degradation. Therefore, a deeper analysis is warranted through the examination of the Cumulative Distribution Function (CDF), as illustrated in Figure 8. It can be seen that 90% of two-dimensional (2D) horizontal errors are less than 30 cm, and 80% of the 2D errors are less than 40 cm of the GPS-only solution using final IGS products and real-time CNES products, respectively. For vertical direction errors of the GPS-only solution, approximately 90% of errors are less than 50 cm and 58 cm using real-time and final products, respectively.

The Galileo-only solution demonstrated a notable improvement in performance for final products compared with real-time. Approximately 90% of Galileo-only solution 2D errors are less than 50 cm and 3.5 m using final and real-time products, respectively. Also, 90% of its vertical errors are less than 50 cm and 2 m using final and real-time products, respectively.

For the combined GPS/Galileo, 90% of both 2D and vertical errors are less than 35 cm using all solutions, with slightly better performance of CNES products in 2D components.

Figure 8. The CDF for the IF-PPP solution using GPS, Galileo, and the combined GPS/Galileo observations on DOY 71.

Figure 8. The CDF for the IF-PPP solution using GPS, Galileo, and the combined GPS/Galileo observations on DOY 71.

5. Discussion

It is becoming more widely acknowledged that the ionosphere-free PPP technique is the preferred solution for attaining cost-effective high-precision GNSS-based positioning. The advanced GNSS receivers that can track multiple frequencies are the bare minimum requirement for such an approach. Recently, advancements in GNSS technology, particularly the emergence of low-cost dual-frequency receivers such as smartphones and the widespread availability of freely accessible GNSS correction products, have significantly enhanced the feasibility and accessibility of the IF-PPP approach, thereby employing it in a wider range of land use and urban sustainability applications. To further analyze the attained positioning accuracy, the RMSE is computed. The RMSE can be estimated using the following equation:

$$RMSE=\pm \sqrt{{\displaystyle \frac{\sum {Error}^2}{n}}}$$

(6)

Figure 9 demonstrates the following:

• For a GPS-only solution, less than 50 cm RMSE values in horizontal, vertical, and three-dimensional (3D) directions using CNES archived real-time products on DOY 70 and DOY 71. However, a notable degradation in positioning accuracy was observed, with RMSE values exceeding 50 cm in the horizontal and 3D component on DOY 72. The final WUM products demonstrated superior performance for the GPS-only solution, yielding RMSE values of approximately 22 cm, 11 cm, and 24 cm in the horizontal, vertical, and 3D directions, respectively.
• The Galileo-only solution exhibits higher RMSE values compared to the real-time GPS-only PPP solutions counterpart for DOY 70 and DOY 71. When employing the CNES real-time products, the Galileo-only solution achieved RMSE values close to 2 m across horizontal and 3D components on DOY 71, as well as vertical and position 3D components on DOY 70. A significant improvement in RMSE values in all components was observed on DOY 72 with 24 cm, 16 cm, and 29 cm in horizontal, vertical, and position 3D components, respectively. Using the final post-processing products, the Galileo-only solution yielded RMSE values of approximately less than 30 cm for all products. A notable degradation in positioning accuracy was observed across all components on DOY 70 using the GRG product. Among the evaluated final products, the GRG solution delivered the best performance on DOY 72, attaining RMSE values of 21 cm, 13 cm, and 29 cm in the horizontal, vertical, and position 3D components, respectively.
• The combined GPS/Galileo solution demonstrates more stable accuracy compared to single-constellation solutions. Using the real-time CNES products, it achieved RMSE values of approximately 50 cm for all directions. On DOY 72, the CNES solution achieved superior RMSE values of 13 cm, 15 cm, and 20 cm in horizontal, vertical, and 3D components, respectively. For the final products, the combined GPS/Galileo solution achieved RMSE values less than 50 cm in all directions, with the WUM products demonstrating superior performance, achieving 21 cm, 19 cm, and 28 cm in horizontal, vertical, and 3D components, respectively, on DOY 72. However, on DOY 70, the combined solution achieved RMSE values greater than 50 cm using GRG products in vertical and 3D components.
• Generally, ionosphere-free PPP solutions with smartphones can achieve less than 50 cm positioning 3D accuracy. Even with a notable degradation in RMSE values reaching 1 m level in real-time and close to 1 m using post-processing products. The observed degradation in PPP solutions can be attributed to poor signal strength, which results in data losses. These losses subsequently reduce the number of observable satellites and increase the PDOP, thereby adversely affecting positioning accuracy.
• Although the positioning accuracy using low-cost Xiaomi 11T modules is encouraging, it is subject to several limitations, including the necessity for pre-mission planning because Xiaomi 11T tracks only the L₅ signal, which is currently transmitted by only 17 out of 32 GPS satellites. This constraint is particularly impactful for dual-frequency positioning. Additionally, the carrier phase measurement losses and comparatively lower signal strength relative to geodetic-grade receivers.

Figure 9. The RMSE values in meters for the IF-PPP solution using GPS, Galileo, and the combined GPS/Galileo observations.

Figure 9. The RMSE values in meters for the IF-PPP solution using GPS, Galileo, and the combined GPS/Galileo observations.

6. Conclusions

The multi-constellation, multi-frequency affordable smartphone, Xiaomi 11T, was investigated for GNSS-based positioning in static mode using the ionosphere-free PPP approach, with the phone centered over a known reference point. The experiment was repeated over three consecutive days to assess the repeatability of the results. Furthermore, significant losses in both carrier measurements and code measurements, particularly for the second frequencies, are observed.

The data quality assessment revealed that the mean C/N0 ratio for the GPS L₁ and Galileo E₁ signals is more stable compared with the GPS L₅ and Galileo E_5a signals; furthermore, the average C/N0 values for signals transmitted by GPS satellites are superior to those transmitted by Galileo satellites.

The findings indicate that the real-time GPS/Galileo PPP solution outperforms the single-constellation solution, achieving a positional accuracy of 13 cm, 15 cm, and 20 cm in two-dimensional, vertical and three-dimensional components while the real-time single constellation PPP solution shows the superiority of Galileo-only solution with 24 cm, 16 cm, and 29 cm in horizontal, vertical and 3D, respectively. However, the Galileo-only PPP processing scenario shows less stability compared with other solutions. Therefore, it can be said that Xiaomi 11T is capable of supporting real-time applications that require decimeter-level 3D position accuracy, such as land use and urban sustainability applications.