Ionosphere-Constrained Single-Frequency PPP with an Android Smartphone and Assessment of GNSS Observations

With the development of Global Navigation Satellite System (GNSS) and the opening of Application Programming Interface (API) of Android terminals, the positioning research of Android terminals has attracted the attention of GNSS community. In this paper, three static experiments were conducted to analyze the raw GNSS observations quality and positioning performances of the smartphones. For the two experimental smartphones, the numbers of visible satellites with dual-frequency signals are unstable and not enough for dual-frequency Precise Point Positioning (PPP) processing all through the day. Therefore, the ionosphere-constrained single-frequency PPP model was employed to improve the positioning with the smartphones, and its performance was evaluated and compared with those of the Single Point Positioning (SPP) and the traditional PPP models. The results show that horizontal positioning accuracies of the smartphones with the improved PPP model are better than 1 m, while those with the SPP and the traditional PPP models are about 2 m.


Introduction
With the development of Global Navigation Satellite System (GNSS) in the 21th century, the number of available navigation satellites has increased significantly. It has formed a multi-system global navigation constellation framework mainly composed of American Global Positioning System (GPS), Russian Global Navigation Satellite System (GLONASS), Chinese BeiDou Navigation Satellite System (BDS) and EU's Galileo system [1]. Moreover, Japanese Quasi-Zenith Satellite System (QZSS) is widely used to supplement GPS services as a regional navigation satellite system. The development of GNSS also promotes the continuous development of location-based service business based on smartphones, and greatly facilitates both industrial production and daily life.
For a long time, only rough positioning results could be obtained from the smartphones. Launched in 2016, the Android 7.0 operating system supports the access to GNSS raw measurements and navigation messages [2], making the Android devices function more like a GNSS receiver. In the same year, Google released GNSSLogger, an open-source program that could help retrieve GNSS raw observations from Android smartphones, including the observations of code pseudorange, carrier phase, and Doppler [3]. In 2017, Geo++ released an application named Geo++ RINEX Logger to provide GNSS raw observation directly in RINEX format [4]. Both of the above two applications cannot output the information of navigation messages. RinexON, released by Flamingo team at the end of June 2018, is able to output multi-GNSS raw data, including broadcast ephemeris, collected disadvantages of smartphones in GNSS data collection, it is necessary to quantitatively analyze the quality of observations of smartphones and to study the method of cycle slip detection.
Although some types of smartphones are designed with the nominal capabilities of tracking dual-frequency GNSS signals, the real measurements are usually far from enough for dual-frequency PPP processing all through the day with the traditional method, due to various reasons such as the frequent interruptions of dual-frequency data. Thus, the single-frequency PPP is still a common processing mode for smartphones, and the ionospheric delay are corrected by the Global Ionospheric Maps (GIM), the products of which can correct about 80% of the ionospheric delay [20]. Although the remaining ionospheric delay can still reach decimeter level, it is sufficient for the single-frequency PPP with smartphones, considering that the precision of code pseudorange measurements from smartphones is nearly 10 m [18]. In theory, GIM can be used to build constraint equations, to improve the reliability of single-frequency PPP processing of smartphones and shorten the convergence time [21]. However, there is a lack of research on the impact of ionosphere constraints on the smartphones PPP.
This paper contributes to GNSS data quality analysis and PPP with Android smartphones. Section 2 represents the principles and methodologies of single-frequency PPP, smoothing code pseudorange and cycle slip detection, in special consideration of the characteristics of data collected by smartphones. In Section 3, the quality of GNSS measurements from two different Android devices and one geodetic receiver are analyzed and compared from the aspects of satellite tracking performance, carrier-to-noise ratio and multipath effects, followed by PPP experiment with GNSS Analysis Software for Multi-constellation and Multi-frequency Precise Positioning (GAMP) [22]. Conclusions are given in Section 5.

The Principles and Methodologies of PPP with Smartphones
Android 7.0 provides positioning related API. The modules related to the raw GNSS observations are GNSS Clock, GNSS Measurement and GNSS Navigation Message. The module GNSS Clock provides quartz clock information of the Android smartphones. The module GNSS Measurement provides observation information of each satellite signal obtained by base frequency processing. The module GNSS Navigation Message provides satellite ephemeris information. The modules GNSS Clock and GNSS Measurement can generate the raw GNSS observations of each satellite, including code pseudorange, carrier phase, Doppler and carrier-to-noise ratio. The generation principle of GNSS raw observations through the modules GNSS Clock and GNSS Measurement is shown in Figure 1 [18]. To overcome the disadvantages of smartphones in GNSS data collection, it is necessary to quantitatively analyze the quality of observations of smartphones and to study the method of cycle slip detection. Although some types of smartphones are designed with the nominal capabilities of tracking dual-frequency GNSS signals, the real measurements are usually far from enough for dual-frequency PPP processing all through the day with the traditional method, due to various reasons such as the frequent interruptions of dual-frequency data. Thus, the single-frequency PPP is still a common processing mode for smartphones, and the ionospheric delay are corrected by the Global Ionospheric Maps (GIM), the products of which can correct about 80% of the ionospheric delay [20]. Although the remaining ionospheric delay can still reach decimeter level, it is sufficient for the single-frequency PPP with smartphones, considering that the precision of code pseudorange measurements from smartphones is nearly 10 m [18]. In theory, GIM can be used to build constraint equations, to improve the reliability of single-frequency PPP processing of smartphones and shorten the convergence time [21]. However, there is a lack of research on the impact of ionosphere constraints on the smartphones PPP.
This paper contributes to GNSS data quality analysis and PPP with Android smartphones. Section 2 represents the principles and methodologies of single-frequency PPP, smoothing code pseudorange and cycle slip detection, in special consideration of the characteristics of data collected by smartphones. In Section 3, the quality of GNSS measurements from two different Android devices and one geodetic receiver are analyzed and compared from the aspects of satellite tracking performance, carrier-to-noise ratio and multipath effects, followed by PPP experiment with GNSS Analysis Software for Multi-constellation and Multi-frequency Precise Positioning (GAMP) [22]. Conclusions are given in Section 5.

The Principles and Methodologies of PPP with Smartphones
Android 7.0 provides positioning related API. The modules related to the raw GNSS observations are GNSS Clock, GNSS Measurement and GNSS Navigation Message. The module GNSS Clock provides quartz clock information of the Android smartphones. The module GNSS Measurement provides observation information of each satellite signal obtained by base frequency processing. The module GNSS Navigation Message provides satellite ephemeris information. The modules GNSS Clock and GNSS Measurement can generate the raw GNSS observations of each satellite, including code pseudorange, carrier phase, Doppler and carrier-to-noise ratio. The generation principle of GNSS raw observations through the modules GNSS Clock and GNSS Measurement is shown in Figure 1 [18].

Ionosphere-Constrained Single-Frequency PPP
Since the numbers of dual-frequency observables tracked by the current smartphones are far from sufficient, the single-frequency PPP model is still the main choice for the positioning research with smartphones at present [17]. Without dual-frequency observables, the ionospheric delay is unable to be reduced through the ionosphere-free combination, and has to be estimated as an additional unknown parameter. Besides, the qualities of code and carrier phase measurements received by smartphone are usually not as high as those by geodetic receiver [18]. To improve the PPP accuracy with smartphone, external ionospheric information is introduced as virtual observations. The model of single-frequency PPP with ionospheric constraint for one satellite-receiver pair can be expressed as.
where p and ϕ represent the observed-minus-computed (OMC) values of the code pseudorange and the carrier phase, respectively; I denotes the virtual observable of the ionospheric constraint calculated by the GIM products; u is the line-of-sight direction vector specific to each satellite; x is the incremental vector of the receiver position with respect to the initial approximate coordinates; δt and Z w are the parameters of receiver clock and Zenith Wet Delay(ZWD) specific to the station; M and λ are the mapping function of ZWD and the signal wavelength; I and N are the ionospheric delay and carrier phase ambiguity specific to certain station, satellite and frequency; ε, ξ and ζ are the sums of unmodeled errors and observing noise corresponding to each observable; Q p , Q ϕ and Q I represent the variances of the corresponding observables. It is worth noting that all the indices of satellite, receiver and frequency have been omitted for simplicity. In this study, the rapid products of orbits and clocks released by the Multi-GNSS Experiment (MGEX) are adopted, and the satellite Differential Code Biases (DCBs) are corrected by the DCB products from the Center for Orbit Determination in Europe (CODE) and the MGEX. The satellite antenna phase center offsets and variations, relativistic effects, zenith dry delay, tidal loadings, and phase windup are corrected by the empirical models [23].

Smoothing Code Pseudorange with Doppler
Although the method of phase smoothing pseudorange is usually used to reduce the noise of code measurements, its performance is prone to be affected by the continuity of phase observation, especially in the cases of poor tracking conditions with smartphones. Compared with the phase observation, the Doppler observation is unlikely to be affected by cycle slips, and its accuracy is higher than that of the code measurement. Therefore, the Doppler observation can be used alternatively to reduce the noise and multipath error of the code measurement [24].
The integral Doppler is equal to the variation of carrier phase during the integral interval, which reflects the variation of geometric distance between the satellite and the smartphone. The algorithm of Doppler smoothing code pseudorange can be expressed as where t i and t i−1 are two adjacent moments; P and P represent the raw and smoothing code pseudorange; D is the Doppler observation; m is a constant set as 75 in the study.

Cycle Slip Detection
Due to the lack of dual-frequency GNSS observations, cycle slip detection is another challenging task for the smartphones. At present, the main cycle slip methods for single-frequency scenario include code-phase comparison, Doppler integration, and higher-order time differencing of carrier phase observations [25][26][27]. In this study, the methods of code-phase comparison and Doppler integration are employed for the detection of cycle slips contained in the data collected by the smartphones.
In the observation equation, the terms of geometric distance, receiver clock and satellite clock can be eliminated through the differencing between the raw measurements of the code pseudorange P and the carrier phase Φ, so we have where the parameters have the same meaning as Equation (1). If no cycle slip occurs, the ambiguity parameter stays constant. The ionospheric delay varies slowly, and so is the code-phase differencing ∆. The temporal variation of ∆ stays relatively stable unless there are cycle slips. As a consequence, the between-epoch differencing of Equation (3) can be used to detect and determine the possible cycle slips.
The abovementioned cycle slip detection method is highly dependent on the quality of the code measurements. To obtain the knowledge about the precisions and stabilities of the measurements with different devices, we investigate the high-order between-epoch differences of raw measurements, and shown in Figure 2. are the typical third-order between-epoch differences of the code (blue) and the carrier phase (orange) measurements, as well as the second-order between-epoch differences of the Doppler (red) measurements. Doppler integration are employed for the detection of cycle slips contained in the data collected by the smartphones.
In the observation equation, the terms of geometric distance, receiver clock and satellite clock can be eliminated through the differencing between the raw measurements of the code pseudorange and the carrier phase , so we have where the parameters have the same meaning as Equation (1). If no cycle slip occurs, the ambiguity parameter stays constant. The ionospheric delay varies slowly, and so is the code-phase differencing . The temporal variation of stays relatively stable unless there are cycle slips. As a consequence, the between-epoch differencing of Equation (3) can be used to detect and determine the possible cycle slips.
The abovementioned cycle slip detection method is highly dependent on the quality of the code measurements. To obtain the knowledge about the precisions and stabilities of the measurements with different devices, we investigate the high-order between-epoch differences of raw measurements, and shown in Figure 2. are the typical third-order between-epoch differences of the code (blue) and the carrier phase (orange) measurements, as well as the second-order between-epoch differences of the Doppler (red) measurements. The code measurements of the two smartphones are far less precise than the those of the geodetic receiver, which is likely to undermine the performance of the cycle slip detection method based on Equation (3). However, the Doppler measurements of all the three devices are comparable in precision and stability, suggesting that the Doppler measurements can be used as supplements of the code and phase measurements in the detection of cycle slips.
Therefore, an indicator based on the difference between the carrier phase and Doppler integral are calculated as [27] where ∆ ( , ) is the variation of the carrier phase between two adjacent epochs. An absolute value of larger than the threshold indicates the cycle slip. The methods of code-phase comparison based on Equation (3) and Doppler integration based on Equation (4) are used together to guarantee the performance of cycle slip detection. In summary, the flowchart of ionosphere-constrained single-frequency PPP for smartphone is shown as Figure 3. The code measurements of the two smartphones are far less precise than the those of the geodetic receiver, which is likely to undermine the performance of the cycle slip detection method based on Equation (3). However, the Doppler measurements of all the three devices are comparable in precision and stability, suggesting that the Doppler measurements can be used as supplements of the code and phase measurements in the detection of cycle slips.
Therefore, an indicator based on the difference between the carrier phase and Doppler integral are calculated as [27] where ∆Φ(t i , t i−1 ) is the variation of the carrier phase between two adjacent epochs. An absolute value of δN larger than the threshold indicates the cycle slip.
Sensors 2020, 20, 5917 6 of 15 The methods of code-phase comparison based on Equation (3) and Doppler integration based on Equation (4) are used together to guarantee the performance of cycle slip detection. In summary, the flowchart of ionosphere-constrained single-frequency PPP for smartphone is shown as Figure 3.

GNSS Data Quality Analysis
The main device used in this experiment is a Huawei Mate30 smartphone (hereinafter referred to as Mate30). For comparison analysis, a Huawei honorV20 smartphone (hereinafter referred to as V20) and a geodetic receiver (Trimble R8) were also used. The Mate30 smartphone is a dual-frequency GNSS smartphone that collects the first frequency signals of GPS, GLONASS, BDS, Galileo and QZSS, and the second frequency signals of GPS, Galileo and QZSS. Although the V20 smartphone is cheaper than the Mate30 smartphone, it also supports dual-frequency observations and all of the five systems. Listed in Table 1 are the GNSS related characteristics of the three devices used in this paper.

GNSS Data Quality Analysis
The main device used in this experiment is a Huawei Mate30 smartphone (hereinafter referred to as Mate30). For comparison analysis, a Huawei honorV20 smartphone (hereinafter referred to as V20) and a geodetic receiver (Trimble R8) were also used. The Mate30 smartphone is a dual-frequency GNSS smartphone that collects the first frequency signals of GPS, GLONASS, BDS, Galileo and QZSS, and the second frequency signals of GPS, Galileo and QZSS. Although the V20 smartphone is cheaper than the Mate30 smartphone, it also supports dual-frequency observations and all of the five systems. Listed in Table 1 are the GNSS related characteristics of the three devices used in this paper.
In the experiment, Trimble R8 is used as the reference, and its antenna is only about 10 cm away from the two smartphones. To compare the observing positioning performances of the two smartphones with those of the geodetic receiver, synchronous observations were conducted with the three devices. Data was collected on the evening of 13 November, the afternoon and the evening of 18 November 2019, and each of the three observing periods lasted for 2-3 h. Since the devices were equipped at almost the same place during the three observing periods, the difference of the surroundings could be neglected. Table 1. Performance features of the Mate30, the V20 smartphones and Trimble R8 geodetic receiver.

Devices
Android Version GNSS Supported 1 Code Carrier Phase Yes Yes 1 G: GPS, R: GLONASS, E: Galileo, C: BDS, J: QZSS. The definition of frequency bands is described in RINEX 3.03 format [28].

Satellite Tracking
Shown in Figure 4 are the numbers of different GNSS satellites with the signal of the first frequency tracked by the geodetic receiver and the two smartphones. The Mate30 smartphone is able to track about 38 satellites in total, while the V20 smartphone tracks only 30 ones. Since the GNSS chip of the Mate30 is nominally supporting BDS-3 signals, it can track more BDS satellites than the V20, which can only track BDS-2 satellites. Compared with the geodetic receiver, both of the two smartphones suffer from frequent fluctuations in the numbers of visible satellites, although they can track as many satellites as, if not more than, the geodetic receivers.

Devices
Android Version GNSS Supported 1 Code Carrier Phase In the experiment, Trimble R8 is used as the reference, and its antenna is only about 10 cm away from the two smartphones. To compare the observing positioning performances of the two smartphones with those of the geodetic receiver, synchronous observations were conducted with the three devices. Data was collected on the evening of 13 November, the afternoon and the evening of 18 November 2019, and each of the three observing periods lasted for 2-3 h. Since the devices were equipped at almost the same place during the three observing periods, the difference of the surroundings could be neglected.

Satellite Tracking
Shown in Figure 4 are the numbers of different GNSS satellites with the signal of the first frequency tracked by the geodetic receiver and the two smartphones. The Mate30 smartphone is able to track about 38 satellites in total, while the V20 smartphone tracks only 30 ones. Since the GNSS chip of the Mate30 is nominally supporting BDS-3 signals, it can track more BDS satellites than the V20, which can only track BDS-2 satellites. Compared with the geodetic receiver, both of the two smartphones suffer from frequent fluctuations in the numbers of visible satellites, although they can track as many satellites as, if not more than, the geodetic receivers.  signals tracked by the V20 smartphone fluctuates between 1 and 9. The dual-frequency measurements collected by either the Mate30 or the V20 are far from sufficient for continuous PPP experiment with the ionosphere-free combination of L1/L5 or E1/E5A observables, and the case might be worse in real scenarios with urban canyons.
dual-frequency measurements collected by either the Mate30 or the V20 are far from sufficient for continuous PPP experiment with the ionosphere-free combination of L1/L5 or E1/E5A observables, and the case might be worse in real scenarios with urban canyons.
The data continuities of GPS, Galileo and QZSS are also compared and the results are shown in Figure 5. The number of GPS, Galileo and QZSS dual-frequency satellites of two smartphones fluctuates seriously. And in a certain period of time, the dual-frequency satellite of Galileo cannot be observed by the two smartphones. Considering that QZSS system is a regional navigation satellite amplification system developed by Japan, adopting the Inclined Geosynchronous Orbit (IGEO), the precision of positioning service provided is limited [22]. Therefore, the reliable dual-frequency measurements collected by the smartphones are still mainly from GPS satellites at present. Figure 5. The numbers of GPS (blue), Galileo (cyan), QZSS (orange) and the total satellites of these three systems (red) with dual-frequency measurements available for the Mate30 smartphone (a,d,g) and the V20 smartphone (b,e,h) and the geodetic receiver Trimble R8 (c,f,i) during the first (a-c), the second (d-f) and the third (g-i) observing periods.

Carrier-to-Noise Ratio
The carrier-to-noise ratio refers to the ratio of the average power of the carrier signal received at the receiver end to the average power of the noise when the signal is interfered in the process of propagation. The carrier-to-noise ratio reflects the noise level of the measurement [28]. The higher the carrier-to-noise ratio is, the better the observation quality is. Shown in Figure 6 are the mean values of carrier-to-noise ratio in three experiments. Generally, the mean carrier-to-noise ratio with the geodetic receiver is the highest among all of the three devices, although for several BDS satellites the mean carrier-to-noise ratio with the Mate30 Figure 5. The numbers of GPS (blue), Galileo (cyan), QZSS (orange) and the total satellites of these three systems (red) with dual-frequency measurements available for the Mate30 smartphone (a,d,g) and the V20 smartphone (b,e,h) and the geodetic receiver Trimble R8 (c,f,i) during the first (a-c), the second (d-f) and the third (g-i) observing periods.
The data continuities of GPS, Galileo and QZSS are also compared and the results are shown in Figure 5. The number of GPS, Galileo and QZSS dual-frequency satellites of two smartphones fluctuates seriously. And in a certain period of time, the dual-frequency satellite of Galileo cannot be observed by the two smartphones. Considering that QZSS system is a regional navigation satellite amplification system developed by Japan, adopting the Inclined Geosynchronous Orbit (IGSO), the precision of positioning service provided is limited [22]. Therefore, the reliable dual-frequency measurements collected by the smartphones are still mainly from GPS satellites at present.

Carrier-to-Noise Ratio
The carrier-to-noise ratio refers to the ratio of the average power of the carrier signal received at the receiver end to the average power of the noise when the signal is interfered in the process of propagation. The carrier-to-noise ratio reflects the noise level of the measurement [28]. The higher the carrier-to-noise ratio is, the better the observation quality is.
Shown in Figure 6 are the mean values of carrier-to-noise ratio in three experiments. Generally, the mean carrier-to-noise ratio with the geodetic receiver is the highest among all of the three devices, although for several BDS satellites the mean carrier-to-noise ratio with the Mate30 smartphone is the highest. The carrier-to-noise ratios with the Mate30 smartphone are around 40 dBHz, obviously better than those with the V20 smartphone. This may be due to better antenna and GNSS chip of the Mate30 smartphone. smartphone is the highest. The carrier-to-noise ratios with the Mate30 smartphone are around 40 dBHz, obviously better than those with the V20 smartphone. This may be due to better antenna and GNSS chip of the Mate30 smartphone. Figure 6. The mean carrier-to-noise ratios of the first frequency with the V20 smartphone (cyan), the Mate30 smartphone (orange) and the geodetic receiver Trimble R8 (blue) in the first (a), the second (b) and the third (c) experiments. Figure 7 shows the typical relationships between the carrier-to-noise ratio and the elevation angle for the three devices. The carrier-to-noise ratio with the geodetic receiver increases as the elevation angle increases, while for the two smartphones, the correlation between carrier-to-noise ratio and elevation angle is not obvious. This could be explained by the different polarization modes. Instead of the right-handed circular polarization, the linear polarization is adopted by the built-in GNSS antennas of the smartphones. Therefore, the smartphones are more vulnerable to signal interferences. In addition, through the comparison between the carrier-to-noise ratios of L1 and L5 observations collected by the smartphones, it is found that the carrier-to-noise ratios of the L5 observations are equivalent to or even better than those of the L1 observations in the cases of low elevations. It can also be inferred that theL5 signal outperforms the L2 signal in anti-jamming in the Figure 6. The mean carrier-to-noise ratios of the first frequency with the V20 smartphone (cyan), the Mate30 smartphone (orange) and the geodetic receiver Trimble R8 (blue) in the first (a), the second (b) and the third (c) experiments. Figure 7 shows the typical relationships between the carrier-to-noise ratio and the elevation angle for the three devices. The carrier-to-noise ratio with the geodetic receiver increases as the elevation angle increases, while for the two smartphones, the correlation between carrier-to-noise ratio and elevation angle is not obvious. This could be explained by the different polarization modes. Instead of the right-handed circular polarization, the linear polarization is adopted by the built-in GNSS antennas of the smartphones. Therefore, the smartphones are more vulnerable to signal interferences.
Sensors 2020, 20, x FOR PEER REVIEW 9 of 15 smartphone is the highest. The carrier-to-noise ratios with the Mate30 smartphone are around 40 dBHz, obviously better than those with the V20 smartphone. This may be due to better antenna and GNSS chip of the Mate30 smartphone.  Figure 7 shows the typical relationships between the carrier-to-noise ratio and the elevation angle for the three devices. The carrier-to-noise ratio with the geodetic receiver increases as the elevation angle increases, while for the two smartphones, the correlation between carrier-to-noise ratio and elevation angle is not obvious. This could be explained by the different polarization modes. Instead of the right-handed circular polarization, the linear polarization is adopted by the built-in GNSS antennas of the smartphones. Therefore, the smartphones are more vulnerable to signal interferences. In addition, through the comparison between the carrier-to-noise ratios of L1 and L5 observations collected by the smartphones, it is found that the carrier-to-noise ratios of the L5 observations are equivalent to or even better than those of the L1 observations in the cases of low elevations. It can also be inferred that theL5 signal outperforms the L2 signal in anti-jamming in the In addition, through the comparison between the carrier-to-noise ratios of L1 and L5 observations collected by the smartphones, it is found that the carrier-to-noise ratios of the L5 observations are equivalent to or even better than those of the L1 observations in the cases of low elevations. It can also be inferred that theL5 signal outperforms the L2 signal in anti-jamming in the cases of low elevations. However, the average carrier-to-noise ratios of the L5 signals received by the smartphones are around 4 dBHz lower than those of the L1 signals. This might be due to the imperfect multi-frequency antenna design of the smartphones, and further study is needed.

Multipath Effect
The propagation direction, amplitude and phase of GNSS signal are prone to be affected by the reflections of the surrounding at the antenna, and the reflected signals can cause multipath effects [29]. The observing environments for smartphone users are complicated, and it is inconvenient for the antenna of a smartphone to suppress the multipath error through hardware like the choke ring. Therefore, the multipath error usually plays a dominant role in the code measurement collected by smartphone [9]. Since the multipath error of code measurement is as 200 times large as that of carrier phase [30,31], we focus on the multipath error of the code measurement in the study.
When dual-frequency observations are available, the code multipath errors can be studied with the multipath combination, which can be expressed as where the subscripts i and j (i j) denote different frequency bands, and f is the frequency value. The combination expressed by Equation (5) mainly contains the multipath error of corresponding code measurement and the linear combination of the ambiguities. If no cycle slip occurs, the ambiguities are considered constants and can be removed through averaging over epochs [32]. The subscripts for receiver and satellite have been omitted here for simplicity. Shown in Figure 8 are the standard deviations of L1 frequency code multipath error of the three devices in the three experiments. The standard deviations of code multipath errors of the Mate30 and the V20 are as ten times large as that of the Trimble R8. This phenomenon shows that the two smartphones have disadvantages in suppressing the multipath effects.
Sensors 2020, 20, x FOR PEER REVIEW 10 of 15 cases of low elevations. However, the average carrier-to-noise ratios of the L5 signals received by the smartphones are around 4 dBHz lower than those of the L1 signals. This might be due to the imperfect multi-frequency antenna design of the smartphones, and further study is needed.

Multipath Effect
The propagation direction, amplitude and phase of GNSS signal are prone to be affected by the reflections of the surrounding at the antenna, and the reflected signals can cause multipath effects [29]. The observing environments for smartphone users are complicated, and it is inconvenient for the antenna of a smartphone to suppress the multipath error through hardware like the choke ring. Therefore, the multipath error usually plays a dominant role in the code measurement collected by smartphone [9]. Since the multipath error of code measurement is as 200 times large as that of carrier phase [30,31], we focus on the multipath error of the code measurement in the study.
When dual-frequency observations are available, the code multipath errors can be studied with the multipath combination, which can be expressed as where the subscripts and ( ≠ ) denote different frequency bands, and is the frequency value. The combination expressed by Equation (5) mainly contains the multipath error of corresponding code measurement and the linear combination of the ambiguities. If no cycle slip occurs, the ambiguities are considered constants and can be removed through averaging over epochs [32]. The subscripts for receiver and satellite have been omitted here for simplicity.
Shown in Figure 8 are the standard deviations of L1 frequency code multipath error of the three devices in the three experiments. The standard deviations of code multipath errors of the Mate30 and the V20 are as ten times large as that of the Trimble R8. This phenomenon shows that the two smartphones have disadvantages in suppressing the multipath effects.

PPP Results
In this paper, a single-frequency PPP processing strategy based on ionosphere constraints is employed. Shown in Table 2 are the setting details of the single-frequency PPP for smartphones. The products of satellite orbit, satellite clock and Earth rotation are downloaded from MGEX data center (http://www.cddis.gsfc.nasa.gov/). Ionospheric delay products are downloaded from CODE. And ionospheric delay is constrained by GIM products of CODE. In order to compare the positioning results with the different strategies and to validate the abovementioned method, three experiments were conducted with different settings. The details of these projects are shown in Table 3.

PPP Results
In this paper, a single-frequency PPP processing strategy based on ionosphere constraints is employed. Shown in Table 2 are the setting details of the single-frequency PPP for smartphones. The products of satellite orbit, satellite clock and Earth rotation are downloaded from MGEX data center (http://www.cddis.gsfc.nasa.gov/). Ionospheric delay products are downloaded from CODE. And ionospheric delay is constrained by GIM products of CODE. In order to compare the positioning results with the different strategies and to validate the abovementioned method, three experiments were conducted with different settings. The details of these projects are shown in Table 3. Table 3. The differences of detailed settings of positioning projects, where improved PPP employs ionosphere-constrained single-frequency PPP model described in Section 2. The other settings of the three projects employed the setting proposed in Table 2.

Options
Processing Strategies SPP Traditional PPP Improved PPP

Code preprocessing
No Gross error elimination [22] The preprocessing strategy proposed in Section 2.2

Cycle slip detection No
The strategy based on satellite lock out [22] The strategy proposed in Section 2.3 Filtering processing No Yes Yes The standard deviations of positioning errors of the Mate30 using different projects are shown in Table 4. Considering that the horizontal position of smartphones is more widely used [10][11][12][13], the horizontal accuracy of smartphones was only recorded and analyzed. The standard deviations of positioning errors in the East and North direction of the Mate30 using the SPP and traditional PPP projects are about 2-4 m. And that of the improved PPP project is less than 1 m. Table 4 show that the positioning accuracy of the Mate30 using the improved PPP project is obviously improved compare with the other two projects. The time series of horizontal positioning errors are shown in Figure 11. When the improved PPP model is employed, the positioning errors in E and N directions during all of the three time periods can converge to less than 1 m and stay relatively stable. With the SPP and traditional PPP model, the positioning errors in E and N directions exceed 2 m, and the positioning results are unstable. In general, the performance of SPP is highly related to the data quality of code pseudorange. The positioning accuracies with the traditional PPP and SPP models are at the same level, although precise orbit and clock products are adopted in the PPP model. The poor performance of the traditional PPP in the above experiments could be explained from two aspects. On one hand, the quality of the code measurements collected by the Mate30 is poor. One the other hand, frequent loss of lock for the satellites make it difficult for the Kalman filter to work with the smartphones. Compared with the traditional PPP model, the improved PPP model is able to smooth code pseudorange with Doppler and to detect cycle slip more effectively, so the positioning accuracy is significantly improved.

Conclusions and Discussion
In this paper, the GNSS raw observations of two smartphones are analyzed through synchronous observations with a geodetic receiver. To study the positioning performances with the smartphones, experiments are conducted with a V20 smartphone and a Mate30 smartphone, as well as a Trimble R8 receiver. With the ionosphere-constrained single-frequency PPP strategy, an improvement in smartphone positioning is achieved. The horizontal positioning accuracy better

Conclusions and Discussion
In this paper, the GNSS raw observations of two smartphones are analyzed through synchronous observations with a geodetic receiver. To study the positioning performances with the smartphones, experiments are conducted with a V20 smartphone and a Mate30 smartphone, as well as a Trimble R8 receiver. With the ionosphere-constrained single-frequency PPP strategy, an improvement in smartphone positioning is achieved. The horizontal positioning accuracy better than 1 m can be reached with the Mate30 smartphone.
Compared with a Trimble R8 geodetic receiver and a V20 smartphone, the GNSS performance of the Mate30 is evaluated. Firstly, there is little difference between the number of observable satellites in the first frequency of the Mate30 and the Trimble R8 receiver. The number of observable satellites with dual-frequency measurements available of the Mate30 and the V20 is not enough for dual-frequency PPP. The satellites lock loss of the Mate30 and the V20 is more frequent than the Trimble R8. The satellite tracking of smartphones is related to its chip. Secondly, the carrier-to-noise ratio of the smartphones is worse than that of the Trimble R8. And the carrier-to-noise ratio of the Mate30 is better than that of the V20. The carrier-to-noise ratio of smartphones has no significant relationship with elevation angle of satellites. Meanwhile, the multipath effect of smartphones is more serious than the Trimble R8. The standard deviations of code multipath errors of the Mate30 and the V20 are about ten times that of the Trimble R8. The performances of the smartphones against multipath effects of are worse than that of the geodetic receiver.
Since the number of navigation satellite with dual-frequency signals observed by smartphones is not enough for dual-frequency PPP, ionosphere-constrained single-frequency PPP model is used for smartphones. In this study, the standard deviations of horizontal positioning errors with the Mate30 are less than 1 m and the Mate30 achieves a relatively stable positioning result. Comparing the different positioning projects, we believe that there are two main reasons for the poor performance using the traditional PPP project of smartphones. For the current smartphones, the data qualities of the code measurements are relatively poor, and the losses of lock for satellites occur frequently. The ionosphere-constrained single-frequency PPP model along with the cycle slip detection method proposed in this work, to a certain extent, circumvents the above disadvantages and has considerable applicability on the smartphones.
The GNSS chip and antenna performance of smartphones is worse than that of geodetic receivers because the design of smartphones needs to consider the beauty and portability. This leads to frequent satellite lock loss, poor code pseudorange quality and serious multipath effects. Therefore, improving hardware quality and algorithm research are effective methods to improve smartphones positioning accuracy. Although the dual-frequency PPP model is unrealistic for smartphones at present due to their incompetence in collecting dual-frequency measurements, it is expected that the performance of PPP with smartphones will be significantly improved in the future with both the rapid development of BDS and the iterative upgrades of smartphones.