Single-Baseline RTK Positioning Using Dual-Frequency GNSS Receivers Inside Smartphones

Global Navigation Satellite System (GNSS) positioning is currently a common practice thanks to the development of mobile devices such as smartphones and tablets. The possibility to obtain raw GNSS measurements, such as pseudoranges and carrier-phase, from these instruments has opened new windows towards precise positioning using smart devices. This work aims to demonstrate the positioning performances in the case of a typical single-base Real-Time Kinematic (RTK) positioning while considering two different kinds of multi-frequency and multi-constellation master stations: a typical geodetic receiver and a smartphone device. The results have shown impressive performances in terms of precision in both cases: with a geodetic receiver as the master station, the reachable precisions are several mm for all 3D components while if a smartphone is used as the master station, the best results can be obtained considering the GPS+Galileo constellations, with a precision of about 2 cm both for 2D and Up components in the case of L1+L5 frequencies, or 3 cm for 2D components and 2 cm for the Up, in the case of an L1 frequency. Moreover, it has been demonstrated that it is not feasible to reach the phase ambiguities fixing: despite this, the precisions are still good and also the obtained 3D accuracies of positioning solutions are less than 1 m. So, it is possible to affirm that these results are very promising in the direction of cooperative positioning using smartphone devices.


Introduction
In the last few years, thanks to the available microtechnology, some significant advances have been made in the field of mass-market positioning. The Global Navigation Satellite System (GNSS) chipsets mounted on new smartphones generation, with their low production cost and the microelectronic components miniaturization, are leaving a footprint in an ever-growing consumer electronics market. This led to the spread of location-based applications and services (LBS), which the user can use to perform numerous spatial related tasks. Navigation, advertising, social networking, entertainment, and health are examples of the numerous LBS operational contexts. However, questions remain in the research field: how does the miniaturization of the sensors degrade their performances, and which is the level of positioning accuracy that is reachable with these devices?
The everyday evidence demonstrates the capability of these devices to perform positioning and navigation, with some meters also showing high accuracy in complex environments. Compared to more complex and expensive geodetic receivers, these smartphones' System of Chipsets exploit external assistance information provided by alternative communication channels like the internet connection of a cellphone network. These techniques, called Assisted GNSS (A-GNSS) improve standard GNSS chipset performances and allow the chipsets to be used in a real-time fashion. In fact A-GNSS reduces the time required to perform the Time To First Fix [1] and improves the positioning accuracy, thereby providing noise within ± 10 m/s, and a C/N 0 average value of approximately 10 dB-Hz lower than the geodetic receiver used as the reference solution [6]. In the same configuration the carrier-phase rate and Doppler data have also been characterized with a value within ± 0.2 m/s. In Liu et al. [7], the zero-baseline approach has been applied for the noise characteristics of the GNSS observation of a smartphone.
At the same time, advanced post-processing algorithms have been applied with the aim of achieving centimeter positioning with smartphones [8,9]. To do this, the first step was the development of parsers capable of extracting the raw measurements in a format more suited to geodetic post-processing. Some developers have created converters that can produce a Radio Technical Commission for Maritime Services (RTCM) or Receiver-Independent Exchange (RINEX) formats files that are useful for use in complex software (GEO++ RINEX logger and rinexON). Thanks to these applications, numerous research has been made to increment the positioning performances exploiting multi-constellation observations, real-time, and post-processing estimation procedures and signal processing. In reference [10], the authors were able to reach sub-meter accuracies with an on-board Doppler filtering algorithm and while considering the Satellite-based Augmentation Systems (SBAS). In reference [11], a decimeter level of accuracy in terms of positioning performances has been achieved following the post-processing approach, made by double differencing raw smartphone observations with those coming from a GNSS Continuously Operating Reference Stations (CORS) network. Also the present authors in reference [12] performed a Network Real Time Kinematic (NRTK) positioning to demonstrate the possibility of obtaining a centimeter-level accuracy through the use of differential corrections provided by CORS networks, even if it was not possible to fix the phase ambiguities in a correct way. Despite this challenge, sub-meter accuracy was obtained using that type of technique.
Another important milestone in smartphone positioning and navigation was in September 2017, when a chip manufacturer company, Broadcom Limited, announced the release of the first dual-frequency GNSS chipset, the BCM47755. Up to 2017, most GNSS chipsets installed inside smartphones were single-frequency receivers able to only provide measurements related to one frequency (the L1 band). In these cases, it is not possible to apply the double or triple differences approach [13,14], or to combine different observations [15]. The ability to use dual-frequencies signals, however, enables a higher level of positioning performances, mainly increasing the signal robustness to environmental impairments and the positioning accuracy.
The release of the first dual-frequency chipset, the first smartphone equipped with dual-frequency GNSS appeared in early June 2018, which was the Xiaomi Mi 8. The availability of signals from two frequencies allows us to correct most of the error sources introduced by ionospheric propagation. At the same time, it opens the way to solving the carrier phase integer ambiguity, enabling Real-Time Kinematic (RTK) and Precise Point Positioning (PPP) algorithms directly on smartphones, as long as the phase measurements are stable; furthermore, the design of the signals in the E5/L5 frequency makes it easier to distinguish real signals from the ones reflected by buildings, reducing the multipath effect [16]. Finally, frequency diversity is among the most regularly quoted solutions to increase robustness to interference and jamming. In addition to such benefits, the enhanced position precision also creates interesting opportunities for novel applications, such as augmented reality, autonomous vehicle navigation, and mapping.
The first research on this GNSS chipset has been made by reference [17] which evaluates the performances of the Xiaomi Mi 8 comparing the L5/E5a and L1/E1 frequencies. Applying double differences on GPS L5 and L1 code observations in a short baseline configuration, the precision of the measurements is 1.3 meters and 2.1 meters, respectively. Carrier phase-based static differential positioning using GPS and Galileo on a very short baseline has provided cm-level precision in the horizontal component and decimeter-level in the vertical component. In reference [18], the dual-frequency GNSS chipset mounted on the Xiaomi Mi 8 has been considered for multipath characterization, comparing the obtained results with those obtainable with a geodetic receiver. The comparison between GPS and Galileo measurements showed a lower multipath error in the last one, although these results are still very far from the values of the geodetic receiver. Again, the antenna represents the main limitation to achieving cm-level accuracy in positioning.
Starting from the previous work made by the authors of reference [12] on single frequency smartphone receiver, in which the RTK positioning has been performed using the differential corrections provided by the CORS network; the main aim of this work is to perform a relative positioning using two different Xiaomi Mi8 smartphones with a double-frequency GNSS chipset embedded. When using a short baseline configuration (less than few kilometers), it is possible to assume that common spatial-related biases affect both devices; thus, the goal is to show the positioning performances of a smartphone in case of static surveys with short baselines, if the master station is a smartphone as the rover station.

Smartphones Dual Frequency GNSS Receivers
As previous stated, until 2018, smartphones multi-constellation GNSS chipsets were able to acquire only one frequency signal from each satellite of the different constellations (GPS L1, Galileo E1, BeiDou B1, and GLONASS L1). In June 2018 the Xiaomi MI 8 smartphone was introduced to the market: this smartphone is the first device equipped with the Broadcom BCM47755 GNSS chipset, the first dual-frequency mass-market receiver designed by the Broadcom Limited company (San Jose, CA, USA). In addition to the previously described frequencies, this chipset uses also the GPS L5 and the Galileo E5a frequencies ( Figure 1). This feature is an important step forward in the positioning field and in particular for real-time smartphone-based navigation. Starting from the previous work made by the authors of reference [12] on single frequency smartphone receiver, in which the RTK positioning has been performed using the differential corrections provided by the CORS network; the main aim of this work is to perform a relative positioning using two different Xiaomi Mi8 smartphones with a double-frequency GNSS chipset embedded. When using a short baseline configuration (less than few kilometers), it is possible to assume that common spatial-related biases affect both devices; thus, the goal is to show the positioning performances of a smartphone in case of static surveys with short baselines, if the master station is a smartphone as the rover station.

Smartphones Dual Frequency GNSS Receivers
As previous stated, until 2018, smartphones multi-constellation GNSS chipsets were able to acquire only one frequency signal from each satellite of the different constellations (GPS L1, Galileo E1, BeiDou B1, and GLONASS L1). In June 2018 the Xiaomi MI 8 smartphone was introduced to the market: this smartphone is the first device equipped with the Broadcom BCM47755 GNSS chipset, the first dual-frequency mass-market receiver designed by the Broadcom Limited company (San Jose, CA, USA). In addition to the previously described frequencies, this chipset uses also the GPS L5 and the Galileo E5a frequencies ( Figure 1). This feature is an important step forward in the positioning field and in particular for real-time smartphone-based navigation. Acquiring observations on more than one frequency allows us to perform the data combination procedure which uses GNSS observations acquired by the same receiver at the same station in order to estimate GNSS biases. The new dual-frequency receiver is able to acquire both code and carrierphase measurements, which means that the combination can be made on both these observables.
In the state of art, the first and most important application of dual-frequency combination methods is the estimation and elimination of the ionospheric effects due to their dependency on the signal frequency. The ionospheric effect is an important error source in GNSS positioning as it generates a delay in the order of tens of meters. Combining code and carrier-phase observations Acquiring observations on more than one frequency allows us to perform the data combination procedure which uses GNSS observations acquired by the same receiver at the same station in order to estimate GNSS biases. The new dual-frequency receiver is able to acquire both code and carrier-phase measurements, which means that the combination can be made on both these observables.
In the state of art, the first and most important application of dual-frequency combination methods is the estimation and elimination of the ionospheric effects due to their dependency on the signal frequency. The ionospheric effect is an important error source in GNSS positioning as it generates a delay in the order of tens of meters. Combining code and carrier-phase observations linearly, it is possible to eliminate the ionospheric effect in the measurements. This procedure is called Iono-free combination. Another combination method is the geometry-free code-code or phase-phase combination, which removes all the errors in the observation equations except for the ionospheric term and the ambiguity parameters. Other possible linear combinations of carrier-phase measurements are the so called wide-line (difference) and narrow-line (sum) combinations.
Finally, frequency diversity could increase signal robustness to interference and jamming together with increasing the capability to distinguish between the real line of sight signals from the reflected ones.

RTK Positioning Using Smartphones
Common trends and research in the domain of centimetric RTK positioning have been already been presented in the introduction and outline the possibility of using carrier-phase measurements to perform RTK smartphone positioning and navigation with the low-grade smartphone antenna (the main error source) and power saving option of the Android OS. Dabove and Di Pietra [12] have demonstrated the possibility to obtain decimetre-level accuracy in smartphone NRTK positioning by processing undifferenced and uncombined observations from a single frequency GNSS chipset. The requirement in this research was to apply differential corrections provided by a GNSS CORS network for a smartphone GNSS receiver in real-time.
On the other hand, the objective of the present work is to address the problem of RTK positioning using smartphones in situations where the differential corrections are not available for many reasons (e.g.; because there is no internet connection or there are no CORS networks). For geodetic surveying, this problem can be addressed using the traditional single-base master-rover configuration of two GNSS receivers: as described in references [13,19], generally one master station (indicated with subscript A in the Equations (1) and (2)) is settled on a known point that can broadcast pseudorange (PRC, Equation (1)) or carrier-phase corrections (CPC, Equation (2)) to a rover receiver through internet connection or radio modem, if pseudorange and carrier-phase measurements are considered, respectively.
In equations (1) and (2) ρ p A represents the geometric range, R p A (t) and φ p A (t) the pseudorange, and carrier-phase measurements, respectively, cdT k and cdt p are the biases related to receiver and satellite clocks multiplied by the speed of light, α i I p k is the ionospheric propagation delay with a known coefficient α i = f 2 1 / f 2 i that depends on the i-th frequency, T p k represents the tropospheric propagation delay, Mi p k and E p k the multipath and the ephemeris error, and finally λ i Ni p k the carrier-phase ambiguity multiplied by the wavelength, under the assumption that the random errors ε p k are not shown in these equations.
After these estimations, the master station can broadcast the PRC and CPC values to the rover receiver, (defined as B) which in turn can exploit them through Equations (3) and (4).
The subscript AB means that the bias is referred to the master-rover combination.
Considering both geodetic and mass-market GNSS receivers [20], if the distance between master and rover receivers is lower than 10 km, it is possible to affirm that the propagation of atmospheric delays and the ephemeris errors is almost the same in both places [21]. Thus, it is possible to eliminate them by differencing measurements of the two receivers: in the case of using carrier-phase measurements, it is possible to reach a centimetric level of accuracy if the phase ambiguity N p AB is estimated (or fixed) as an integer number [11,[22][23][24][25].
Starting from these considerations, the present work investigates two different situations of real-time positioning: firstly, it is interesting to verify the accuracy and precision of a smartphone device used as rover if a CORS is used as a master. Then, this master station is replaced with a smartphone receiver, while always considering a smartphone as the rover.

Test Setup
As discussed in the Introduction, one of the problems encountered using smartphone GNSS devices is to be able to know if the GNSS measurements are pre-filtered from the internal chipset. For this reason, a specific tool has been developed by the authors in order to get raw measurements directly from the device without any other pre-filtering operation. A dedicated code developed by the authors has been considered for processing all data collected in real-time, both from the master and rover receivers, in order to perform the single-base RTK positioning. As described in the previous section, two different receivers have been settled on a known point as a master station: the first one is a multi-frequency and multi-constellation GNSS receiver (TORI permanent station) that is part of the EUREF permanent network (www.epncb.oma.be/). The second one is a multi-frequency and multi-constellation smartphone device (Xiaomi Mi8). The main characteristics of these devices are summarized in Table 1. The rover device considered in these tests has the same characteristics of the smartphone used as the master station: in this case, the rover receiver (about 1 km far from the master station) has been settled on a known point in order to compare the estimated results with the reference coordinates. These reference results have been obtained using a geodetic GNSS receiver settled for 12 hours on the same point and post-processing. These observations followed a network adjustment computed with the Bernese GPS 5.0 software in the same reference frame of the master stations: ETRF2000(2008.0) [26,27]. The GNSS positioning has been performed considering different sessions with a length of about 10 min during November and December 2018, repeated in different days and hours (in order to make all results have independent atmospheric conditions and satellite geometry distributions), and with a sampling rate of 1 Hz. The entire conditions around the smartphones have been considered, paying attention to avoid multipath effects, electromagnetic disturbances, and building obstructions.

Experimental Results
In this section, the obtained results are discussed while considering the two tested configurations separately. Generally, for each epoch it was possible to track 8 GPS, 8 GLONASS, 6 Galileo, and 11 BeiDou satellites, respectively, as shown in Figure 2, obtaining a maximum GDOP value equal to 1.3. These values refer to the average of the different sessions. BeiDou satellites, respectively, as shown in Figure 2, obtaining a maximum GDOP value equal to 1.3. These values refer to the average of the different sessions. From a quality point of view of the signals, it is possible to note (Figures 3 and 4) that in some cases, the quality is not good, even if the cutoff angle has been chosen to be equal to 10°. This happens when the signal to noise ratio (SNR) value is less than 25 dB-Hz, defining the satellite signal being as too noisy to be processed. In this context, only satellites with an SNR value greater than 28 dB-Hz and with an elevation greater than 15° are considered. Applying these filters, the number of available satellites decreases to 21: 7 GPS, 4 GLONASS, 3 Galileo, and 7 BeiDou. From a quality point of view of the signals, it is possible to note (Figures 3 and 4) that in some cases, the quality is not good, even if the cutoff angle has been chosen to be equal to 10 • . This happens when the signal to noise ratio (SNR) value is less than 25 dB-Hz, defining the satellite signal being as too noisy to be processed. In this context, only satellites with an SNR value greater than 28 dB-Hz and with an elevation greater than 15 • are considered. Applying these filters, the number of available satellites decreases to 21: 7 GPS, 4 GLONASS, 3 Galileo, and 7 BeiDou.   According to Table 2 and considering only satellites that provides SNR values greater than 28 dB-Hz, it is possible to affirm that the noise of signals is still quite high, so the expected result could be noisy.   According to Table 2 and considering only satellites that provides SNR values greater than 28 dB-Hz, it is possible to affirm that the noise of signals is still quite high, so the expected result could be noisy. According to Table 2 and considering only satellites that provides SNR values greater than 28 dB-Hz, it is possible to affirm that the noise of signals is still quite high, so the expected result could be noisy. As previously written, two different scenarios have been considered (Table 3) whose results are reported separately. All data are processed considering a modified version of RTKLIB 2.4.3 [28], while only using the "continuous" method for the integer ambiguity resolution and a tight combination for multi-GNSS RTK positioning. As described in reference [12], "continuous" means that integer ambiguities are continuously estimated and resolved. Moreover, the "ratio test" for the standard integer ambiguity validation strategy has been considered. This factor, that can be considered also as a threshold, means the ratio of the squared sum of the residuals with the second best integer vector to the the best integer vector, as shown in (5). So, when the previous inequality (5) is satisfied, the ambiguities are defined as integer values, so it is possible to define that solution as "fix", otherwise as "float". As described in reference [12], a common value for the threshold is equal to 3, while it can be extended to 30 in order to guarantee a better and more feasible estimation.
Even if BeiDou satellites can be tracked by both receivers, the software used in these research activities is not able to process this constellation properly. Thus, we unfortunately are not able to provide results that also consider BeiDou satellites.

Case 1: Geodetic Master-Smartphone Rover
The first considered case is represented by a typical relative RTK positioning where the master station is composed by a geodetic multi-frequency and multi-constellation receiver (CORS station) settled on a well-known point and a rover device. This should represent the best possible solution for a relative positioning approach.
Considering only the L1 frequency, GPS constellation, and "continuous" method for the ambiguity resolution, the results are quite good in terms of float solutions, even if 15% of epochs are estimated with phase ambiguities declared as "FIX" (where FIX means that they are estimated as integer values) but in a wrong way, as shown in Figure 5. As detailed in reference [12], the goal is not to reach a "FIX" solution, but it is preferable to guarantee the continuity and the quality (in terms of precision and accuracy) of the solutions without fixing the phase ambiguities as integer values. For this reason, all data have been processed again using a threshold for the ratio-test equal to 30: this means if the ratio of the squared sum of the residuals with the second best integer vector to with the best integer one is greater than this threshold value, the phase ambiguities are declared as "FIXED", otherwise they are declared as "FLOAT".
ambiguities but the quality of carrier-phase measurements is too bad for reaching a good "FIX" solution, as described in reference [12]. Although it is quite common to set the ratio threshold to be equal to 3 [20], in this case the variability of carrier-phase measurements allows the software to reach the fixing of the phase ambiguities with 15% ( Figure 5) of epochs but in a wrong way. The RMS values in the second case are slightly better than in case of FIX+FLOAT solutions, even if these values are still around 0.2-0.4 m and 0.5 m for North, East, and up components, respectively.   As shown from Figure 6, the average values between estimated and reference coordinates are not substantially changed, even if there is a strong improvement in terms of the precision of solutions. As shown from Table 4 the standard deviation (std) values decrease from about 14 cm and 52 cm in the case of FIX+FLOAT solutions up to 0.2 cm and 0.5 cm in the FLOAT-only case, considering the 2D and Up components, respectively. This means that the software is trying to fix the phase ambiguities but the quality of carrier-phase measurements is too bad for reaching a good "FIX" solution, as described in reference [12]. Although it is quite common to set the ratio threshold to be equal to 3 [20], in this case the variability of carrier-phase measurements allows the software to reach the fixing of the phase ambiguities with 15% ( Figure 5)  As shown from Table 4 the standard deviation (std) values decrease from about 14 cm and 52 cm in the case of FIX+FLOAT solutions up to 0.2 cm and 0.5 cm in the FLOAT-only case, considering the 2D and Up components, respectively. This means that the software is trying to fix the phase ambiguities but the quality of carrier-phase measurements is too bad for reaching a good "FIX" solution, as described in reference [12]. Although it is quite common to set the ratio threshold to be equal to 3 [20], in this case the variability of carrier-phase measurements allows the software to reach the fixing of the phase ambiguities with 15% ( Figure 5)      If the second frequency (L5) is considered, the results are definitely better: the percentage of FIX solutions decreases by up to 0.6% ( Figure 6) and an improvement in terms of precision and accuracy is observed. As shown in Table 5, the use of L5 frequency allows the increasing of the precision (std) with an order of magnitude, going from about 14 cm and 30 cm for planimetry and up components in case of L1-only solution up to 1.5 cm and 3.8 cm in case of L1+L5 approach. These results can be still improved if the threshold value of the ratio-test is increased up to 30 (Figure 7): Table 6 shows that the std values are closed to 0.1 cm and 0.4 cm for planimetry and up components in the case of FLOAT-only solutions, while they are about 1.5 cm and 3.8 cm in the case of the FIX+FLOAT approach. Also RMS values are decreased, even if the difference is not so high: in this case the main improvement is for the up component, where the RMS value is decreased by about 12 cm, from 59.6 cm to 47.6 cm.  If the second frequency (L5) is considered, the results are definitely better: the percentage of FIX solutions decreases by up to 0.6% ( Figure 6) and an improvement in terms of precision and accuracy is observed. As shown in Table 5, the use of L5 frequency allows the increasing of the precision (std) with an order of magnitude, going from about 14 cm and 30 cm for planimetry and up components in case of L1-only solution up to 1.5 cm and 3.8 cm in case of L1+L5 approach. These results can be still improved if the threshold value of the ratio-test is increased up to 30 ( Figure 7): Table 6 shows that the std values are closed to 0.1 cm and 0.4 cm for planimetry and up components in the case of FLOAT-only solutions, while they are about 1.5 cm and 3.8 cm in the case of the FIX+FLOAT approach. Also RMS values are decreased, even if the difference is not so high: in this case the main improvement is for the up component, where the RMS value is decreased by about 12 cm, from 59.6 cm to 47.6 cm.    The previous results, shown in Tables 3 and 4.; are representative of those obtained in many other sessions that are not presented in this paper: thus, both mean and standard deviation values can be considered as reference values for this positioning technique, using these sensors.

Case 2: Smartphone Master-Smartphone Rover
In this second case, the relative positioning is performed considering one smartphone as master device and another smartphone as rover. This represents an innovative approach where both the master and rover are mobile devices: this is a preliminary step towards cooperative positioning using GNSS signals extracted by smartphones. As was previously written, all data have been collected simultaneously with the geodetic receiver, in order to compare results considering the same satellites (signal quality and geometry distribution) and atmospheric conditions. Moreover, based on previous results, only FLOAT solutions have been analyzed. The obtained results are very promising, which are reported in Tables 7-10. Considering the L1+L5 frequencies of GPS constellation, it is possible to observe 2D positioning accuracy at less than 1 meter and accuracy of the Up component at less than 2 meters (Figure 8). Moreover, although the accuracy is not increased with respect to the single frequency solution, the standard deviations decrease to about 1 cm. Also, the RMS values are decreased, with a high improvement especially for the north and up components (from 1.147 m and 1.386 m up to 0.230 m and 0.463 m, respectively). In this second case, the relative positioning is performed considering one smartphone as master device and another smartphone as rover. This represents an innovative approach where both the master and rover are mobile devices: this is a preliminary step towards cooperative positioning using GNSS signals extracted by smartphones. As was previously written, all data have been collected simultaneously with the geodetic receiver, in order to compare results considering the same satellites (signal quality and geometry distribution) and atmospheric conditions. Moreover, based on previous results, only FLOAT solutions have been analyzed. The obtained results are very promising, which are reported in Tables 7-10. Considering the L1+L5 frequencies of GPS constellation, it is possible to observe 2D positioning accuracy at less than 1 meter and accuracy of the Up component at less than 2 meters (Figure 8). Moreover, although the accuracy is not increased with respect to the single frequency solution, the standard deviations decrease to about 1 cm. Also, the RMS values are decreased, with a high improvement especially for the north and up components (from 1.147 m and 1.386 m up to 0.230 m and 0.463 m, respectively).   When GLONASS measurements are also considered, a slightly different behaviour is observed. Although the positioning solution is similar to the GPS-only, both the accuracy and the precision decrease when dual-constellation measurements are considered (Figure 9). This means that GLONASS measurements introduce some noise in the positioning estimation. Also, RMS values are slightly worse, even if no substantial differences can be observed with respect to the previous case.    The test has continued introducing Galileo constellation which presents, for the GPS-only case, a better dual-frequency solution. In this case, the positioning estimation benefits from the new measurements (Table 8 and Figure 10). This behaviour is confirmed in the last test, where GLONASS measurements have been removed and the GPS+Galileo solution has been considered ( Figure 11). For 2D positioning, less than 5 cm accuracy is achieved with a standard deviation of 1 cm. Observing the Up component, the best accuracy is obtained when all constellations are considered with the single frequency L1 (about 16 cm). Also RMS values are improved, especially for the planimetric components (    Figure 11. Comparison between L1 and L1+L5 solutions considering GPS+Galileo constellations and ratio =30.
All previous results are comparable with those obtained in many other sessions that are not presented in this paper. Thus, they can be considered independent by the sessions.

Conclusions
The precise positioning using mobile devices is still currently a challenge. The goal of cm-level accuracy in real-time has not yet been reached, mainly due to the quality of GNSS raw measurements obtained from smartphones. As discussed in previous studies, this is not the final purpose of the All previous results are comparable with those obtained in many other sessions that are not presented in this paper. Thus, they can be considered independent by the sessions.

Conclusions
The precise positioning using mobile devices is still currently a challenge. The goal of cm-level accuracy in real-time has not yet been reached, mainly due to the quality of GNSS raw measurements obtained from smartphones. As discussed in previous studies, this is not the final purpose of the employment of these devices, especially because there are some unclear aspects, such as the difficulty of determining the exact position of the smartphone GNSS antenna. Even if the position of the GNSS chipset is known in most of the manufacturer schemas, the antenna position is usually not highlighted. So, the idea is to focus the attention on the precision of the solution, in order to guarantee high reliability of the obtained results.
From this study, it is confirmed that it is possible to reach a cm-level of precision if an RTK single-baseline positioning approach is considered, even if the master device is a smartphone too. Firstly, a typical RTK positioning using a geodetic receiver as master and a smartphone as rover is considered: this has represented the "best" possible scenario where a smartphone device can work in real-time, under the assumption that a CORS network is not available. In this case, this work has demonstrated once again that it is not useful to reach a fixed solution using smartphone devices, because both the quality of GNSS signals and the software available today for real-time positioning are not able to fix the phase ambiguities in the right way. Considering the FLOAT-only solutions, it is possible to reach a precision of about few mm both in the case of single-or multi-frequency solutions.
The exploitation of multi-constellation GNSS chipsets allows us to obtain better precision with respect to the GPS-only results, especially in when considering the smartphone-smartphone baseline: the best results can be obtained when considering the GPS+Galileo constellations, with a precision of about 2 cm both for 2D and Up components in the case of L1+L5 frequencies, or 3 cm for 2D components and 2 cm for the Up component in the case of an L1 frequency. When the GLONASS constellation is also added, the results are worse. In case of the employment of the only L1 frequency, the precision is about 13 cm for 2D components and 80 cm for the Up, while when adding the L5 frequency there is an improvement only for this last component, reaching a precision of about 50 cm. The accuracies are not bad too, allowing the achievement of a sub-meter solution for 2D components in all cases and a level of accuracy of about 1 m for the Up component.
In conclusion, it is possible to affirm that these results are very promising for cooperative positioning using smartphone devices in outdoor environments. Funding: This research received no external funding but it is part of the research activities made at the PIC4SeR Interdepartmental Centre of Politecnico di Torino (Italy).