Estimation of tropospheric parameters with GNSS smartphones in a differential approach

With the introduction of the operating system Android 7 Nougat in the year 2016, it became possible to access Global Navigation Satellite System (GNSS) code and carrier phase observations. These observations can be processed with the state-of-the-art GNSS processing software packages, which allows an in-depth evaluation of the smartphone’s GNSS performance. The availability of carrier phase observations enables sub-decimeter-level positioning. A few years ago, smartphones wearing dual-frequency GNSS chipsets hit the mass market. In this study, we investigate the capability of such a device for the estimation of tropospheric delays. Static measurements carried out over the period of two weeks are performed using a Google Pixel 4 XL smartphone. The measurements are processed using relative positioning methods with a baseline length of about 33 kilometers, where a continuously operating reference station (CORS) acts as a base. The estimated differential zenith tropospheric wet delay (dZWD), obtained for the smartphone are then combined with absolute values computed at the reference station, in order to obtain time series of Zenith Total Delay (ZTD). Using this method, we demonstrate that high-precision ZTDs can be successfully determined from smartphone GNSS observations. When comparing the estimated tropospheric delays with those determined at a nearby geodetic receiver to assess the accuracy of the acquired time series of ZTD, differences in the range of few millimeters to a centimeter are visible. We examine the impact of various error sources, such as antenna phase center variations and residual effects of the ionosphere. Given that the obtained accuracies are at the level of a centimeter and below, the suggested method shows the potential to resolve small-scale tropospheric structures in near real-time


Introduction
The majority of the GNSS receivers used are embedded in smartphones (Paziewski 2020, EUSPA EO and GNSS market report 2022). Under favorable conditions, a positioning accuracy of few meters can be achieved (e.g. Van Diggelen 2016, Specht et al 2019) using pseudorange absolute positioning methods (i.e. single point positioning (SPP), e.g. Hofmann-Wellenhof et al 2008). Up to 2016, Android smartphones could only provide the calculated positions, thus it was also not possible to access or process the collected measurements using post-processing software packages (e.g. Zangenehnejad and . With the introduction of Android 7 Nougat in 2016, it became possible to access the GNSS raw measurements (Malkos 2016). For the first time, this allowed developers to investigate both carrier phase and code measurements, as well as decoded navigation messages. Advanced GNSS processing strategies could now be implemented, which improved the GNSS performance (European GNSS Agency 2017). The introduction of filtering methods (e.g. Hatch filters, Shin et al 2017) or C/N0-based weighting methods (e.g. Banville et al 2019 led to further improvements in positioning accuracy. However, for highest demands carrier phase observations and ambiguity fixing are still the key factors to achieve centimeter-level positioning accuracy with GNSS (Teunissen and Verhagen 2009). In view of highprecision applications, it is worth mentioning that the GNSS measurements from smartphones are not directly accessible in a format that can be read by standard geodetic GNSS postprocessing software. To address this issue, several apps have been developed that allow recording the raw GNSS measurements using the Receiver Independent Exchange (RINEX) format (Gurtner and Estey 2007), for example the Geo++ RINEX Logger or the Camaliot app 5 .
Until 2018, smartphones were only equipped with singlefrequency GNSS receivers. Since then, low-cost GNSS chips with multi-GNSS functionality became more and more interesting for mass-market applications (Robustelli et al 2019). In the year 2018, Xiaomi launched the Mi 8 model, which was the first dual-frequency GNSS smartphone on the mass market. It wears the Broadcom BCM47755 chip, which allows collection of dual-frequency GPS (L1, L5) and Galileo (E1, E5a) measurements, see (GPS World Staff 2018). The frequency bands L5/E5a are expected to have little or no signal interference because they fall into a protected aeronautical navigation band (Parkinson et al 2020). Since the launch of the Xiaomi Mi 8, an increasing number of dual-frequency GNSS smartphones became available-at the beginning of the year 5 https://camaliot.org/. 2020, there were already 41 smartphones from 10 manufacturers available, which were equipped with dual-frequency GNSS chipsets (European GNSS Agency 2020).
In recent years, many studies have been conducted with the aim to process carrier phase observations from these dualfrequency GNSS smartphones using high-precision positioning methods. An overview on the current state and perspectives of GNSS smartphone positioning, including high-precision positioning applications, was given by (Paziewski 2020) and (Zangenehnejad and Gao 2021). For a short baseline, (Dabove and Di Pietra 2019) performed single-baseline real time kinematic (RTK) positioning with a Xiaomi Mi 8 smartphone. Both a geodetic receiver and a smartphone were used as a base station. While considering float ambiguity solutions, the attainable precision for the smartphone positions was at the cm-level, and 3D accuracies were on the sub-meter level. For short-and medium-length baselines (up to 20 km), (Netthonglang et al 2019) showed for the Xiaomi Mi 8 that integer ambiguity fixing is feasible, and a position accuracy on the cm-level was obtained. Furthermore, it was demonstrated that the antenna phase center (PC) corrections are at the level of few cm as well. Using various smartphones, (Paziewski et al 2021) achieved cm-level accuracy for positioning on short baselines, but also reported drifts in many carrier phase observables. Magalhães et al (2021) investigated the positioning performance of the Xiaomi Mi 8 for relative positioning on medium-length to long baselines. They confirmed that ambiguity resolution is feasible for baselines with lengths up to several tens of kilometers, and the authors reported that it is possible to obtain an RMSE of less than 30 cm for baselines longer than 100 km. Elmezayen and El-Rabbany (2019) used precise point positioning (PPP) to process the measurements from Xiaomi Mi 8. They achieved decimeter-level positioning accuracy in the static and meterlevel positioning accuracy in the kinematic mode under postprocessed and real-time conditions. Other authors reported similar accuracies (Chen et al 2019, Aggrey et al 2020. Using external antennas, Wen et al 2020, and recently  also showed that PPP with integer ambiguity resolution is feasible for smartphones. However, the combination of a poor observation quality resulting mainly from the inbuilt smartphone GNSS antennas-together with a lower number of GNSS observations in the L5/E5 frequency bandhinders the achievement of centimeter-level smartphone PPP performance, where it is necessary to form the ionospherefree linear combination (Hofmann-Wellenhof et al 2008). This widely confirms the expectations that due to the higher frequency, the data quality of smartphone L1 carrier phase observations are superior to those of the L5/E5 band. In addition, it was found by Wanninger and Hesselbarth (2020), Paziewski et al (2021), Li et al (2022) or Gao et al (2021) that for certain devices and observables the integer property of carrier phase measurements is lost. Therefore, PPP could not yet reach the quality of baseline processing, where an ionospheric linear combination must not necessarily be formed (unlike as for conventional PPP processing). It was also observed that smartphone GNSS performance depends on the attitude of the phone. Li et al (2022) reported that for a number of investigated phones, the best results were obtained when the phone was in an upward position, rather than when placed horizontally. Despite the recent developments, the linearly-polarized GNSS antennas are still a limiting factor in smartphone positioning performance (Siddakatte et al 2017). Thus, in the case of strong multipath or other interferences, the positioning accuracy could decrease to tens of meters for code-based SPP (e.g. Robustelli et al 2019, Zangenehnejad and Gao 2021), as example.
For high-precision GNSS smartphone applications, Netthonglang et al (2019) and other authors highlighted the added value of antenna PC corrections for improving ambiguity resolution success rates. Wanninger and Heßelbarth (2020) estimated phase center offsets (PCOs) and phase center variations (PCVs) and reported PVCs at the level of 1-2 cm for the Huawei P30 smartphone. With the PC corrections introduced into the processing, they could fix significantly more ambiguities for GPS L1 observations. However, for the L5 band the calibration could not be performed yet due to problems with the ambiguity fixing. For a Huawei Mate 20 X, Darugna et al (2021) showed that the L1 PCV pattern can reach up to 2 cm, with values higher by a factor two to three for the L5 frequency band. From GNSS-derived zenith wet delays (ZWDs), observations of atmopheric water vapor can be derived (e.g. Langley et al 2017), which can then be used for the assimilation in numerical weather prediction algorithms (e.g. Yu et al 2017;Jones et al 2020). Typically, geodetic GNSS receivers are used for the retrieval of high-precision ZWDs. These receivers provide high-quality measurements, but are relatively expensive. However, lowcost GNSS receivers can be also employed for the retrieval of either ZWDs or vertical total electron content (VTEC), including also single-frequency devices (Zhang et al 2018, Zhao et al 2019. Recent efforts include also utilization of smartphone data for extraction of VTEC from the geometryfree linear combination of carrier phase observations (Bruno et al 2021, Navarro et al 2021, Xu et al 2022. In addition, estimating tropospheric parameters from GNSS receivers in smartphones could offer a cost-effective way to densify existing GNSS permanent networks, since these devices are in use in large quantities worldwide. An initial assessment of the estimated zenith total delay (ZTD) from smart devices was performed by Tagliaferro et al (2019). In their study, the authors used an HTC Nexus 9 tablet and a Xiaomi Mi 8 smartphone to collect raw GNSS measurements in a static setup. From the Mi 8, the ZTD was estimated from both the single-and dual-frequency measurements. To correct the ionospheric delay for the single-frequency measurements the satellite-specific epoch-differenced ionospheric delay method was applied (Deng et al 2009). As a result, the ZTD determined with the single-frequency measurements of the Mi 8 showed a better agreement with the ZTD time series from a nearby Continuously Operating Reference Station (CORS) than that from the dual-frequency measurements. Benvenuto et al (2021) also performed an analysis of the ZTD estimated from GNSS measurements of a Xiaomi Mi 8 smartphone. The processing of the data was performed using the online application CSRS-PPP (Tétreault et al 2005) and a modified version of the open-source software RTKLIB (Everett 2021). From the analysis it becomes clear that the processing strategy plays a crucial role in the analysis of smartphone data. ZTD differences up to 20 cm are possible, especially when applying standard settings to GNSS data of lower data quality. Thus, Marques et al (2020) suggests a slightly different method to estimate the tropospheric water vapor from dense GNSS networks, based on a feed-forward implementation of PPP and GNSS tomography. To test the developed method, a simulator testbed was created, which allowed for performing different experiments in a controlled environment. In a follow-up study, Lehtola et al (2022) developed a method to improve the simultaneous convergence of slant wet delay and positioning estimates and evaluated it using simulated observations from the same smartphone network.
Based on the existing literature, a first insight into the quality of ZTDs derived from smartphone GNSS measurements can be obtained. The existing studies cover periods from a few hours up to one day, maximum. However, for meteorological applications the long-term stability of the solution is as crucial as the short-term quality. Thus, in this study the possibility to determine high-precision troposphere parameters from smartphone-derived GNSS measurements over longer time spans is investigated. For this purpose, we collected static measurements over a period of two weeks. For data collection, a Pixel 4 XL smartphone from Google equipped with a dualfrequency GNSS chip was used. No modifications were made to the smartphone. A freely available app was installed for data recording. For the GNSS data processing we used the RTKLIB demo5 b34c version (Everett 2021), with a specifically tailored setting for the processing of data acquired from smartphone GNSS receivers. Based on the works of the authors reported above we have chosen a relative positioning configuration, with a baseline length of about 33 km. From the smartphone GNSS measurements, the differential troposphere parameters were determined using a static relative positioning method, where a geodetic GNSS receiver of a CORS network acts as the base. We computed a L1-only and a L1 + L5 solution, considering observations from GPS and Galileo. The estimated tropospheric differential zenith wet delay (dZWD) was then added to the absolute troposphere estimates obtained at the CORS, in order to calculate the absolute ZTD at the smartphone location. In order to assess the quality of the results, we compared the obtained ZTD with the ZTD computed for another CORS station not involved in the processing but located only few meters away from the smartphone. In this contribution, we analyze also the impact of other error sources on the ZTD determination, i.e. missing antenna PC calibrations, poor quality of carrier phase observations in the L5 frequency band, as well as prospective residual errors stemming from the ionosphere. This paper is organized as follows: The sections 'Data' and 'Methods' explain how the measurements were collected and outline the software and products used for the processing of the collected data. The 'Results and Discussion' section highlights and discusses the most important results of the experiment and discusses potential error sources. Finally, in the last section, some important conclusions are drawn, and a short outlook is given.

Smartphone GNSS measurements
For the experiments conducted in this project, the Pixel 4 XL smartphone from Google was used. This device is equipped with the Qualcomm Snapdragon 855 mobile platform that supports GNSS measurements of the systems GPS, GLONASS, Galileo, and BeiDou. For both GPS and Galileo, it is possible to perform measurements on the two carrier frequencies L1, L5, and E1, E5a, respectively. In contrast, only singlefrequency measurements on L1/B1 are possible for the systems GLONASS and BeiDou. On the smartphone used in this project, the operating system Android 11 was installed. Further technical information about the used device is provided in table 1.
GNSS measurements were carried out between 22 October and 4 November 2021, on the roof of the HPV building at ETH Campus Hönggerberg in Zurich, Switzerland. For this purpose, a special platform with a smartphone holder was designed that allows to keep a smartphone in an upward position and to protect it from bad weather conditions with a radome. The radome used has been manufactured by Leica Geosystems for the AR25 choke ring antenna. For the measurements, the smartphone platform was installed on a geodetic pillar (see figure 1). For simplicity, this station is called SMA1 in the following sections. The Google Pixel 4 XL smartphone was mounted under the radome in an upright position, and it was oriented so that the back of the phone was pointing to the north and the display to the south (figure 1). The GNSS measurements of the smartphone were recorded using the Geo++ RINEX logger app (version 2.1.6) (Geo++ GmbH 2021). With this app, it was possible to collect measurements of the four GNSS systems GPS, Galileo, GLONASS, and BeiDou. The data were acquired with a sampling rate of 1 Hz and for each hour a separate RINEX file was created. During the measurements, the so-called duty cycling was switched off. Duty cycling is designed to keep the power consumption of the GNSS hardware as low as possible. Therefore, the GNSS receiver is repeatedly turned on and off, usually recording data for 200 ms, followed by a period where the receiver is shut down for 800 ms. This process would have resulted in cycle slips because the receiver loses the lock to the GNSS signals due to interruptions in the measurements (Robustelli and Pugliano 2020).

CORS GNSS data
To perform the relative positioning of the smartphone w.r.t. the CORS, measurements from the Automated GNSS Network for Switzerland (AGNES) were utilized. This CORS network consists of 31 stations distributed throughout Switzerland (Brockmann et al 2002). For this project, GNSS measurements from AGNES station FRI3 are used as a reference for forming the baseline (base station). The sampling rate of this data is 1 Hz. In addition to the GNSS measurements, also the troposphere estimates for the CORS stations ETHZ and FRI3 were provided by the Swiss Federal Office of Topography (swisstopo). The ZTDs of the reference stations were estimated in post-processing in a network solution, with a temporal resolution of 1 h, using the Bernese GNSS Software v5.2 (Dach et al 2015), based on the ionosphere-free linear combination. In the processing, the Vienna Mapping Function 1 was used together with a troposphere gradient estimation in 24 h intervals according to the model of Chen and Herring (1997). Together with the data of approximately 200 other permanent GNSS stations over Europe, the parameters of the ANGES network were estimated using final CODE (Center for Orbit Determination in Europe) products and observations from GPS, GLONASS, Galileo and BeiDou . The cut-off elevation angle was set to 3 • . SMA1 was located on the same building as the CORS stations ETH2 and ETHZ. For the processing of the smartphone data, a baseline of approximately 33 km was formed between the CORS station FRI3 and SMA1. Figure 2 shows the location of the CORS ETH2, ETHZ and FRI3, as well as the location of the smartphone (station SMA1). All CORS considered here are operated with a Trimble NetR9 geodetic receiver; FRI3 and ETH2 are equipped with a Trimble choke ring antenna of type TRM59800.00 (no radome), and ETHZ uses a Trimble choke ring of type TRM29659.00 (no radome).

GNSS baseline processing
For the processing of the smartphone GNSS measurements, the open-source GNSS software RTKLIB demo5 b34c was used, which is a modified version of RTKLIB 2.4.3, developed at the Tokyo University of Marine Science and Technology (Takasu andYasuda 2009, Everett 2021). According to the developer, the demo5 version is optimized for the processing of measurements from low-cost GNSS receivers. Meanwhile, the developers provide a version that is specifically tailored for smartphone GNSS data processing (Everett et al 2022). The quantity of interest is the GNSS-derived tropospheric ZTD. It consists of the zenith hydrostatic delay (ZHD) and ZWD  (Hofmann-Wellenhof et al 2008). Since the used version of RTKLIB only outputs the estimated ZTD, the software was modified to output both the ZHD and ZWD as separate values. RTKLIB models the hydrostatic part of the ZTD-the ZHDby using the Saastamoinen model (Saastamoinen 1973). The input parameters of the Saastamoinen ZHD are atmospheric pressure, temperature and partial pressure of water vapor, which in turn depend on the geodetic height. The equations are to be found in the official RTKLIB manual (Takasu 2022) as well. By default, RTKLIB estimates the tropospheric delay at both ends of the baseline, i.e. at the rover and the base station (although SMA1 is static, we will call it 'rover' here). This corresponds to the parameterization that is applied in the 'Long baseline DD measurement model' described in the appendix of the RTKLIB manual (Takasu 2022). This is not an ideal configuration for this study since we are interested in deriving tropospheric parameters at the rover. Therefore, RTKLIB was further modified to estimate the dZWD between the rover and the base. For the processing with RTKLIB the multi-GNSS broadcast ephemeris files from CDDIS and the multi-GNSS rapid products from GeoForschungszentrum (GFZ) Potsdam were used. Additionally, we also computed a real-time solution using the broadcast information only. In RTKLIB the positioning mode 'static' was selected, which indicates that the software performs a carrier-phase-based static relative positioning, where the rover is not considered to move. Concerning the measurements, the GPS and Galileo systems were considered in the processing. For the SMA1-FRI3 baseline, two solutions were calculated: one considering the L1 + E1 observations (referred to as L1 solution) and one additionally considering L5 + E5a observations (referred to as L1 + L5 solution), respectively. For both configurations, an average of 14 satellites were used in the processing. We did not compute the ionosphere-free linear combination, since RTKLIB currently does not support ambiguity fixing for this processing mode. The elevation mask was set to 10 • , and we did not consider tropospheric horizontal gradients. The epoch-to-epoch ZWD variability was set to 0.1 mm (1-sigma process noise) and the measurement noise was set to 6 mm and 2 m (same as for the elevation-dependent terms) for the carrier phase and code, respectively. Ionospheric delays were corrected for by using the Klobuchar model. Table 2 summarizes the processing strategy for the single-and dual-frequency solutions.
We applied PCO + PCV corrections for FRI3. Starting with Android 11 (API Level 30), it is possible to read out the PCO and PCV corrections on selected smartphones using the GNSSAntennaInfo class (Google 2021b). However, no PC corrections were available for the Google Pixel 4 XL used in this project. Further configuration settings can be found in the RTKLIB configuration file in the supplementary material. In RTKLIB, the Earth-Centered Earth-Fixed (ECEF) coordinates (static) as well as the tropospheric parameters were estimated for each epoch in an Extended Kalman Filter (EKF). The float ambiguities were fixed after convergence using RTK-LIB's 'fix-and-hold' method (Takasu 2022).

Smartphone ZTD computation
Since the CORS tropospheric parameters were available on an hourly basis, it was necessary to determine an hourly value from the differential tropospheric ZWD (dZWD) estimates from the smartphone data. For this purpose, an hourly median was computed for each full hour. Furthermore, by using this smoothing method, the noise of the estimates, which is still at the level of few centimeters, was reduced as well. Then the absolute ZTD values at the smartphone rover SMA1 were calculated using the estimated troposphere parameters from the relative positioning, along with the parameters determined at the FRI3 CORS (base) as with: ZTD Rover Absolute ZTD at the rover (target parameter) ZTD Ref_Base Absolute ZTD at the base (obtained from CORS solution) Figure 3. Different quantities used for the calculation of the absolute ZTD at the rover station. The dZWD was determined between the smartphone (SMA1) and the base (CORS FRI3), and the ZHD at FRI3 and SMA1 were computed by using the Saastamoinen model. Having the estimated ZTD at the base available, the ZTD at the rover can be computed by means of equation (1).
dZWD Rover_Base Differential ZWD between rover and base (estimated) ZHD Rover ZHD at the rover (computed with Saastamoinen) ZHD Base ZHD at the base (computed with Saastamoinen) The dZWD Rover_Base was estimated in the relative positioning mode after introducing the a priori hydrostatic delays (ZHD Rover and ZHD Base ). These were computed using the Saastamoinen model. Thereby we approximated the geodetic height by the ellipsoidal heights of the stations. Figure 3 illustrates the different quantities which are used to calculate the absolute ZTD at the rover. We only considered the epochs for which the estimated tropospheric delay from RTKLIB could be obtained with fixed integer ambiguities, since we observed that the SMA1 troposphere float solution can contain spurious signals, which affect the results. In case the ambiguities could not be fixed, the ZTD was kept constant until the ambiguities could be fixed again. This method was preferred over an interpolation because it can also be implemented in realtime. To make the ZTD at station SMA1 comparable to the ZTD at the nearby AGNES station ETHZ, a height correction of −0.3 mm per 1 m height difference was applied (following Saastamoinen), which yields a value of about one millimeter for a height difference of 3 m.

ZTD retrieval
The obtained absolute ZTD at the smartphone SMA1 is compared with the reference ZTD at the nearby AGNES station ETHZ. The period under consideration ranges from 22 October to 4 November 2021. Figure 4 shows a comparison between the calculated ZTD for SMA1, computed by means of equation (1), and the reference ZTD of the CORS station ETHZ (see also figure 2). As explained in the last section, the values at station SMA1 were determined by forming a baseline between FRI3 and SMA1. This baseline has a length of 32.9 km, and the height difference is 134.9 m. Plot (a) of figure 4 shows the results for the L1 solution, plot (b) shows the results for the L1 + L5 solution. From plot (a) it can be seen that the calculated ZTD based on single-frequency measurements shows in many parts a very good agreement w.r.t. the reference values calculated for ETHZ. Even very small variations in the ZTD (related to changes in ZWD)-at a magnitude of few centimeters-can be resolved (e.g. 22 October, 26 October, 30 October, 3 November). On other days, e.g. 24 October or 31 October, the variations are a bit higher, but still at the level of few centimeters only. For the L1 + L5 case there is a reasonable agreement as well. However, the estimates are somewhat noisier and biases w.r.t. both the singlefrequency case and the ETHZ reference values are visible. Possible explanations for these effects are uncorrected PCOs and PCVs of the smartphone. Although for a different device, Darugna et al (2021) reported significantly higher PCVs for the L5 band than for the L1 band. Together with a significantly higher carrier phase observation noise level, missing PCVs are supposed to be a main limiting factor for the ambiguity-fixing success rate for L5/E5a (see section 4.3). Figure 5 shows the estimated dZWD for the single-frequency (plot (a)) and the dual-frequency case (plot (b)). It can be noticed that the noise level of the dual-frequency solution is higher, and there are more outliers visible as well (e.g. 1 November to 3 November). As described in section 3, we used a median filter to down-sample the SMA1 dZWDs from 1 s to 1 h resolution ( figure 4). This also has the positive effect that noise originating from the poorer quality of the smartphone GNSS observations is effectively suppressed. This comes at the cost of a lower time resolution. However, for assimilation of GNSS tropospheric delays into numerical weather prediction models for short-range forecasting (Offiler 2010), this temporal resolution is still appropriate. Figure A1 and A2 in the appendix compare the case of the unfiltered dZWD estimates to the case of the median-filtered values. Each figure shows the singlefrequency (plot (a)) and the dual-frequency estimates (plot (b)). Beside the smoothing effects of the hourly median, it can be clearly seen that the filtered L1 solution is also less noisy than the L1 + L5 solution. Especially for the latter it can also be noticed that for phases with float ambiguities (indicated by the flat curves, i.e. 1 November to 3 November) the effect of the poorer quality of the carrier phase observations on L5 has an adverse effect on the quality of the estimated dZWD. We will discuss this in detail in section 4.3.
Additionally, figure 6 shows the L1 solution for the ZTD using broadcast data only for the GNSS processing. Only minor differences w.r.t. the baseline solution shown in figure 4 can be observed (e.g. 22 October, 1 November). In general, both solutions show a high agreement, as it can be expected for short and medium-length baselines.

Quality assessment of the retrieved ZTDs
The blue curves in figure 7 show the differences in ZTD between smartphone SMA1 and CORS station ETHZ of figure 4, for both the single-frequency (plot (a)) and the dual-frequency case (plot (b)). The smartphone estimates are biased by approx. 3-4 mm for the L1 solution, and by approx.  12 mm for the L1 + L5 solution. In addition, for SMA1, we also computed a very-short-baseline solution to CORS ETH2 (approx. 20 m), which is shown by the red curve. Because of the noisier L5 carrier phase observations, the dual-frequency solution shows a higher RMS. The bias of −12 mm in the L1 + L5 solution can be explained by the missing PCV corrections for the Pixel smartphone. Naturally, the very-short baseline solution (red) shows less noise than the mediumlength baseline, but in terms of bias, the solutions behave similar. Overall, the results for the dZWD derived for the single-frequency case show an agreement of better than one centimeter, even over this time span of two weeks, and thus fulfill the demands for high-precision GNSS-derived troposphere products (e.g. for the assimilation into numerical weather models or the computation of integrated water vapor products, see table 1 in Offiler 2010).
To investigate the smartphone and the geodetic solution shown in figure 4(a) in more detail, we analyze the differential ZTD (dZTD) for the SMA1 and the ETHZ solution (w.r.t. FRI3 for both cases). The results are presented in figure 8. Overall, there is a good agreement between the two dZTD time series. Many features that are visible in the reference data can also be found in the estimated values from the smartphone measurements. The mean difference between the two time series is 3 mm and the RMS of the difference is 8 mm. Many transient signals can be resolved, such as on 22 October, 28 October, or in the period from 1 November to 4 November. Overall, the smartphone tropospheric estimates closely follow the trends indicated by the geodetic estimates.
However, there are still unexplained artifacts, such as the transients on 24 October, 29 October and 31 October. The strategy to keep the dZWD fixed, once ambiguities are float, works reasonably well. Such periods can be seen on 30 October, or 1 November, for example. Additionally, figure 9 shows the differences between the ZTDs of station SMA1 and ETHZ for the L1 broadcast solution presented in figure 6. It can be    seen that the RMS of this solution is slightly higher. Besides this, it agrees well with the solution that utilizes the precise orbit products.
To determine how long it takes for the Kalman filter estimation to converge, the epoch-wise estimated ECEF coordinates were transformed into a local topocentric coordinate system. Figure 10 shows the North, East, and Up components of the first eight hours of data for the baseline SMA1-FRI3 using single-frequency measurements. It is visible that a precision of ±1 cm for the horizontal components is reached after approximately 30 min. For the vertical component, cm-level precision can be reached after around 1 h and 15 min.
It is also worth mentioning that an important difference between geodetic-grade GNSS hardware and GNSS hardware in smartphones is the type and the characteristics of the antennas. Geodetic-grade GNSS antennas are designed to provide high resistance against multipath together with a high PC stability. Typically, a choke ring is mounted around the sensitive antenna element to reduce the impact of reflected signals (Maqsood et al 2017). This type of antenna is rather heavy and costly to produce. GNSS antennas for mobile devices must be as light and cost-effective as possible. To achieve these goals, typically an inverted-F antenna is used. This antenna is omnidirectional and linearly polarized. It can receive direct line-of-sight signals, which are right-hand circularly polarized, and reflected signals, which are left-hand circularly polarized (Maqsood et al 2017). Consequently, these antennas have virtually no protection against multipath. A possible way to reduce the impact of reflected signals would be to add a ground plane under the smartphone. Tomaštík and Varga (2021), demonstrated that the use of a simple ground plane improves the accuracy of the determined positions and reduces the multipath effect by 60%-70%. In the future, such a ground plane could be added to the measurement setup to investigate the impact on the coordinates and the troposphere estimates.

Quality assessment of the GNSS processing
To further investigate the quality of the obtained results, we also analyzed the ambiguity resolution success rates for both the L1 solution and the L1 + L5 solution. The percentage of epochs with fixed ambiguities is shown in table 3. It can be seen that more than 90% of the epochs have fixed ambiguities when using L1 data only. These success rates are at the same level of what has been reported by Li et al (2022). If a dual-frequency solution is calculated the percentage of epochs with fixed ambiguities is close to 80%, which is a consequence of ambiguity fixing issues on L5, where only few ambiguities could be fixed. Typically, the inclusion of a second frequency simplifies the ambiguity fixing process, since wide lane and narrow lane linear combinations can be formed. However, in the suboptimal case considered here, L1 and L5 ambiguities are fixed separately. The inclusion of the L5 frequency in our case did not lead to further improvements, but had a negative impact on the results. When comparing the residuals of the pseudorange and carrier phase measurements on the frequencies L1 and L5, significant differences can be observed. Figure 11 shows the residuals for the frequencies L1 and L5 for 22 October 2021, which corresponds to the first day of measurement, for both GPS and Galileo. It can be seen that the pseudorange residuals on L5 are significantly smaller than on L1. This difference can be attributed to the fact that L5 has a higher chipping rate than L1 and thus allows a higher measurement accuracy (since it is less susceptible to multipath), when using pseudorange observations. Considering the quality of smartphone observations, the L1 carrier phase residuals also show reasonable values (at the level of a few cm), when compared to results presented in other studies (e.g. Paziewski et al 2021). On the other hand, the phase residuals are much larger on L5 than on L1. Since the receiver-internal tracking loops can only resolve a fraction of the carrier phase wavelength, L5 noise must be expected to be slightly higher than on L1 and due to the antenna design issues, the carrier-to-noise density of the L5 observations is significantly reduced. This can result in ambiguity fixing problems, and, as a consequence, in higher phase errors in the float solution, and the quality of the tropospheric estimates will suffer  as well. However, this alone does not explain the higher magnitude of L5 noise. Beside the noise aspects, missing PCV will also affect the ambiguity fixing success rate. For the Mate 20 X, Darugna et al (2021) reported that without antenna calibration, no reliable ambiguity fixing could be performed. For a Huawei P30, Wanninger and Heßelbarth (2020), could calibrate L1 PCVs only, since no reliable and complete ambiguity fixing could be obtained for the other signals. Similar to Netthonglang et al (2019), we also derived the PCs for the Pixel 4 XL in a veryshort baseline approach. For this, we defined the antenna reference point (ARP) to be at the top center of the phone. The details can be found in appendix Antenna phase calibration. The main results are shown in table 4. The obtained values are similar in magnitude to those obtained for the Xiaomi Mi 8, where the PC is located at the top-left corner of the phone, see Netthonglang et al (2019) and Zeng et al (2022). In the case of the Pixel 4 XL, the PC was determined to be in the top-right corner. However, we observe a large discrepancy of 2.5 cm, when analyzing the combined PC of the L1 + L5 solution w.r.t. the L1 PC solution. In addition, significantly larger patterns in the elevation-depended residuals of the L1 + L5 solution are observed. This can be related to the missing antenna phase calibrations (figures A4 and A5).
The satellite visibility of the GPS satellites at the stations SMA1 and ETH2 for the first measurement day (DOY 295) is shown in figure 12. It should be noted that these plots represent the raw GNSS measurements without adding an elevation mask. Figure 12(b) shows that many GPS satellites were tracked by the smartphone only on a single frequency. This can be explained by the fact that not all GPS satellites broadcast L5 signals. Currently, the L5 signal is only available on GPS Block IIF and Block III satellites. The first Block IIF satellite was launched in the year 2010 and the first Block III satellite in 2019 (Parkinson et al 2020). On 20 November 2021, there were 30 GPS satellites operational whereas 16 of them were broadcasting signals on the L5 frequency (National Coordination Office 2021).
When using relative positioning software that forms an ionosphere-free linear combination (not pursued in this study), the satellites that were only observed on one frequency are eliminated in the processing. This can then lead to a significant reduction in the number of GPS satellites, which can make the processing of the measurements challenging, especially in view of the quality of observations in the L5 band. According to the National Coordination Office (2020), by 2027 there will be 24 GPS satellites in orbit transmitting the signal on L5. Therefore, it will be possible to continuously observe an increasing number of GPS satellites on two frequencies when using the Google Pixel 4 XL smartphone in the next few years. Currently, there are fewer Galileo satellites in orbit, but all of them are broadcasting the E5a signal. Consequently, the smartphone could collect dual-frequency measurements from all Galileo satellites. When comparing the measurements of the smartphone with those of the geodetic receiver ( figure 12(a)), it is noticeable that there are significantly more cycle slips detected in the smartphone data. Especially the dual-frequency smartphone data is more affected (bottom plot, green bars), which can be attributed to the aforementioned poorer performance of the L5 signal tracking. An in-depth investigation of the cause for these frequently occurring cycle slips, as well as of the cause of the poorer L5 signal quality is outside of the scope of this study. However, interference effects caused by poorer smartphone GNSS antenna characteristics (e.g. polarization issues) could be a candidate for further investigations.

Impact of ionosphere on differential tropospheric estimates
The common approach in GNSS precise positioning is to utilize an ionosphere-free linear combination of dual-frequency observations carried out by a single receiver to remove the first-order ionospheric effects (up to 99.9% of the total effect). In the baseline approach, however, a similar effect can be achieved, when observations (either on L1 or L5) simultaneously taken by two receivers to the same satellite pair are combined (the double-difference approach). For relatively short baselines, the impact of ionospheric effects on the target parameters is marginal due to a rather smooth spatial behavior of the ionosphere at middle latitudes. The SMA1-FRI3 and ETHZ-FRI3 baselines (approx. 33 km) can be however considered as medium in terms of length and thus residual ionosphere effects may have a visible impact on the quality of the target parameters, i.e. station coordinates, dZWD estimates and the phase integer ambiguity resolution process. Additionally, this error might be significantly increased for pairs of receivers located at both high latitudes and close to the geomagnetic equator as well as during periods of high solar activity or during geomagnetic storms (Odijk 2001, Figure 13. Differential ZTD estimates (combined runs) between ETH2 and FRI3 stations acquired using the modified version of RTKLIB. Again, the solutions from swisstopo are used as a reference. Baseline-based solutions computed with (a) L1 measurements and (b) an ionosphere-free combination of measurements at L1 and L2. Park et al 2016, Sieradzki andPaziewski 2016). Therefore, for longer baselines, one needs to address this phenomenon with either corrections (Odijk 2000, Grejner-Brzezinska et al 2004 or solutions, where double-difference slant ionosphere delays are treated as yet another estimable parameter (Odolinski and Teunissen 2019).
The prospective impact of residual ionosphere effects on the accuracy of differential tropospheric estimates (for the SMA1-FRI3 baseline) was investigated for the ETH2-FRI3 baseline by comparing the differential ZTDs from the baseline solution on L1 (combined forward and backward filter runs) with equivalent estimates derived from the network solution for ETH2 and FRI3 as provided by swisstopo. In addition, the L1-only solution was complemented with the ionosphere-free baseline solution using observations carried out on L1 and L2. The results for the 14 days, corresponding to the period of the considered smartphone observations, are shown in figure 13. The dZTD time series derived from the L1/L2 ionosphere-free measurements are in a good agreement with the PPP-based solution, with an RMS of 0.2 cm. The difference between the L1 solution and L1/L2 solution is mainly caused by the residual ionosphere delays and the measurement noise, which can degrade the dZTD estimation. For the investigated period, the RMS differences between the dZTD estimates from the singlefrequency case (L1 solution) and reference solution reached 0.4 cm. Taking into account both the resulting RMS differences and potential disparities in dZTDs originating from the utilization of two different software packages in this comparison, the impact of ionosphere on the differential tropospheric estimates for the considered baseline and period can still be considered as small. Its magnitude is below the reported precision level of the smartphone-based ZTD estimates, as stated in section 4.1. For longer baselines and utilization of only a single frequency, residual ionospheric effects may need to be handled properly, however, so that they do not degrade the quality of the tropospheric estimates and impact negatively the ambiguity resolution process (ambiguity success rates). On the other hand, the prospective densification of the GNSS network with smartphones through the differential approach with baseline lengths of up to 10-15 km is not considered to be problematic in this regard as the ionosphere effects at mid-latitude regions for such baselines would be even smaller and could in principle be neglected for most of the time (Odijk 2000, Fermi et al 2019. Therefore, relative positioning strategies can be beneficial for single-frequency low-cost devices as the modeling of ionospheric effects or estimation of ionospheric parameters can be avoided in this case. The additional benefit of such an approach is that one does not rely here on the ionosphere-free linear combination of observations (carrier phase or pseudorange), which are characterized by a significantly amplified noise and multipath compared to original observations, i.e. by a factor of three w.r.t. observations carried out on L1. Therefore, local networks consisting of both high-grade and low-cost receivers may benefit from single-frequency relative solutions for meteorological applications (Fermi et al 2019).

Conclusion and outlook
This study investigated whether precise tropospheric parameters can be determined from the measurements of an GNSS smartphone. For this purpose, static measurements over a period of two weeks were performed continuously with a Google Pixel 4 XL. A modified version of the open-source software RTKLIB was used for the processing of the measurements in a L1 solution, as well in a combined L1 + L5 solution. Relative positioning over a medium-length baseline (33 km) was applied, where a CORS acted as base. The estimated differential tropospheric parameters (dZWD) obtained for the smartphone were then utilized to compute absolute ZTD values, using the troposphere estimates from the geodeticgrade base station. The tropospheric parameters obtained from the smartphone processing show a very good agreement with those obtained from a close-by geodetic CORS station. For the L1 solution, we report a bias of few millimeters, and an RMS value of less than a centimeter when the smartphonebased ZTDs are compared with the ZTD of a geodetic reference solution. The bias can mainly be attributed to missing antenna PC corrections of the smartphone, which was verified by a simple very-short-baseline calibration method. When considering a combined L1 + L5 solution, the observed bias increases to the level of 1 cm, which can be attributed to significantly higher antenna pattern corrections for the L5 frequency. For the smartphone under consideration, we also observed that noise on L5 carrier phase observations is higher by a factor 2-3 than noise on L1. These effects contribute to a poorer ambiguity success rate, as well as to a lower precision of the ZTD estimates of the L1 + L5 solution, compared to L1 only. We also showed that, for the experimental scenario under investigation, residual ionospheric effects are small, however, for processing with longer baselines or at different latitudes, accurate ionospheric corrections (or a linear combination) should be considered. For the estimated tropospheric parameters it could also be shown that a near real-time parameter retrieval (with a delay of up to one hour) can reach the same level of accuracy as in post-processing.
It has been shown that reliable, high-precision estimates of ZTDs can be obtained by processing single-frequency GNSS smartphone measurements. This is encouraging since currently only a few manufacturers provide Android smartphones that are equipped with dual-frequency GNSS chipsets. Concerning the quality of smartphone carrier phase observations, the findings presented here are in accordance with those presented in similar investigations, yet we observed very high noise on L5 observations. Future studies should address the calibration of antenna PC correction for the Pixel smartphones. This increase in L5 noise has to be further investigated, however, interference effects could play a role here (e.g. Garcia-Pena et al 2020). To the end, high L5 noise and remaining biases hinder centimeter-level PPP. From previous analysis with GNSS tropospheric estimates of comparable quality and assimilation of these parameters into weather nowcasting models, a clear improvement have been reported (e.g. Yu et al 2017;Jones et al 2020). Thus, the use of near real-time smartphone data in meteorological application is seen as a promising future application for dense networks of single-frequency/dual-frequency low-cost receivers, especially if exploited in conjunction with a network of dualfrequency reference stations. Furthermore, such data can help to detect severe weather events (Jones et al 2020). A crowdsourcing campaign in this direction is currently ongoing in the frame of the CAMALIOT project to collect large datasets of raw GNSS measurements from smartphones (Navarro et al 2021). In the future, such datasets will be crucial for algorithm development and to assess the potential of smartphone-based applications in densified GNSS networks under realistic scenarios.

Data availability statement
The data that support the findings of this study are available upon request from the authors. Figure A3. Location of antenna reference point (ARP) and approximate mean phase centers for the frequencies L1 (blue) and L1 + L5 (green).

Antenna phase calibration
To calculate the approximate PC for the Google Pixel 4 XL, an ARP had to be defined. In principle, the ARP can be chosen freely, but it should be located at a well-defined location on the device and accessible from outside of the antenna. The ARP was defined as the intersection between the longitudinal axis and the top edge of the device (figure A3). The coordinates of the mean PC were calculated with respect to this ARP, using relative positioning.
Measurements from a geodetic receiver, with a calibrated antenna installed on the pillar, were used for this purpose. As a base, the ETH2 station was selected, which allows forming a short baseline of approximately 24 m. Therefore, no tropospheric refraction had to be considered. The mean PCs were calculated from the smartphone measurements collected on DOY 295 and 296. During these measurements, the radome was installed on the smartphone holder. An elevation mask of 10 • was used in the processing of the measurements. Since it was not possible to calculate a L5-only solution with RTKLIB, a combined solution with L1 and L5 was computed instead. The approximate locations of the mean PCs for the L1 and L1 + L5 frequencies are shown in figure A3. Both mean PCs are located in the upper right half of the device. The horizontal offsets of the determined mean PCs are in the range of a few millimeters to two centimeters. It is noticeable that the mean PC of L1 + L5 is located about 2.5 cm below that of L1. We computed carrier phase residuals w.r.t. the mean PCs Figure A4. Phase residuals with respect to the mean L1 + L5 phase center. Residuals that exceed the limits are displayed in either dark red or dark blue, depending on the sign. of the dual-frequency solution (figure A4). The pattern shows a distinct east-west difference for L5 (bottom plot)-there is a tendency towards negative values in the east direction and positive values in the west direction. A similar pattern is also visible for L1 but with an opposite sign (top plot), presumably being affected by the L5 patterns. It is also evident that the L5 phase residuals show a larger variation than those of L1. Figure A5 shows the phase residuals for the mean L1 PC. The residuals are mostly smaller than those calculated with respect to the L1 + L5 PC. These calibration results indicate that (a) pattern variations on L1 are on the level of approximately 1-2 cm in magnitude, and (b) that the pattern variations for L5 are to be expected significantly larger than for the L1 case. Figure A5. Phase residuals on the frequency L1 with respect to the mean L1 phase center. Residuals that exceed the limits are displayed in either dark red or dark blue, depending on the sign.