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Automated Processing of Low-Cost GNSS Receiver Data

Simon Banville, Canadian Geodetic Survey, Natural Resources Canada (NRCan) Gérard Lachapelle, University of Calgary

Reza Ghoddousi-Fard, Canadian Geodetic Survey, Natural Resources Canada (NRCan) Paul Gratton, University of Calgary

BIOGRAPHIES

Simon Banville is a senior geodetic engineer for the Canadian Geodetic Survey (CGS) of NRCan, working on precise point positioning (PPP) using global navigation satellite systems (GNSS). He obtained his PhD degree in 2014 from the Department of Geodesy and Geomatics Engineering at the University of New Brunswick (UNB), Canada, under the supervision of Dr. Richard B. Langley. He is the recipient of the Institute of Navigation (ION) 2014 Parkinson Award.

Gérard Lachapelle is Professor Emeritus at the University of Calgary. He has been involved with GNSS since 1980 and has contributed to many facets of GNSS methods, algorithms and software. He was a professor in the Department of Geomatics Engineering from 1988 to his formal retirement in 2015. Prior to this, he and a group of engineers started a Calgary-based company to conduct GPS software and hardware R&D and develop related applications.

Dr. Reza Ghoddousi-Fard is a research scientist for the CGS of NRCan. He first joined NRCan as a post-doctoral fellow in early 2009 supported by both CGS and their Geomagnetic Laboratory. He obtained his Ph.D. from the Department of Geodesy and Geomatics Engineering at UNB. His main area of expertise is in atmospheric modelling using GNSS. He has also taught a number of geomatics courses as a university lecturer.

Paul Gratton graduated with a BSc in geomatics engineering from the University of Calgary in Spring 2019. He has been involved in PPP research on both low-cost and high-end GNSS receivers since 2018, resulting in co-authorship of several publications. He is still with the Department of Geomatics Engineering at the University of Calgary, pursuing a master’s degree.

ABSTRACT

The availability of raw observations from smartphones and tablets brings new challenges to GNSS data processing. Low-cost GNSS chipsets, combined with omnidirectional antennas, can lead to measurements highly contaminated by noise and multipath. Therefore, data quality depends not only on the device but also on the environment. Such a diversity is complex to handle for automated GNSS data processing services such as the NRCan precise point positioning (PPP) service. Processing strategies developed for geodetic receivers now require adaptations to be suitable for low-cost devices: 1) carrier-to-noise weighting should replace elevation-dependent weighting; 2) precise ionospheric corrections with meaningful quality indicators should be available; 3) the residual tropospheric zenith delay parameter should not be estimated in the PPP filter, which calls for more accurate a priori tropospheric models; and 4) quality control algorithms should rely on geometry-based rather than geometry-free approaches. With such modifications, static PPP solutions using data collected with a Huawei Mate 20X smartphone can converge to cm-level accuracies under favorable signal tracking conditions.

INTRODUCTION

Since 2003, the Canadian Geodetic Survey of Natural Resources Canada (NRCan) offers an online precise point positioning (PPP) service called CSRS-PPP [1]. Users collect GNSS data in the field, which they then submit to the service via a web interface or a desktop application. Depending on the user dynamics, the service computes either a static position or a trajectory and returns a processing report via email. In 2018, the CSRS-PPP service supported 6,605 active users having submitted approximately 568,000 datasets. While most users collect dual-frequency GNSS observations and target cm-level accuracy, low-cost GNSS receivers are an emerging trend that requires further considerations.

Proceedings of Institute of Navigation GNSS+2019 conference, Miami, 16-20 September 2019

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Since Google enabled raw GNSS data collection from smartphones in 2016, a plethora of research has been conducted to assess data quality of various devices [2, 3], evaluate their performance in multiple environments [4, 5], and improve positioning accuracy [6, 7]. While processing raw GNSS observations from smartphones is still at an experimental stage, it is expected that low-cost GNSS devices will soon gain in popularity for applications requiring decimetre- to metre-level accuracies. Newly launched dual-frequency GNSS chips for smartphones may further contribute to improving accuracy by tracking modernized signals [8] and offering a means to correct for ionospheric effects [9, 10]. Given that advances in processing strategies driving down accuracy could also open the door to new applications, NRCan is modernizing its CSRS-PPP service to better serve the needs of mass-market users. Automated processing of low-cost GNSS receiver data is subject to several challenges. First, data quality characterized by noise and multipath can vary substantially from one dataset to another, as opposed to the more predictable high-grade geodetic receivers. In addition, lower signal-to-noise ratio can impede carrier-phase tracking, potentially causing tracking interruptions known as cycle slips. Despite these limitations, NRCan has implemented many features related to low-cost receivers in its CSRS-PPP service, including handling of carrier-phase observations and related quality checks, automatic determination of code noise and multipath levels for obtaining more realistic precision estimates, and using an improved a priori tropospheric model. A summary of recent improvements related to single-frequency users is provided in Table 1. Table 1 Modifications to the CSRS-PPP service related to single-frequency users

Version Date introduced Modifications

2.11 2018-08-16 Use carrier-phase observations with quality control Estimate slant ionospheric delay parameters

2.21 2018-12-17 Quantify code noise and multipath for stochastic modelling Ingest VMF1 products for a priori tropospheric zenith delay 2.26 2019-02-27 Adjust RINEX reader quality checks for smartphone data

This paper describes strategies implemented or considered for implementation in the CSRS-PPP service for the processing of data from low-cost GNSS receivers. It should be kept in mind that these strategies are adopted to fit the majority of users and are not necessarily optimal for all users. The single-frequency PPP functional model currently implemented in CSRS-PPP is first described. Newly implemented or upcoming features related to stochastic modelling, as well as ionospheric and tropospheric effects are then presented, followed by a description of quality-control algorithms. Experimental results comparing processing strategies are presented and the paper concludes by summarizing our findings.

FUNCTIONAL MODEL The GNSS functional model for carrier-phase (𝐿) and code (𝐶) observations currently used by CSRS-PPP for low-cost GNSS receivers can be expressed as: 𝐿#$,&' = 𝐿$,&

' − 𝜌+,$' + 𝑑𝑡' − 𝑇' + 𝐼+

' + 𝑏$,&' (1a)

= 𝒆' ⋅ Δ𝒙 + 𝑑𝑇 − 𝜇$ ⋅ Δ𝐼' + 𝜆$9𝑁$' + 𝑏$,&; (1b)

𝐶

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𝐿#$,&' = 𝒆' ⋅ Δ𝒙 + 𝑑𝑇???? − 𝜇$ ⋅ Δ𝐼' + 𝜆$𝑁@$

' (3) 𝐶

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Figure 1: Set up used in the stochastic modelling investigations

Figure 2 shows GPS C1C code residuals from PPP solutions computed in static mode. Residuals from the Huawei smartphone show the largest noise as expected given the use of an inverted-F antenna. Due mainly to multipath, the correlation with elevation angle seems inexistent but a negative correlation is observed with the C/N0 values. The u-blox receiver was connected to a patch antenna and its location on the ground eliminated reflected signals from below, thereby greatly mitigating multipath effects. As a consequence, the correlation between code residuals and elevation angle significantly increased, and both elevation and C/N0 characterize residual noise similarly. Note that the u-blox receiver output C/N0 values rounded to the nearest integer.

a) Huawei Mate 20X b) u-blox M8P

Figure 2: GPS C1C code residuals as a function of elevation angle and carrier-to-noise ratio (C/N0) for a) a Huawei

Mate 20X smartphone; b) a u-blox M8P Two observations can be made from the above analysis. First, the antenna certainly plays a critical role in data quality, but so does the environment, antenna design and location, GNSS chip design, etc. Since these factors are unknown in an online positioning service, scaling of the a priori standard deviation at zenith has been implemented in CSRS-PPP starting with version 2.21. A first processing run is used to assess the mean code noise level for each signal from PPP residuals, i.e. a customized value for 𝜎+, and this value is then used to define the elevation-dependent stochastic model using (5) for the second run. As a result, reported standard deviations should be more representative of data quality. The second observation is that C/N0 is indeed a better indicator of observation quality than elevation angle because multipath is dominant and affects C/N0 values. To verify the impact of observation stochastic modelling on positioning, we first look at epoch-by-epoch GPS+GLONASS code-only solutions, i.e., solutions computed independently from one epoch to another. To

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better isolate the contribution of code noise, precise slant ionospheric delays are derived from the Leica GS16 receiver. Figure 3 compares the RMS errors of the latitude, longitude and height components over the full dataset for three stochastic models:

1. Default: elevation-dependent weighting model of (5) using 𝜎+ = 3𝑚 for both GPS and GLONASS 2. Scaled: elevation-dependent weighting model of (5) with signal-specific values of 𝜎+ derived from the residuals 3. C/N0: C/N0 weighting model of (6) with signal-specific a and b coefficients derived from the residuals

a) Huawei Mate 20X b) u-blox M8P

Figure 3: RMS errors of epoch-by-epoch GPS+GLONASS code-only solutions with different stochastic models

Figure 3 reveals that the stochastic model can play a critical role for low-cost GNSS devices. The Mate 20X smartphone provided very noisy GLONASS observations (see also Figure 12) and, since the default model assigns the same weight to GPS and GLONASS code observables, the solution is negatively impacted by GLONASS data. When the observation standard deviations are scaled appropriately for each system, the solution improves significantly and provides results almost identical to a GPS-only solution (not shown here). Weighting observations using C/N0 values provided further improvements, with position errors reduced by over 50% compared to the default settings. For the u-blox receiver, the disparity between GPS and GLONASS data quality is much smaller and scaling observation variances offered little gain. Furthermore, Figure 2b indicated that both elevation-dependent and C/N0 weighting schemes are representative of the u-blox observation noise for this dataset and, consequently, using C/N0 measurements did not result in any improvement. Nevertheless, this analysis indicates that the use of carrier-to-noise ratio measurements can lead to improved accuracy for low-cost GNSS devices.

IONOSPHERE A critical error source for single-frequency receivers is the ionosphere. This section analyzes several aspects related to this error source, namely the modelling strategy within the PPP filter, as well as the a priori correction sources such as global ionospheric maps and regional corrections. Modelling Several approaches can be adopted to mitigate the impact of ionospheric effects on position estimates. A summary is provided in Table 2. Table 2 Possible approaches to modelling the ionosphere in PPP

Approach A priori correction Parameter estimation Fixed ionosphere Yes No Thin-shell model Optional Yes (VTEC expansion)

GRAPHIC No No Stochastic Yes Yes (slant delays, 1/satellite)

In the fixed-ionosphere approach, slant ionospheric delays in the PPP functional model are considered as fixed quantities and are not estimated in the filter. This approach is often adopted in network RTK or PPP-RTK solutions since precise ionospheric corrections are available from a local network of ground stations [15]. This approach can also be used with ionospheric corrections from global ionospheric maps (GIMs) but, since these corrections contain errors at the decimetre to metre level,

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significant correlations are introduced between the carrier-phase and code observables. These correlations must be properly accounted for in the PPP stochastic model to maintain the relative weights between observable types [16]. The downside of the fixed ionosphere approach is that any bias contained in the ionospheric corrections will propagate into the position estimates. Using the thin-shell model implies the estimation of a vertical total electron content (VTEC) parameter in the PPP filter and, possibly, gradients [17]. A priori constraints from GIMs can be applied to improve filter convergence. This approach allows accounting for local VTEC deviations from the global model. However, due to limitations in the thin-shell model, such as electron asymmetry and unknown shell height, it is likely that unmodelled delays will again affect position estimates. The group and phase ionospheric calibration (GRAPHIC) signal [18] consists of forming a linear combination of carrier-phase and code observations to cancel ionospheric effects. The resulting combination inherits from the ambiguous nature of the carrier-phase observable and a change in geometry is required to separate ambiguity parameters from other parameters in the PPP filter. The GRAPHIC method has proven to be very efficient with geodetic receivers exhibiting low code-noise characteristics [19, 20]. However, low-cost receivers have much higher code noise and are more likely to be affected by multipath. As a result, these errors propagate into filter parameters and yield very noisy or biased position time series. The last option is the stochastic approach in which the PPP filter includes slant ionospheric delay parameters, i.e. one parameter per satellite per epoch. The main benefit of this approach is its flexibility. If these ionospheric parameters are considered to be independent between epochs, this approach provides results similar to the GRAPHIC combination. By using process noise to link slant ionospheric delay parameters in time, smoother estimates are obtained, which translates into reduced noise for the position estimates. The approach also allows external constraints from a GIM or a local network to be included in the solution, potentially providing position results close to the fixed-ionosphere model often used in PPP-RTK. For these reasons, this approach has been adopted in CSRS-PPP since version 2.11. With single-frequency receivers, PPP estimates of slant ionospheric delay parameters are necessarily contaminated by code noise. When code observations contain large noise or when they are strongly contaminated by multipath, their usefulness for the estimation of Δ𝐼' becomes limited. In times of quiet ionospheric activity, the residual error from the a priori model can be much smaller than the errors inherent to this type of observable. For this reason, it makes sense to give more weight to the external ionospheric constraints than to the measurements. This aspect will be investigated in section “Experimental Results.” Global ionospheric maps Global ionospheric maps (GIMs) are grids of VTEC values derived from GNSS data. The grids provided as a part of the NRCan EMRG GIMs have a spacing of 2.5o by 5o for latitude and longitude, respectively, and provide VTEC at an altitude of 450 km [21]. The International GNSS Service (IGS) reports an accuracy in the range of 2-8 TEC units (TECU) for GIMs, corresponding to approximately 16-130 cm of delay on the GPS L1 frequency [22]. However, like most IGS analysis enters, the EMRG products also report RMS grids to better characterize the uncertainty at each grid node. To derive RMS grids, differences between VTEC observations and the fitted model are first computed. The RMS error of these residuals is then obtained on a station-by-station basis, and spherical harmonic coefficients are estimated to provide a smooth spatial variation. From these coefficients, values at grid points are derived and output in the IONEX format [23]. The EMRG products implementing this strategy are publicly available since April 2015 [24]. The errors (𝜀) in slant TEC (STEC) derived from GIMs can be evaluated using precise slant ionospheric delays derived from dual-frequency GNSS data processing using PPP with ambiguity resolution (PPP-AR) [25, 26]: 𝑚Z' ⋅ VTEC_Z`

' − 𝐼aaaPbc' = 𝜀9𝐼_Z`

' ; + 𝑏d (7) where 𝑚Z

' is the single-layer mapping function. When ambiguities are fixed to correct integer values, slant ionospheric delays derived from PPP-AR are precise at the millimeter level [27]. However, they contain a receiver-dependent bias common to all satellites (𝑏d). Therefore, the mean value from all differences between GIM and PPP-AR STEC values must be removed to evaluate the precision of GIMs. Removing the mean does not affect the validity of the analysis since the receiver clock and ambiguity parameters can absorb such an offset in single-frequency PPP. While errors in the satellite differential code biases (DCBs) would also contaminate equation (7), there are considered negligible for this analysis.

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Figure 4a shows STEC errors in the EMRG GIM during the 1.5-hour test presented in section “Stochastic Modelling.” Each color/marker combination represents a different satellite. The standard deviation of all values equals 10.7 cm, corresponding to 0.66 TECU. It should be kept in mind that, over such a short period of time, a common bias in the GIM STEC values can be fully absorbed by the 𝑏d term of (7) and lead to optimistic results. Still, time correlation is obvious in the STEC error time series and should ideally be accounted for in the PPP filter. Figure 4b displays a histogram of all STEC errors contained in Figure 4a, divided by their corresponding precision computed from the GIM RMS maps. All ratio values are below 1.0, with a RMS of 0.32, which indicates that errors are within the reported precision of the GIM.

a) GIM STEC errors b) GIM error/precision ratio

Figure 4: a) Errors in STEC values derived from the EMRG GIM on 2019-05-14 in Ottawa; b) Ratio of STEC error vs precision reported in the GIM IONEX file

This analysis of STEC errors and their relationship with input precision is repeated on a daily basis for the period of 2015-2018 for station ALGO, located in Algonquin Park, Canada. PPP-AR solutions were computed using the CNES/CLS orbit and clock products [28]. While the precision of the EMRG GIM is dependent on the period of the solar cycle, a standard deviation of about 25 cm (1.5 TECU) is observed during low solar activity for this mid-latitude site. The corresponding precision indicators from the GIM RMS maps are fairly representative in all cases, with an error/precision ratio in the vicinity of 1. Therefore, the EMRG RMS calculation approach for deriving meaningful GIM RMS maps should allow weighting this information adequately in the PPP filter.

Figure 5: Daily values of STEC errors from the EMRG GIM and the RMS of the error/precision ratio for station

ALGO located in Canada

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Regional slant ionospheric delay corrections In a future version of CSRS-PPP, precise slant ionospheric delays will be derived from PPP-AR solutions for approximately 200 stations located within Canada or its surroundings (Figure 6). Since slant ionospheric delays from PPP contain receiver-dependent biases, between-satellite single-differenced delays will then be interpolated at the user position using Kriging, such that the following pseudo-observations can be added to the functional model as: 𝐼cI_'e − 𝐼+

'e = Δ𝐼e − Δ𝐼' (8) where j and k represent two satellites. The precision of these interpolated delays depends on the distribution of reference stations around a user, along with the spatial variability of the ionosphere expressed through the Kriging covariance function. The latter is computed using residuals from the EMRG GIM, but it is still under investigation and is not described in further details herein.

Figure 6: Example of reference stations used to compute precise slant ionospheric delays using PPP-AR

Similar to Figure 4, slant ionospheric delay errors obtained from the regional STEC corrections using Kriging are depicted in Figure 7a. Since NRCan station NRC1 is located only 8.9 km away from the data collection site, very precise corrections can be provided to the user, with a standard deviation of 6 mm. This is an order of magnitude better than the GIM predictions obtained previously. The quality indicator associated with these predicted delays, derived from the Kriging covariance functions, are realistic due to the short baseline, as seen in Figure 7b. However, it becomes more complex to derive meaningful indicators when larger inter-station distances are involved.

a) Regional STEC errors b) Regional STEC error/precision ratio

Figure 7: a) Errors in STEC values derived from the regional network on 2019-05-14 in Ottawa; b) Ratio of STEC error vs precision derived from the Kriging covariance functions

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TROPOSPHERE Mitigating tropospheric effects can be achieved using temperature, pressure and humidity values at the user location. These quantities can be obtained either from blind models consisting of long-term predictions based on historical data, or from global meteorological observations. Since 2008, CSRS-PPP has been using the global pressure and temperature (GPT) model [29] to compute a priori values for the tropospheric zenith delay (TZD), along with global mapping functions (GMF) [30] to map this zenith delay at the satellite elevation angle. Since TZD predictions contain errors, an additional parameter is typically set up in the PPP filter to model the residual TZD. To gain better insights into the magnitude of residual TZD values, the evolution of this quantity over 2018 at two locations in Canada is analyzed in Figure 8. PPP solutions are computed using dual-frequency geodetic receivers and the residual TZD parameter is plotted based on different a priori tropospheric models. The first station is located in Halifax, on the east coast of Canada, hence on the shore of the Atlantic ocean. Due to water proximity and the occurrence of weather fronts, neglecting the wet delay in the GPT model leads to large residual values, as shown in Figure 8a. The root mean square (RMS) value for the residual TZD based on the GPT model is 8 cm, with peaks close to 25 cm. Instead of using blind models, observations or short-term predictions of temperature, pressure and humidity values can be beneficial for PPP [31]. For instance, the Vienna Mapping Function 1 (VMF1) products contain hydrostatic and wet tropospheric zenith delays as well as mapping function coefficients derived from numerical weather models [32]. Using these products reduces substantially the RMS of residual TZD estimates to 1.6 cm, as shown in Figure 8a. Since VMF1 products are available with a delay of a couple of days, forecast products are also available as a part of VMF1-FC [33] for near real-time submissions. Using these predicted values provide very similar results with an RMS error of 1.8 cm. In drier regions, such as high altitude or near the poles, it is expected that the GPT model performs much better. This is confirmed in Figure 8b for a station in Priddis, located south of Calgary in the Canadian Prairies at the foot of the Rocky Mountains. Since the altitude of this station is close to 1250 m, water vapor in the atmosphere is much lower. In this case, all models perform similarly and large peak values are not present.

a) Halifax (HLFX) b) Priddis (PRDS)

Figure 8: Residual tropospheric zenith delay derived from dual-frequency PPP solutions in a) Halifax, on the east

coast of Canada; and b) in Priddis, located in the Canadian Prairies at the foot of the Rocky Mountains. Since tropospheric errors are highly correlated with height estimates, residual TZD errors will impact the position accuracy of single-frequency PPP solutions. To illustrate this effect, 24-hour static PPP solutions are computed using single-frequency measurements at station HLFX. Since this station is equipped with a geodetic receiver and a choke-ring antenna, measurement quality allows the solution to converge to cm-level accuracies when error sources are correctly modelled. As such, it becomes possible to correlate height error in the PPP solution with residual TZD errors, as shown in Figure 9. In this plot, the GPT error is the mean residual TZD value over the day. Since residual errors such as the ionosphere may still adversely affect the solutions, height errors are not null when the TZD is correctly modelled. However, there is a clear trend indicating that errors in the a priori TZD model are amplified in height estimates derived from single-frequency PPP solutions.

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Figure 9: Height errors obtained from 24-hour static PPP solutions computed using single-frequency measurements at

station HLFX, and their relationship with errors in the a priori TZD model (GPT) Starting with CSRS-PPP version 2.21, VMF1 products are utilized when final orbit and clock products become available. The VMF1-FC products are currently under evaluation and should be introduced in the near future before VMF1 products become available. While the PPP filter includes both a residual TZD and gradient parameters when processing dual-frequency observations, a different parameterization is suggested for single-frequency users [34]. Given the quality of the a priori tropospheric delays derived from VMF1 products, this error source is considered as a known quantity for low-cost (single-frequency) GNSS receivers and a residual TZD parameter is not included on the right-hand side of equations 3 and 4.

QUALITY CONTROL Carrier phase observations were introduced in CSRS-PPP single-frequency solutions starting with version 2.11. This feature required the implementation of a cycle-slip detection algorithm capable of identifying carrier-phase discontinuities in the presence of large code noise. The adopted algorithm is based on a geometry-based solution using time-differenced observations [35], and a brief summary is provided below. Time-differenced observations between two consecutive epochs can be expressed as: 𝛿𝐿#$,&

' = 𝒆' ⋅ 𝛿Δ𝒙+ 𝛿𝑑𝑇???? − 𝜇$ ⋅ 𝛿𝐼' + 𝜆$𝛿𝑁@$' (9)

where the 𝛿 symbol represents the variation of a quantity between epochs. In case of a static receiver, the displacement between epochs is null and does not need to be estimated. The time variation of slant ionospheric delays is typically negligible under short time intervals and normal ionospheric activity. To improve the computational efficiency of the approach, ionospheric parameters are not set up in the time-differenced solution but observation variances are increased to account for this effect. Since ambiguity parameters are constant values by definition, their variations will only differ from zero in the presence of cycle slips. Under the null hypothesis, it is assumed that no cycle slips are present. Given the above considerations, the functional models for static and moving receivers become:

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𝛿𝐿#$,&' = 𝛿𝑑𝑇???? (static receiver) (10a)

𝛿𝐿#$,&' = 𝒆' ⋅ 𝛿Δ𝒙+ 𝛿𝑑𝑇???? (moving receiver) (10b)

Using all satellites available, the unknown parameters are estimated in a weighted least-squares adjustment. Residuals are then checked for compatibility with the model using: 𝒗h𝑷𝒗 < 𝜒l (11) where 𝒗 is the vector of residuals, 𝑷 is the observation weight matrix and 𝜒l is the threshold value from the central chi-square distribution. If this test fails, outliers (i.e., observations containing cycle slips and/or unmodelled errors) are identified using the improved local analysis method (ILAM) [36]. In the event that this step fails due, for example, to multiple cycle slips and low redundancy, all observations are flagged as containing cycle slips. Figure 10 shows the time-differenced carrier-phase residuals (𝒗) for all satellites at each epoch for the Huawei Mate 20X dataset introduced in section “Stochastic Model.” Each color/marker pair represents data from one satellite. With the receiver being stationary, the time-differenced model of (10a) is applied. Since data was collected at a 1-Hz sampling rate, the time variation of ionospheric delays is small and residuals show that time-differenced carrier-phase measurements agree within a few centimetres among satellites. This level of consistency allows for the reliable identification of small cycle slips or outliers, marked with black circles on the figure. Note that the threshold for rejection is not a constant, but rather varies as a function of observation variance.

Figure 10: Residuals from a time-differenced solution based on carrier-phase observations collected with a Huawei

Mate 20X smartphone. Observations identified as outliers are circled in black

EXPERIMENTAL RESULTS The aim of this section to is evaluate the performance of single-frequency PPP solutions based on the concepts presented above. Table 3 gives an overview of the software configurations evaluated. The ‘Online’ solution is the software currently supporting CSRS-PPP. In this configuration, code noise is being assessed prior to computing the final solutions to provide more realistic standard deviations; furthermore, tropospheric corrections are being computed using the VMF1 products and quality control is performed using the geometry-based approach presented above. The next solution, labeled ‘GIM’, uses similar settings but adds constraints from GIMs at every epoch instead of once per arc. This strategy aims at stabilizing the estimation of slant ionospheric delays in the presence of noisy code observations. Solution ‘C/N0’ tests the benefits of using C/N0 values to weight code observables. Finally, the ‘STEC’ solution includes precise slant ionospheric delay corrections for users located in Canada.

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Table 3 – PPP software configurations evaluated Solution ID Troposphere Ionosphere Stochastic model

Online VMF1 GIM (once per arc) Scaled GIM VMF1 GIM (every epoch) Scaled C/N0 VMF1 GIM (every epoch) C/N0 STEC VMF1 Regional STEC C/N0

A challenge associated with software testing for low-cost GNSS equipment is data availability. While there are archives of data from globally distributed geodetic receivers, the pool of data from smartphones or similar devices to draw from is very limited. In addition, data quality (noise, carrier phase continuity) variations between such low-cost units are significant. Therefore, we organized the data collection campaigns summarized in Table 4. These campaigns were mainly conducted in low-multipath environments such as a mountain summit and open fields, except for the 2019-06-19 campaign which took place on the multipath-prone rooftop of the CCIT building of the University of Calgary. Table 4 – Campaign descriptions

ID Date GPS Time Location (Canada) A 2019-04-02 17:10 - 18:10 Prairie Mountain, Kananaskis, AB B 2019-05-14 17:15 - 18:45 Experimental Farm, Ottawa, ON C 2019-06-11 18:35 - 20:35 Nose Hill Park, Calgary, AB D 2019-06-19 19:00 - 21:00 CCIT building, University of Calgary, AB E 2019-07-02 20:30 - 22:30 Nose Hill Park, Calgary, AB (unit #1) F 2019-07-02 20:30 - 22:30 Nose Hill Park, Calgary, AB (unit #2)

All campaigns used the Huawei Mate 20X smartphone, containing a multi-GNSS dual-frequency chip manufactured by Hi-Silicon. It is capable of tracking all GNSS (GPS, GLONASS, Galileo, BeiDou and QZSS) and outputs the L1/L5 signals for GPS, Galileo and QZSS. In this study, only single-frequency GPS and GLONASS L1 observations are processed since GPS L5, Galileo, BeiDou and QZSS are not currently supported by CSRS-PPP. Duty cycling was off, hence continuous carrier-phase observations were obtained [6]. Units remained stationary for the total duration of the sessions. For all campaigns, a Leica GS16 geodetic receiver is included in the setup to allow accurate georeferencing using a PPP solution, similar to Figure 1. Differential solutions between this georeferenced geodetic receiver and low-cost devices then allows one to obtain the position of their phase centers to the centimetre level. These positions have also been validated from tape measurements between units. All data from low-cost units were collected at a 1-Hz sampling interval and processed in static mode. PPP solutions are computed using the NRCan rapid orbit products and the decoupled satellite clock products [37]. Figure 11 displays the horizontal and vertical errors from single-frequency PPP solutions computed by the software configurations listed in Table 3. The results at any epoch are based on the cumulated measurements since the start of the observation sequence. The six subplots of Figure 11 correspond to the six campaigns of Table 4. Several conclusions can be drawn from these plots. First, even with the same device, data quality is subject to significant fluctuations depending on the environment and the level of multipath. For instance, data collected on a mountain summit (Figure 11a) shows a smooth and rapid convergence since multipath is very low. In contrast, data collected on a rooftop with surrounding multipath sources is associated to errors of several meters during the initial minutes of processing (Figure 11d). To better appreciate differences in data quality between these two datasets, Figure 12 shows that the GPS and GLONASS code residuals are approximately five times larger on the CCIT building (campaign D) than on the mountain summit (campaign A), despite the same device being used in both campaigns. The code residuals RMS for all datasets is also included in Figure 12 for comparison. Processing strategy also considerably affects results. The software currently supporting CSRS-PPP offers a solution that is sometimes unstable. An obvious example is Figure 11e where position estimates never fully converge. The stochastic approach to estimating ionospheric errors works well with high-quality measurements, but the model is weak with noisy observations. To mitigate this issue, more weight is assigned to the GIM by adding constraints at every epoch in the PPP filter (solution labeled ‘GIM’). The downside of this approach is that PPP solutions become more sensitive to the quality of GIMs, which may become detrimental for high-quality geodetic receivers operating in single-frequency mode or during ionospheric storms. Achieving the proper balance in the stochastic model is complex and requires further testing.

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a) 2019-04-02 (Mountain summit) b) 2019-05-14 (Experimental Farm – Ottawa)

c) 2019-06-11 (Nose Hill Park – Calgary) d) 2019-06-19 (CCIT roof – Univ. of Calgary)

e) 2019-07-02 (Nose Hill Park – Calgary; 1st unit) f) 2019-07-02 (Nose Hill Park – Calgary; 2nd unit)

Figure 11: Position solutions of Huawei Mate 20X in different environments

Another aspect of stochastic modelling to consider consists of using C/N0 values to weight code observations. It appears that using this weighting strategy is especially beneficial for the initial epochs of the solution. For instance, in Figure 11d, the horizontal error exceeds 25 meters when using the standard elevation-dependent weighting scheme. Using the carrier-to-noise

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ratio reduces this error to below 10 m. From our limited set of results, it appears that the C/N0 weighting strategy is especially beneficial for these initial epochs in a high multipath environment.

Figure 12: Standard deviations of GPS and GLONASS C1C code residuals for campaigns described in Table 4

Incorporating precise ionospheric information from a regional network is highly beneficial to the solution. When users are located close to reference stations, cm-level accuracies can be obtained after convergence. The ‘STEC’ solutions also tend to achieve a more uniform convergence than other processing strategies. Such a performance is possible thanks to the good quality of carrier-phase observations provided by the Huawei Mate 20X. With slant ionospheric delays tightly constrained using precise STEC information, it also becomes possible to fix carrier-phase ambiguities. To illustrate this concept, data from the Ottawa dataset is processed using the ‘STEC’ configuration of Table 4. Even though the receiver was stationary, the data was processed in kinematic mode, i.e., by making no assumption on the receiver dynamics. Carrier-phase tracking was continuous for most satellites, as shown in Figure 10. Ambiguity resolution was performed for GPS only and allowed resolving 93% of the ambiguities. Figure 13 shows that cm-level accuracies are obtained and that the short-term variation of horizontal positions is at the millimetre level. While a moving receiver might experience larger noise and more signal discontinuities, these experimental results indicate that, under certain circumstances, smartphones could already be used for high-precision positioning.

CONCLUSIONS With low-cost GNSS devices, data quality is strongly dependent on hardware and environment. Therefore, tuning the PPP functional and stochastic models to each dataset is the best option to obtain the most accurate results. In the NRCan CSRS-PPP service, submissions are processed in an automated fashion. The PPP software configuration must then be suitable for the majority of users. Since the initial implementation was mainly tested with single-frequency data from geodetic receivers, this investigation aimed at identifying weaknesses in the adopted strategy. The planar inverted-F antennas used in smartphones have a gain pattern allowing to track signals from all directions, resulting in larger code noise and multipath. As a result, the correlation between code noise and elevation angle is weak, and C/N0 was found to better characterize code noise. Fitting code residuals to a C/N0-dependent function provided improved code-based positioning results and, therefore, smaller errors for the initial epochs of PPP solutions. When code residuals are similarly correlated with both the elevation angle and C/N0, the choice of weighting function does not appear to be critical.

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Figure 13: Single-frequency kinematic PPP-AR with regional ionospheric corrections using data from the Huawei

Mate 20X on 2019-05-14 in Ottawa (note: the receiver was stationary) Modelling of the ionosphere in the PPP filter has a significant impact on single-frequency solutions. The stochastic approach, consisting of estimating one parameter per satellite per epoch, is very flexible. With geodetic receivers, this approach allows estimating slant ionospheric delays, leading to accurate positioning results. However, it was found that short datasets highly contaminated by noise and multipath can lead to unstable position estimates. To mitigate this issue, constraints from global ionospheric maps were introduced at each epoch rather than once per arc, as initially implemented. This strategy would inevitably degrade position estimates from high-end receivers operating in single-frequency mode, although most single-frequency users use low-cost devices. High ionospheric activity could also negatively impact solutions, but it is not yet known how signal tracking in smartphones and other low-cost receivers behaves during ionospheric storms. A solution to these problems consists of using precise STEC corrections derived from a regional network of stations. Such corrections are key to enabling cm-level accuracy with single-frequency receivers. Mismodelling of the a priori tropospheric zenith delay was found to cause dm-level height errors in parts of Canada where water vapor content is high. As a result, the GPT/GMF blind model was replaced by the VMF1 and VMF1-FC products. The accuracy of these products is sufficient to support cm-level positioning in most cases. Given the quality of these products and the noise level of low-cost GNSS devices, it was deemed preferable not to estimate a residual tropospheric zenith delay parameter in the PPP filter. Testing the concepts presented in this study with additional low-cost devices is mandatory before they can be implemented into CSRS-PPP. The latest low-cost GNSS chips, such as the one contained in the Huawei smartphone used in this study, have dual-frequency multi-GNSS capabilities. Further analysis of these signals, including performance in kinematic mode, are analyzed by [38].

ACKNOWLEDGMENTS The authors would like to thank Matthew Goode from u-blox for providing the u-blox M8P receiver. This paper is published as NRCan contribution number 20180418.

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