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### Session C1a: Applications of GNSS Measurements from Smartphones

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**Ionospheric Refraction Estimation From Smartphone GNSS Measurements**

*Caitlyn Hayden and Sunil Bisnath, York University*

**Date/Time:** Wednesday, Sep. 18, 9:43 a.m.

Introduction

Ionospheric refraction is a significant source of error in GNSS applications, with potential position errors reaching up to 10s of meters in magnitude (Doherty et al., 1997). As such, corrections are necessary to produce accurate position solutions. Current methods of determining these corrections from observed ionospheric refraction estimates require expensive geodetic receivers, and publicly available models can have relatively low spatial resolution. One example are widely used Global Ionospheric Maps (GIMs), which have spatial resolution of 2.5 degrees in latitude by 5.0 degrees in longitude and interpolation between grid spacing is applied to obtain corrections (Jerez et al., 2022). The critical driving factor behind these challenges is the requirement for high quality estimations to ensure modelled corrections are accurate. However, considering the statistical properties of averaging a large number of many different lower-quality estimates; a sufficiently large amount of observation samples obtained from different receivers may have a small enough standard error of the mean to well estimate the population mean with a high level of accuracy. As ionospheric refraction can be estimated using dual-frequency GNSS, the increasing prevalence of dual-frequency capable smartphone chipsets means a large amount of low quality ionospheric estimates can be obtainable through crowd-sourcing. Therefore, this paper aims to propose an ionospheric model that applies averaged dual-frequency smartphone estimates to determine ionospheric corrections.

Methods

To assess the feasibility of using smartphone data to accurately estimate ionospheric delays, three datasets of two dual-frequency smartphones (Samsung Galaxy S21+ and Xiaomi Mi8) and a geodetic receiver (NovAtel OEM7 Span) are processed using PPP.

Statistical properties of the ionospheric estimates are examined to determine if accurate estimates are obtainable, and approximately how many observations this would require. Due to many random errors in smartphone observations, the standard deviations of their ionospheric estimates are large, typically reaching values of multiple meters. However, this variability relates to the quality of the individual observations. To reduce high variability in estimates applied to the model, samples of these low quality estimates can be averaged. Thus, by creating samples of many epoch-by-epoch observations from an individual receiver-satellite pairing, the mean values of these samples provide less varied ionospheric delay estimates. To describe the variability of these sample means and assess their expected accuracies, the standard error of the mean is calculated.

For time intervals of 1, 2, 5, and 10 minutes, the variation and peak magnitudes of ionospheric delay rates of change drastically reduce with increased time (Doherty et al., 1994). So, high frequency fluctuations in ionospheric delays affect observations and should cause slight variations that are not due to random errors. As the goal is to accurately estimate the effect of the ionosphere on observed GNSS signals, this time interval of one minute is selected in an attempt to reduce the effects of random errors caused by the smartphone without removing high frequency variations caused by the ionosphere. Thus with an observation frequency of 1 Hz, each minute (assuming no epochs are rejected) can be averaged as a single estimation by obtaining the mean of ionospheric estimates from every 60 of the smartphone’s epochs.

Additional Experiments

To increase accuracy, the standard deviation of the sample means is reduced by applying corrections to remove phone estimate biases caused by unknown antenna offsets. Also determined is if biases between phones of the same model are consistent enough to apply the same corrections. With these bias corrections, vertical total electron content (VTEC) estimations are calculated from the means of ionospheric delay estimates from multiple nearby smartphones, and estimates that are spatially and temporally close are used to calculate local ionospheric corrections.

Dual-frequency smartphone data are collected from different phones under a variety of different conditions that mimic real-world situations. This includes scenarios such as different methods of transportation, varying phone orientations, and changing environmental obstructions. These diverse environmental conditions are expected to introduce additional random noise similar to a realistic crowd-sourcing case, while also removing between phone estimate correlations caused by identical movement paths. Local ionospheric delays will be estimated with these data and additional simulated datasets to examine how different conditions affect estimation accuracies. Correlations between these smartphone ionospheric estimates and conditional factors or other observed values such as number of satellites will be calculated and used to determine whether applying any environment or observation based weighting to the modelling process would significantly improve estimations.

Findings

From processing the initial three datasets, individual smartphone ionospheric estimates are found to be unreliable due to considerable noise and some bias. This result fits with expectations for issues in smartphone data caused by noise due to low receiver quality and biases due to the unknown antenna offset within the phones (Lehtola et al., 2019). Upon examination, the slant ionospheric delay estimates for different smartphone-satellite pairs are found to follow a normal distribution, with many of the 60 epoch samples following normal or skewed normal distributions as well. Additionally, compared to the geodetic receiver mounted on the same vehicle, there is some consistency in the bias of each individual smartphone both within and between datasets. Considering the similar mounting/orientation of the receivers across the observations it appears that these systematic errors are caused by unknown hardware offsets that can potentially be corrected. These findings are illustrated in Figure 1, where there is a significantly large spread across the epoch-by-epoch estimates but a one minute moving average of each phone is more consistent with geodetic rover results offset by systematic bias.

This moving average shows visually similar overall trends between the noisier smartphone estimates and the geodetic receivers; indicating that some of the variation between static geodetic base estimates and smartphone estimates is caused by mounting all three receivers on the same moving vehicle subject to the same conditions.

Continuing with results from these datasets, the standard deviations of different smartphone sample means and their standard error of the means are calculated for various different satellites across the datasets and compared to the standard deviation of the base station. The mean standard error of the mean for the samples of smartphone estimates from each satellite is 0.137 m. Compared to the mean standard deviation of 1.605 m for the raw estimates, estimates produced from the samples have greatly decreased variability and the effects of noise are drastically reduced. However, because the systematic errors have not been corrected, these estimates are skewed when compared to the geodetic receiver. This indicates that the effects of noise in the smartphone estimates can be mitigated to increase precision, but to increase accuracy to the desired levels, biases must either be accounted for or random and normally distributed such that increasing the number of smartphone receivers would reduce their impact.

Another challenge is the lack of available data. Dual-frequency smartphones are increasingly common, but dual-frequency smartphone data is not obtainable from all visible satellites. Thus, satellite specific ionospheric corrections are not possible and corrections are limited to VTEC maps.

Conclusions and Future Work

It has been determined that although dual-frequency smartphone estimates of ionospheric delay are inaccurate due to noise, large numbers of samples of smartphone observations reach a small enough standard error of the mean for the expected accuracy of their mean to reach geodetic receiver levels of accuracy. Future work will look at reliably correcting systematic errors and applying large amounts of dual-frequency smartphone data to generating ionospheric maps with higher spatial resolution than currently available global maps.

The goal is to apply these results to the creation and testing of multiple different models for generating ionospheric maps. Larger datasets will be collected with multiple dual-frequency smartphones, simulated smartphone datasets, and static geodetic receivers for testing. From these datasets, multiple averaged smartphone VTEC estimates across a local area will be estimated and applied to different models to generate local ionospheric maps. The performance of the different maps will be compared to other pre-existing publicly available ionospheric models and estimates obtained from the static geodetic receivers to determine if smartphone ionospheric estimates can be reliably applied to increase the precision and spatial resolution of an ionospheric map.

References

Doherty, P. H., Gendron, P. J., Loh, R., & Anderson, D. N. (1997). The spatial and temporal variations in ionospheric range delay, 231–240. Retrieved March 1, 2024, from http://www.ion.org/publications/abstract.cfm?jp=p&articleID=2794

Doherty, P. H., Raffi, E., Klobuchar, J., & El-Arini, M. B. (1994). Statistics of time rate of change of ionospheric range delay, 1589–1598. Retrieved March 1, 2024, from http://www.ion.org/publications/abstract.cfm?jp=p&articleID=3981

Jerez, G. O., Hernandez-Pajares, M., Goss, A., da Silva, C. M., Alves, D. B. M., & Monico, J. F. G. (2022). Impact and synergies of GIM error estimates on the VTEC interpolation and single-frequency PPP at low latitude region. GPS Solutions 26(2), 40. https://doi.org/10.1007/s10291-022-01228-0

Lehtola, V. V., Soderholm, S., Koivisto, M., & Montloin, L. (2019). Exploring gnss crowdsourcing feasibility: Combinations of measurements for modeling smartphone and higher end gnss receiver performance. Sensors 19(13). https://doi.org/10.3390/s19133018

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