# Stochastic Modeling of Smartphones GNSS Observations Using LS-VCE and Application to Samsung S20
## 5 Summary and Conclusions  
Thanks to the new API implemented on Android 7 and later versions, the utilization of smartphones for various applications such as cadastral surveying, mapping surveying applications, and navigation has been significantly increasing due to cost-effective GNSS smartphones. However, there are still various challenges that prevent users from obtaining highly accurate results using smartphone observations.  
In this study, we have investigated reliable stochastic modeling of smartphone GNSS observations and developed a C/N0 and elevation-dependent weighting method. We obtained a reliable stochastic model using the LS-VCE method and employing the DD code and phase observations from a very short baseline (two Samsung S20 devices placed close to each other on a pillar). The model performance has been evaluated by single-frequency PPP with a Samsung S20 smartphone. The following conclusions can be drawn from our study on reliable stochastic modeling using LS-VCE and application to Samsung S20 smartphones:  
1. The estimated coefficients for each constellation and each observation type are as follows: \(\hat{a}_{code}^{GPS}=0.35\times 10^{5}\), \(\hat{a}_{code}^{GPS}=0.04\times 10^{5}\) for GPS and \(\hat{a}_{code}^{GLO}=1.08\times 10^{5}\), \(\hat{a}_{code}^{GLO}=0.04\times 10^{5}\) for GLONASS as reported in Table 5;
2. There is no significant correlation between the GPS code and carrier phase observations on the L1 frequency. The same conclusions hold for the GLONASS constellation;
3. The results of the study confirmed an improvement of 25.1% and 32.7% on the RMS of horizontal positioning and the 50 th percentile error, respectively, when employing the obtained stochastic model. This research provides insights into the potential of high-precision smartphone positioning and highlights the importance of the proper choice of functional and stochastic models in achieving this goal.  
Our future research will focus on developing a more reliable stochastic model for other constellations as well as the second frequency (L5/E5a).  
All the authors have contributed to the presented work. The first author, [PERSON], analyzed the static and kinematic datasets, prepared the plots, and wrote the draft of the manuscript. The second author, [PERSON], supervised manuscript development and the direction of the research, revised the paper, and provided further analysis. All authors participated in formulating the idea and in discussing the proposed approach and results. All authors have read and agreed to the published version of the manuscript.  
The financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is greatly acknowledged. The first author greatly acknowledges the funding support provided by the Izaak Walton Killam Memorial Scholarship.  
Not applicable.  
Data Availability Statement: The data that support the findings of this study are available upon request from the corresponding author, via [EMAIL_ADDRESS].  
We are grateful to Profound Positioning Inc. (PPI) for providing the Xiaomi Mi8 and Samsung S20 devices to collect data used in this paper.  
The authors declare no conflict of interest.