An enhanced stochastic approach for code observations collected from Android smartphones

Smartphone-based positioning, navigation, and timing applications have been among the most popular topics within the GNSS community since 2016 when Google announced that raw GNSS observations are publicly available. However, achieving high positioning accuracy with smartphones is troublesome because of their specific limitations, such as the high noise level of observations, low protection against multipath, and discontinuities in carrier phase observations. Due to considerable discontinuities in carrier phase observations, code observations still play a crucial role in smartphone-based positioning applications. Subsequently, a realistic stochastic approach is mandatory to obtain the utmost positioning performance. This is especially true since the stochastic behavior of code observations for geodetic receivers and Android smartphones are quite different i.e., GNSS observations obtained from a smartphone are much noisier. The signal strength of GNSS signals collected from Android smartphones is also not very stable and is significantly lower when compared with geodetic receivers. Unlike observations obtained from geodetic receivers, no significant dependency between observation noise and elevation angle can be observed in smartphone observations. Therefore, conventional stochastic models, mainly based on the satellite elevation angle, are not enough to represent the stochastic behavior of smartphone observations. In this context, this study provides an enhanced stochastic approach for code observations obtained from Android smartphones. The corresponding approach includes a weighting scheme based on carrier-to-noise ratio (C/N0) values representing the signal strength of GNSS code observations. Besides, depending on their observation noises, this approach assigns different model coefficients for each constellation, which means differences between the navigation systems can be considered in adequate observation weighting. This approach also uses a robust Kalman filter method based on the IGG (Institute of Geodesy and Geophysics) III function to compensate for the effects of outliers and incorrectly weighted observations on the filtering performance. In this study, GPS, GLONASS, Galileo, and BeiDou code observations collected from a Xiaomi Mi 8 are processed to evaluate the performance of the proposed stochastic model. Firstly, observation noises are analyzed utilizing code-minus-phase observations, and the results show that GLONASS observations are considerably noisier than observations from other systems. Following, probability distributions of observation noises are evaluated to determine a realistic stochastic model, and the SIGMA- model with different coefficients for each constellation is adopted in this study. The Standard Point Positioning (SPP) method is also used to analyze the positioning performance of the proposed model. The results indicate that the proposed model can provide a 3D positioning accuracy of 1.5 m with the smartphone in static mode, which means the model improves the positioning accuracy by 36.9% compared to the conventional elevation-dependent stochastic approach. From these results, it can be said that the enhanced stochastic approach, based on C/N0 values and computing model coefficients for each constellation differently, can better reflect the stochastic behavior of code observations collected by Android smartphones.