An optimized stochastic model for smartphone GNSS positioning

With the increasing popularity of high-precision applications of smartphone, more and more scholars carry out studies in the field of smartphone GNSS positioning. In the previous studies, more attention has been paid to data quality control, data preprocessing and observation models. However, the research on stochastic models is rare. The stochastic model is significant for the subsequent optimal positioning parameter estimation, meanwhile, the stochastic models of smartphones and professional geodetic receivers are very different for the completely different characteristics of smartphone GNSS observations. It is necessary to develop a stochastic model suitable for smartphone observations. Based on the characteristics of smartphone observations, this paper proposes an optimized stochastic model. The specific process of this method is as follows: firstly, the code-minus-phase (C-L) combi-nation and double-differenced measurement were used to quantify the noise of smartphone code and phase observations. Then, an optimized carrier-to-noise density ratio (C/N0) dependent stochastic model was proposed on the basis of the characteristic of smartphone observations. To validate the superiority of the proposed model, single point positioning (SPP) and real time kinematic (RTK) experiments were carried out by Xiaomi 8 in 2 days. The 3-dimensional root mean squares (RMS) of SPP were 6.18 and 5.38 m, with improvements varying within 0.00%-10.02% compared with the customary models. Likewise, the RMS of RTK were 0.14 and 0.24 m, with improvements fitting in range of 10.06%-39.92%. This research plays an important role in improving the positioning accuracy of smartphone and promoting the popularization of high-precision applications.