Application of UofC Model based Multi-GNSS PPP to Smartphones GNSS Positioning

The use of low-cost and ultra-low-cost receivers has been drastically increasing due to their low cost compared to the high-end geodetic receivers. Early smartphones only provided single-frequency GNSS observations. However, dual-frequency GNSS smartphone has been launched in recent years which enables the user to make ionospheric-free (IF) linear combinations between observations of two frequencies to eliminate the first-order ionospheric delay. Such an IF combination would increase the noise level of observations. To overcome the problem of large noise of traditional IF pseudorange combination, the University of Calgary (UofC) model can be employed. It employs the IF linear combinations of carrier-phase and the two averages of the pseudorange and carrier-phase observations on the same frequency. In the case of dual-frequency smartphones, there are limited number of satellites which could transmit navigation signals at both frequencies (L1 and L5 for GPS and E1 and E5a for Galileo) which makes the position determination difficult or even impossible using only dual-frequency observations. The solution to make use of all GNSS measurements is to employ a model consisting of both dual-frequency UofC model and the single-frequency (SF) ionosphere-corrected code and phase measurements of the remaining satellites. In addition to the functional model, the stochastic model plays an important role in GNSS positioning. The least-square variance component estimation (LS-VCE) method is applied to the double-difference (DD) code observations of two Xiaomi Mi 8 devices to obtain suitable variances for GPS, GLONASS and Galileo. The performance of the UofC model combined with the SF ionosphere-corrected model is investigated in both static and kinematic modes, while introducing a more reliable stochastic model in smartphone positioning. The results confirmed that introducing a more reliable stochastic model would improve the PPP performance in both static and kinematic modes. In the static test, an improvement of 8.3% and 17.9% was achieved on the root mean square (RMS) of horizontal positioning error and its 50th percentile error, respectively. Using our kinematic dataset and the data provided by Google, an approximate improvement of about 20% on the RMS of horizontal positioning error and its 50th percentile error was also observed while employing a more reliable stochastic model.