## 1 Introduction
The results confirmed an improvement in the RTK positioning accuracy in both static and dynamic tests using the proposed method. Various researchers have also been conducting investigations into the feasibility of ambiguity resolution with a smartphone receiver. For example, [PERSON] et al. [34] first investigated the quality of L5/E5a/B2a signals, their superiorities in IAR and precise positioning with respect to the L1/E1/B1 signals from GPS, QZSS, Galileo and Beidou\(-\)2/3 satellites. The authors then proposed a new weighting model that takes into account the variation range of C/N0, providing a better weighting model than the traditional weighting model, thus improving the positioning accuracy. The results indicated that the L5/E5a/B2a signals could generally obtain higher IAR fix-rate and positioning accuracies than the L1/E1/B1 signals. [PERSON] et al. [35] compared the best integer equivariant (BIE) estimator to the integer least squares (ILS) and float contenders using GNSS data collected by Google Pixel 4 smartphones for short-baseline RTK positioning. The results indicated that the BIE estimator will always give a better RTK positioning performance than that of the ILS and float solutions while using both single- and dual-frequency smartphone measurements for the combination of GPS + Galileo + QZSS + BDS. [PERSON] et al. [36] investigated the effect factors for integer property of phase ambiguities, data quality, IAR efficiency and positioning accuracy for the smartphone. The results indicated that the smartphone brands, operating systems and smartphone attitudes would affect the integer property of phase ambiguities and data quality. The kinematic positioning results showed the meter-level accuracy with an embedded antenna, and the centimeter to decimeter-level accuracy with the external antenna. Finally, we should note that although the results of current studies are promising, we still need more effort to achieve satisfying accuracy for many location-based services. In 2021 and 2022, the Android GPS team of Google hosted two Google smartphone decimeter challenges (GSDC), where various smartphone GNSS datasets of real vehicular applications were used to determine smartphone positioning accuracies [37]. It was revealed that meter-level accuracy is generally achieved by the leading participants, which is still not enough to enable smartphone precise positioning. Several challenges must be taken into account in order to further improve smartphone positioning such as: carefully analyzing the smartphone GNSS observations, investigating the environment effect and smartphone holding modes and improving positioning algorithm and implementation. It is obvious that the quality of the GNSS observations plays an important role in the final positioning performance. Currently the GNSS pseudorange, carrier-phase and Doppler observations are not directly accessible from the API 24 implemented in Android 7 or higher. They have to be generated by smartphone users from the GNSS raw information accessible through Google's application programming interface (API), namely android.location (API level 24). Various Apps for smartphone GNSS data logging and GNSS observations generation have been developed and two of them are widely used as described in the following. In 2016, Google released an open source application, namely GnssLogger App, which logs the raw measurements of the GnssClock and GnssMeasurement classes from the android.location API. This information can then be used to generate the GPS time, pseudorange, carrier-phase and Doppler observations, which, however, must be done by the users themselves. Later In 2017, the Geo++ GmbH Company released an open-source application, namely Geo++ RINEX Logger App, capable of providing the GNSS pseudorange, carrier-phase and Doppler observations in the Receiver INdependent Exchange (RINEX) format [38].