## 1 Introduction  
Precise position information available from smartphones is of great importance when enabling many smartphone-based location-based service (LBS) applications. Since the GNSS observations, including carrier-phase, became available to users from smart devices running Android Nougat (version 7.0) in 2016, many methods and algorithms have been developed to enable precise positioning using these mass-market devices, such as analysis of GNSS smartphone observations [1, 2, 3, 4, 5], PPP smartphone positioning [6, 7, 8, 9, 10], real-time kinematic (RTK) smartphone positioning [11, 12, 13, 14, 15] and GNSS/INS integration using smartphone observations [16, 17, 18]. A comprehensive review of the recent advances and research done in the field of GNSS smartphone positioning, including those published up until 2021, can be found in [19, 20], while some more recent contributions in 2022 are provided in the following. [PERSON] [21] investigated the real-time standalone positioning accuracy employing the single-frequency code observations form the three smartphones, Xiaomi Mi8, Google Pixel 4 and Pixel 4 XL, in the kinematic mode. The study addressed two issues: (1) comparing the ultra-rapid and IGS real-time service (IGS-RTS) and (2) investigating the effect of an improved weighting model, utilizing the variance component estimation method, on the positioning accuracy. The experimental tests indicated that the use of IGS-RTS products augments had better performance compared with the ultra-rapid products. Moreover, introducing the actual stochastic characteristics of multi-GNSS observations improved the smartphone positioning performance by 11.0% on average. [PERSON] et al. [22] proposed a combined elevation angle and carrier-to-noise density ratio (C/N0) weighting method for smartphone-based GNSS PPP by normalizing the C/N0-derived variances to the scale of the elevation-angle-derived variances. The results indicated an improvement in the three-dimensional positioning accuracy by 22.7% and 24.2% in an open-sky area, and by 52.0% and 26.0% in a constrained visibility area, compared with the elevation-angle-only and C/N0-only weighting methods, respectively. [PERSON] and [PERSON] [23] proposed a mixed single- and dual-frequency quad-constellation PPP model to improve the smartphone positioning performance by taking advantage of all available GNSS observations. The effectiveness of the proposed model has then been investigated using both static and kinematic tests. Based on the results, the mixed frequency model could effectively improve the positioning performance compared to the traditional dual-frequency PPP and the single-frequency PPP. [PERSON] et al. [24] proposed a real-time PPP algorithm for land vehicle navigation with smart devices. The smartphones were placed on the roof and the dashboard. The positioning accuracy of vehicle-roof mode was in the order of 1.0 m for the horizontal component and 1.5 m for the vertical component, while the positioning accuracy of the dashboard test were about 1.0-1.5 m in the horizontal direction and 1-2 m in the vertical direction. [PERSON] et al. [25] proposed an uncombined PPP-RTK model to achieve rapid integer ambiguity resolution (IAR) with the regional atmospheric augmentation with an external low-cost helical antenna. The results indicated that PPP rapid ambiguity resolution could be achieved using the smart devices' GNSS raw observations with a low-cost helical antenna. The method, therefore, has the potential to provide high-precision positioning services and can be widely used in massive market applications because of the advantages of low weight, low-power consumption and portability. [PERSON] et al. [26] investigated the performance of ionospheric total electron content (TEC) determined by GNSS dual-frequency measurements derived from the Xiaomi Mi8, as an example.