## 1 Introduction  
With the development of satellite navigation and positioning technologies, users' demand for global navigation satellite system (GNSS) equipment with accurate positioning has steadily increased. Thus, developing high-precision applications based on low-cost GNSS equipment has become a dominant trend. Smartphones are one of the most used low-cost GNSS devices, accounting for 80% of the total number of GNSS devices available worldwide [1]. Compared with professional GNSS equipment, a smartphone has small size, low cost, and ease of use. However, the main shortcoming of the smartphone GNSS module is its poor positioning accuracy, with the standard single-point positioning precision being typically approximately 10 m on the horizontal plane [2], greatly limiting its use for professional applications. Research on smartphone GNSS modules has been conducted for many years, but before 2016, users could only obtain position, velocity, time, altitude, azimuth, and other final positioning information from a smartphone [3], thus restricting the development of smartphone GNSS technology. In May 2016, Google opened the GNSS raw measurement application programming interface for smartphones in the Android Nougat (version 7.0) operating system [4]. Since then, users can directly access observations including pseudo-range, carrier phase, and Doppler observable from a smartphone. Such data accessibility has greatly contributed to the development of high-precision smartphone GNSS modulestoward positioning at the decimetre level or even the centimetre level, thus expanding their adoption in the GNSS market. Broadcom launched a dual-frequency GNSS chip, and Xiaomi Mi 8 was the world's first smartphone with a dual-frequency GNSS function. Thereafter, smartphones equipped with chips made in China, such as Huawei P40 and Huawei Mate40, have integrated tri-frequency and quad-frequency GNSS functions. Currently, many smartphones are endowed with multi-constellation and multi-frequency capabilities, and their signal volume is comparable to that of survey-grade receivers, likely enabling high-precision positioning. By leveraging the aforementioned advances, many studies have been conducted on smartphone GNSS raw measurements, aiming to comprehensively analyse the observation quality and positioning performance of various smartphones and implement high-precision applications. However, owing to the embedded low-cost antenna and chip, smartphone GNSS modules present many problems. Typically, the carrier-to-noise-density ratio (C/N0) of a smartphone is approximately 10 dB-Hz lower than that of a geodetic receiver, and it is more sensitive to multipath interference [5]. In addition, the correlation of the observation quality with C/N0 is stronger than that with the elevation [6], and the pseudo-range noise of a smartphone is approximately 10 times larger than that of a geodetic receiver. Moreover, the carrier-phase noise is approximately 3-5 times larger than that of a geodetic receiver [7], and it is sensitive to the duty cycle mechanism [6,8]. Consequently, the carrier phase presents frequent cycle slips and continuous loss of lock. Although these observation problems greatly limit accuracy, high-precision positioning at the centimetre level is still achievable in smartphones [5]. Technologies such as precise point positioning, real-time kinematic (RTK) positioning, and network RTK positioning have been used to develop high-precision applications for smartphones. [PERSON] et al. [9] used GNSS raw measurements from smartphones for positioning tests, achieving decimetre-level accuracy through relative positioning. [PERSON] et al. [10] equipped both a base station and a rover with smartphones, achieving decimetre-level RTK positioning accuracy and centimetre-level repeatability. [PERSON] et al. [5] implemented a method for precise point positioning based on the time-difference carrier phase using a Nexus 9 smart device achieving sub-metre-level positioning accuracy. [PERSON] et al.