## 3 Characteristics of Xiaomi Mi 8 Raw GNSS Observations
### Carrier Phase Observations  
To achieve high-precision positioning with smartphones, it may be necessary to use carrier phase observations, which are up to 100 times more precise than pseudorange observations. The characteristics of carrier phase observations in terms of observation noise and cycle slips are discussed below.  
A third-derivative approach is applied to analyze the noise of carrier phase observations, which excludes the low-frequency measurement delays while preserving the high-frequency noise [30]. Figure 12 shows the carrier phase noise comparison of Xiaomi Mi 8 and Septentrio PolaRx5 receiver. The following features are seen from Figure 12: (1) The carrier phase noise of the survey-grade receiver ranges from \(-0.5\) to \(0.5\) cm, while the noise of Xiaomi Mi 8 is larger; this may be caused by the low-cost linear polarized PIF antenna embedded in the smartphone. Regardless, the carrier phase noise of Xiaomi Mi 8 is less than 2 cm, which means it may have potential for high precision positioning applications. (2) For unknown reasons, abnormal interruption of signal tracking occurs frequently, as seen on satellite E30.  
In addition to the noise level of carrier phase observations, the characteristics of the cycle slip are also important factors which may impact the high-precision positioning performance of smartphones. It can be seen from Figure 2 that, due to the low cost linear polarization antenna embedded in Xiaomi Mi 8, frequent ADRS exists, especially at low elevations. At the same time, in the static test, with the survey-grade antenna and receiver set up as a reference station near the Xiaomi Mi 8, the cycle slips in the Xiaomi Mi 8 carrier phase observations are also detected by double-difference (DD) observations between stations and epochs. The statistical information of Xiaomi Mi 8 carrier phase cycle slips under static and dynamic environments is given in Table 2, in which the ADRS number is the cycle slips marked by Xiaomi Mi 8 itself, detected cycle slips are the number of detected cycle slips by the DD observations, and cycle slip percentage is the ADRS number divided by the total carrier phase observations for each system and frequency. Clearly, in the static test, the cycle slip percentage remains below 0.862%, except that of GLONASS which is as large as 1.823%. It should be noted that most ADRS labels are confirmed as correct, but a few cycle slips are not marked. Thus, in the following positioning tests, when using carrier phase observations, the ADRS labels are used as references in the cycle slip  
Figure 12: The carrier phase noise comparison of Xiaomi Mi 8 and Septentrio receiver for satellites G08/E30/J03/C07/R10 about (**a**) L1/E1 and (**b**) L5/E5 measurements. The carrier phase noises of Xiaomi Mi 8 are shown by red dots, and the carrier phase noises of the Septentrio receiver are shown by green dots.  
detection. As to the GNSS data collected in a dynamic open environment (track 1), the carrier phase cycle slip percentages of most satellites and frequencies are over 18.37%. In dynamic GNSS-degraded environments (track 2), the carrier phase cycle slip percentages further increase to over 30.31%, even to 62.25% for GLONASS satellites. Considering that the pseudorange outlier percentage in the complex dynamic environment shown in Table 1 is also much higher than that in the open static environment, it is concluded that the PPP or RTK method using carrier phases, which requires the ambiguity resolution, is not suitable for Xiaomi Mi 8 high precision navigation in urban environments. Therefore, this paper develops a new algorithm for Xiaomi Mi 8 navigation. On one hand, this algorithm should make full use of the high accuracy phase observations; at the same time, it should take into account the frequent carrier phase cycle slips and high percentage of pseudorange gross errors in raw GNSS observations in a complex dynamic environment, and avoid estimating the ambiguities. The details of the algorithm are discussed in Section 4.