## 2 Carrier Phase Observations for Static Measurements Provided by GNSS Chipsets  
Obtaining high static positioning accuracies using GNSS technology strictly depends on carrier phase observations and the capability to fix their ambiguities to the correct integer values. Therefore, recently, scientists have been paying special attention to the analysis of such signals being tracked by smartphones. An example of raw measurements data collected by a Huawei P30 Pro smartphone (Union of Huawei Investment & Holding Co., Ltd., Shenzhen, China) is presented in Figure 1.  
As we can see from Figure 1, the smartphone recorded the following GNSS data:  
- GPS L1, L5 carrier phase measurements transmitted at 1575.42 and 1176.45 MHz frequencies. - GPS pseudoranges P(L1) and P(L5). - GALILEO E1, E5a carrier phase measurements. - GALILEO pseudoranges P(E1) and P(E5a). - GLONASS L1 carrier phase measurements and pseudoranges. It should be noted that the GPS L1 and L5 frequencies correspond with GALILEO E1 and E5a center frequencies. However, whereas all the satellites of GALILEO provide the L5 signal, in GPS, there are currently only 14 of them (where 12 are transmitted by satellites from the GPS IIF block and 2  
Figure 1: Single epoch for a Huawei P30 Pro smartphone collected in RINEX 3.03 (Receiver Independent Exchange Format 3.03). from the GPS III block). In the case of double frequencies of L1-L5 GPS data in a relative positioning (static or RTK), we can write the following double-difference (DD) observation equations [19]:  
\[\phi_{L1}(t)=\frac{\varrho(t)}{\lambda_{L1}}+N1+\varepsilon_{\phi_{L1}}(t) \tag{1}\]  
\[P(L1)=\varrho(t)+\varepsilon_{PL1}(t) \tag{2}\]  
\[\phi_{LS}(t)=\frac{\varrho(t)}{\lambda_{L5}}+N5+\varepsilon_{\phi_{LS}}(t) \tag{3}\]  
\[P(L5)=\varrho(t)+\varepsilon_{PL5}(t) \tag{4}\]  
where: \(\phi_{L1},\phi_{L5}\)--observations of DD phase measurements for L1 and L5 frequencies (in cycles), P(L1) and P(L5)--observations of DD in code measurements (m), and \(\varepsilon_{\phi_{L1}},\varepsilon_{\phi_{L5}},\varepsilon_{PL1},\ \varepsilon_{PL5}\)--errors of phase and code DD observations. In some papers, mainly the signal-to-noise ratio has been analyzed, but we decided to focus on single epoch double-difference N1(P1) and N1(P5) float GPS-only solutions based on P(L1) and P(L5) codes, using Equations (1), (2) and (4), according to the formulas:  
\[N1(P1)=\phi_{L1}(t)-\frac{P(L1)}{\lambda_{L1}} \tag{5}\]  
\[N1(P5)=\phi_{L1}(t)-\frac{P(L5)}{\lambda_{L1}} \tag{6}\]  
Time series of residuals of double-difference single epoch N1(P1) and N1(P5) GPS-only combinations for a geodetic receiver and smartphone is presented in Section 6. Concerning the ratio of the power of the carrier phase signal to the power of noise, it should be noted that it is the most important factor depending on the class of receiver and type of antenna. There are limitations of embedded smartphone GNSS antennas addressed to the subject of low gain and low multipath elimination. Additionally, for precise positioning, mobile phone antennas require accurate phase center offset determination. Recent attempts focused on obtaining phase center information for the Huawei P30 were followed in Reference [20], where ambiguity fixing for a short baseline between the reference antenna and antenna being calibrated was required. After fixing ambiguities on L1 only, the authors showed that the antenna is located on the top of the smartphone (obtained with centimeters level of accuracy), which may be insufficient for precise static measurements. This is the main drawback to achieve high-accuracy positioning, especially because of problems with determining its exact location, which is usually not pointed out by the manufacturers. In GNSS static measurements, we need to deal with additional factors concerning not only the type of equipment we use (receivers, antennas), but also with methods of planning and conducting the field surveys.