# The Implementation of Precise Point Positioning (PPP): A Comprehensive Review
## 4 Practical Considerations and Experimental Results
### Static Results  
Static PPP offers distinct advantages in specific applications, notably surveying and mapping. Conventionally, static PPP algorithms undergo evaluation using data from IGS stations. In this work, we utilized the daily GNSS observations of IGS stations, available in RINEX format, and a 30-second sampling rate through the IGS data center [86]. The YELL station was chosen randomly for static PPP testing. The station reference position is obtained from the SINEX (Solution INdependent EXchange) file, one of the IGS products (it comes with the extension (*.snx)).  
Our measurements were based on pseudorange and carrier-phase observations, with measurement standard deviation (STD) values determined inversely proportional to thesquared sine of satellite elevation angles. An elevation mask of 7\({}^{\circ}\) was also applied to filter out low-elevation satellites. Since carrier-phase measurements are much more precise than pseudoranges, the carrier-phase STD was reduced to be (1/100) of the code STD. To account for variations in signal-to-noise ratios and signal structures between GPS and GLONASS, STD values for GLONASS code observations were scaled by a factor of 3, and phase observations were scaled by a factor of 1.5, as detailed in [87].  
As PPP standalone positioning lacks a deterministic system model, we relied on the stochastic characteristics of the states to describe uncertainties in the system model (Q matrix). In our model, the three position parameters were considered random constants. The receiver clock bias was modeled as white noise, whereas the ISB between GLONASS and GPS, along with the zenith wet delay, were modeled as random walk processes. Float ambiguities were treated as random constants, with initial parameters obtained from a Least Squares (LS) SPP solution.  
Figure 4 depicts the 3D position errors for the YELL station in Yellowknife, Canada, observed over a 24-hour period on 20 July 2023. The number of visible GPS/GLONASS satellites fluctuated between 15 and 22 during the day. The position root mean square errors (RMSE) measured 1.2 cm, 1.1 cm, and 1.3 cm for the east, north, and up directions, respectively. These errors were calculated after the initial 20 min to exclude the impact of initial convergence. All three errors converged to fewer than 10 cm after approximately 10 min and fewer than 2 cm after about 45 min.  
In some applications with a mix of kinematic and static dynamics, the assumption that the receiver is static is no longer valid. Therefore, the data have to be processed in a kinematic mode, which means the receiver position can change every epoch and cannot be modeled as a random constant. For instance, in land vehicle navigation, positions can be modeled as random walk processes with substantial uncertainty, e.g., (100 m/\(\sqrt{\mathrm{s}}\)). Also, the position can be initialized every epoch from an LS SPP. Motion constraints, if there are any, can also be applied.  
We processed the same data from the YELL station in kinematic mode, disregarding the static assumption, to illustrate the different impacts of static and kinematic positioning on static data. As shown in Figure 5, position errors exhibit less smoothness than the static case. Furthermore, the RMSE errors are relatively higher, measuring 3.1 cm, 2.6 cm, and 6.3 cm for the east, north, and up directions, respectively. These values are calculated excluding the first 20 min and the last hour. The spikes in errors at the end of the day result from the interpolation of precise satellite corrections using edge points, causing a lack of centered interpolation points. In contrast, such interpolation at edge points had a lesser effect on the static case because the assumption of constant receiver location prevented  
Figure 4: An illustration of static DF-PPP positioning utilizing data from the YELL station on 20 July 2023.  
abrupt position changes. While the east and north position errors dropped below 10 cm after around 30 min, the up direction took a few hours and was not as stable.