## 4 Results
### Evaluation of Single Point Positioning Error  
The analysis of SPP in Easting, Northing and Up are summarised in the Tables 10-12. In particular, the tables show the means referring to sub-datasets \(\Delta\)E, \(\Delta\)N, and \(\Delta\)U: \(\Delta\)E\({}_{\text{Mm}}\), \(\Delta\)N\({}_{\text{Mm}}\), \(\Delta\)U\({}_{\text{Mm}}\) and \(\Delta\)E\({}_{\text{Km}}\),  
From Tables 10-12, it is possible to obtain information about the mean error for Single Point Positioning. For the Easting coordinate, at 60 min, the major error is equal to 0.706 m for the \(\Delta\)E\({}_{\text{Km}}\) sub-dataset, while the minor one is equal to 0.439 m for \(\Delta\)E\({}_{\text{Mm}}\). For the Northing positioning at 60 min, the major error is committed for the \(\Delta\)N sub-dataset and is equal to 2.509 m, while the minor Northing error is, instead, equal to 1.984 m for \(\Delta\)N\({}_{\text{Mm}}\) and \(\Delta\)N\({}_{\text{Km}}\). At 60 min, the major positioning error Up is recorded for sub-databases, \(\Delta\)U\({}_{\text{Mm}}\) and \(\Delta\)U\({}_{\text{Km}}\), and is equal to 5.916 m; the minor one is equal to 5.346 m for the sub-database \(\Delta\)U.  
By observing the R\({}^{2}\) values, it is possible to assess the functional relationships between the averages of the SPP errors (for each sub-dataset) and the acquisition time; in particular, linear regression was used for all sub-datasets.  
Unlike DGNSS positioning, by observing the coefficient of determination R\({}^{2}\), it is possible to note that for the SPP, there is generally a linear relationship between the observation times and positioning errors that is between moderate and strong.  
For a more cautious assessment of the degree of relationship between variables, it is advisable to analyse the R\({}^{2}\) values for the sub-datasets according to the positionings of Easting, Northing and Up.  
The sub-datasets for Easting, \(\Delta\)E, \(\Delta\)E\({}_{\text{Mm}}\) and \(\Delta\)E\({}_{\text{Km}}\), show the strongest and most consistent linear functional relationship between variables, with R\({}^{2}\) values equal to 0.94, 0.88 and 0.92. For Northing positioning, the sub-dataset \(\Delta\)N\({}_{\text{Km}}\) demonstrates a strong relationship between variables with a value of R\({}^{2}\) = 0.94; however, \(\Delta\)N and \(\Delta\)N\({}_{\text{Mm}}\), with values equal to 0.66 and 0.58, instead demonstrate a moderate relationship between variables. As a precaution, a moderate relationship between the variables can be assumed, but of course, it is not as strong as that for the Easting positioning. The absolute highest R\({}^{2}\) value is expressed by the Up sub-dataset \(\Delta\)U\({}_{\text{Km}}\) (R\({}^{2}\) = 0.98), and not to be underestimated is the \(\Delta\)U with an R\({}^{2}\) = 0.93 but it is equally true that the Up positioning also expresses the lowest value with \(\Delta\)U\({}_{\text{Mm}}\) (R\({}^{2}\) = 0.49). Even for the UP positioning, it can be conservatively assumed that there is no more than a moderate linear relationship between the variables [30].  
Figure 5 shows an example of the linear regression performed for the sub-datasets \(\Delta\)E, \(\Delta\)N and \(\Delta\)U in Single Point Positioning.