# Galileo Single Point Positioning Assessment Including FOC Satellites in Eccentric Orbits
## 1 Introduction
They analyzed Milena (E14) and Doresa (E18) broadcast ephemeris in [5; 6] and their code multipath error [7] by using the short time Fourier transform and wavelet analysis [8] showing that multipath performance of Milena (E14) and Doresa (E18) satellites are the same as the other Galileo FOC satellites also when a mobile phone is used as the receiver [9]. In 2017, [PERSON] and [PERSON] analyzed Galileo E5's RTK performance [10]. They showed that instantaneous ambiguity resolution is possible if a multipath correction is done, but in their analysis, they excluded both the Milena (E14) and Doresa (E18) satellites; [PERSON] et al. [11] tested the performance of a single-frequency L5/E5a array-aided state-space RTK algorithm including in the solution also the Doresa (E18) satellite. In 2018, [PERSON] et al. [12] investigated the potential use of the Milena (E14) and Doresa (E18) satellites for positioning purposes. They evaluated the applicability of these satellites to precise GNSS positioning focusing on relative kinematic positioning as an instantaneous solution in multi-baseline mode. Their study revealed that the Milena (E14) and Doresa (E18) satellites were fully usable in most geodetic surveying when precise ephemerides of the satellites are provided. [PERSON] et al. [13] studied the formal and the empirical ambiguity success rates for long baselines with different frequency combinations of Galileo signals including both the Milena (E14) and Doresa (E18) satellites. Actually, it is very important to have two additional satellites available since currently, the Galileo system is not yet complete and the accuracy in the position increases as the number of visible satellites increases. Indeed, an in-depth study on the use of these satellites in the single-point positioning domain has not yet been carried out, and this prompted us to undertake this study. Figure 1 shows the ground track of Milena (E14) plotted in blue, Doresa (E18) plotted in red, E1 plotted in yellow, and E2 plotted in green, over a period of 24 h on DOY 52 2018. From the figure, it can be noted that the maximum latitude of the Milena (E14) and Doresa (E18) satellites is smaller than that of the other two Galileo satellites depicted. This is due to the lower inclination of the Milena  
(E14) and Doresa (E18) orbits of 49.850 degrees with respect to the 56.0 degrees of the other Galileo satellites; indeed the maximum latitude of a satellite ground track is equal to the orbital inclination angle. For an ideal Keplerian orbit, the orbital period \(T\) is set by:  
\[T=2\pi\sqrt{\frac{a^{3}}{\mu}} \tag{1}\]  
where \(a\) is the semi-major axis of the orbit and \(\mu=3.986005\cdot 10^{5}\)\(\frac{\mathrm{km}^{3}}{\mathrm{g}^{2}}\) is the product of the universal gravitational constant and the mass of the Earth. Thus, the Galileo satellites in nominal orbit have an orbital period of about 14.08 h. The Milena (E14) and Doresa (E18) satellites instead, due to the lower semi-major axis (see Table 1) of the orbit, show an orbital period of 12.97 h. The effects of the different orbital periods can be noticed by looking at the figure: the nodes (i.e., points where the trace intersects the Equator line) are unequally spaced in the tracks of the Milena and Doresa satellites with respect to the other FOC satellites represented ([PERSON] et al. [14]). The main objective of this paper is the evaluation of the Milena (E14) and Doresa (E18) satellites' performance in the single-point positioning domain for the E1, E5a, E5b, and E5 signals. In order to provide a good indication of the positioning performance of elliptical satellites, we first evaluated the availability in terms of the number of visible satellites, of the Dilution of Precision parameters (DOP), and the percentage of time span over which the position solutions can be acquired. After this analysis, the single-point positioning solution was calculated every second for the E1, E5a, E5b, and E5 frequencies by using first broadcast ephemerides and then precise ones.