# Galileo Single Point Positioning Assessment Including FOC Satellites in Eccentric Orbits

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Methodology

#### 2.2. Experimental Setup

_{0}below 30 dB/Hz.

## 3. Results

_{0}) of the Milena (E14), Doresa (E18), E1, E2, and E19 (IOV) Galileo satellites with respect to satellite elevation angle for the different frequencies E1, E5a, E5b, and E5 depicted in Panels (a)–(d), respectively, during DOYs 52–71 of 2018. Each panel shows the average of C/N

_{0}over elevation bins of 10 degrees. In the figure, the E19 satellite was added as representative of IOV satellites. The signals transmitted by the E19 satellite showed a lower level of C/N

_{0}than those transmitted by the FOC satellites. This occurred because IOV satellites have less transmission power than FOC satellites since 27 May 2014 [1], when a power anomaly on the E20 satellite led the E5 and E6 signals to a permanent loss of power. After this failure, all IOV satellites were backed-off, and thus, their signals have less transmitted power than the FOC satellites. The evolution of the C/N

_{0}of the E14 and E18 satellites is similar to that of the other FOC satellites in the YEL2 site. As expected, the Milena (E14) and Doresa (E18) satellites showed a higher C/N

_{0}with respect to the other FOC satellites, confirming results shown by Paziewski et al. [12]. This behavior is due to lower altitude of Milena (E14) and Doresa (E18) caused by their elliptical orbit.

_{0}) at the different frequencies of the Milena (E14) and Doresa (E18) satellites. Panel (a) is related to the Milena (E14) satellite, while Panel (b) to Doresa (E18). In both panels, the E1, E5a, E5b, and E5 signals are plotted in blue, red, yellow, and purple, respectively. The E1 signal had a C/N

_{0}higher than the E5a signal up to 30 degrees. Between 30 degrees and 35 degrees, the two signals showed the same C/N

_{0}, and then, starting from 40 degrees, E5a had a C/N

_{0}higher than the E1 signal. Results reported in figure confirm the results reported by Zaminpardaz [10] with the exception of the E1 and the E5a signals at low elevation angles.

## 4. Discussion

- The evolution of the C/N
_{0}of the E14 and E18 satellites was similar to that of the other FOC satellites in the YEL2 site. As expected, the Milena (E14) and Doresa (E18) satellites showed a higher C/N_{0}with respect to the other FOC satellites, confirming results shown in previous studies. This behavior was due to the lower altitude of Milena (E14) and Doresa (E18) caused by their elliptical orbit. The comparison between the carrier-to-noise density ratio (C/N_{0}) at the different frequencies of the Milena (E14) and Doresa (E18) satellites revealed that for both satellites, the E5 signal had a C/N_{0}higher than the others. Starting from 40 degrees, it can be seen that the E5b signal had a C/N_{0}higher than the E5a signal and this higher than E1. For elevation angles lower than 30 degrees, the E1 signal showed a carrier-to-noise density ratio higher than E5b. - As expected, the inclusion of the two satellites improved:
- -
- the system availability, varying it from 94.1–97.94%.
- -
- the GDOP, PDOP, HDOP, and VDOP parameters in each DOY analyzed;
- -
- the percentages of achieved positioning solutions by about 5% regardless of the frequency used.

- When the broadcast ephemerides were used, nevertheless, the above results of the inclusion of the satellites worsened both the horizontal and vertical accuracy of the solution. The deterioration of the horizontal accuracy went from 0.17 m with the E5a frequency measurements to 0.74 m with the E1 measurements. The reduction of vertical accuracy went from 0.68 m for the E5a to 1.2 m for the E1 measurements. This was not completely expected as both the HDOP and VDOP parameters decreased when these satellites were included in the solution calculation. However, if precise ephemerides are used instead of broadcast ones, both the horizontal and the vertical accuracy remained stable; actually, for the E5b frequency, the DRMS improved by almost 0.5 m.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Ground tracks of the Milena (E14), Doresa (E18), E1, and E2 Galileo satellites depicted in blue, red, yellow, and green, respectively, on DOY 52 2018. In the figure, for better readability, only four satellites are shown.

**Figure 2.**Flowchart representation of the algorithm developed for the determination of receiver position and Dilution Of Precision (DOP) parameters; TGD stands for Time Group Delay, while brdc for broadcast.

**Figure 3.**Carrier-to-Noise density ratio (C/N

_{0}) of the Milena (E14), Doresa (E18), E1, E2, and E19 (IOV) Galileo satellites (depicted in blue, red, yellow, green, and purple dotted lines, respectively) on different frequencies as a function of satellite elevation. The E1, E5a, E5b, and E5 frequencies are reported in (

**a**–

**d**), respectively. Each panel shows the average of C/N

_{0}over elevation bins of 10 degrees. Data plotted refer to DOYs 52–71 of 2018.

**Figure 4.**Carrier-to-noise density ratio (C/N

_{0}) of the Milena (E14) and Doresa (E18) satellites on different frequencies, E1 (blue), E5a (red), E5b (yellow), and E5 (purple), as a function of satellite elevation plotted in (

**a**,

**b**) respectively.

**Figure 5.**Percentage of epochs with the same satellite number. The height of each bin represents the percentage of epochs with the number of satellites indicated on the xaxis. Blue bars refer to the Galileo configuration without the Milena (E14) and Doresa (E18) satellites, while red bars refer to the Galileo constellation including the Milena (E14) and Doresa (E18) satellites.

**Figure 6.**Time evolution of the dilution of precision parameters of the Galileo constellation in the YEL2location. The blue points represent DOP values occurring when the Milena (E14) and Doresa (E18) satellites were excluded. The red points represent DOP values obtained including the Milena (E14) and Doresa (E18) satellites. The ticks on the x axis are spaced 86,400 s (equal to one day); in this way, each tick corresponds to a day.

**Figure 8.**Daily dilution of precision comparison of the Galileo constellation in the YEL2 location excluding (blue bars) and including (red bars) the Milena (E14) and Doresa (E18) satellites. GDOP (Geometric Dilution Of Precision), PDOP (Position Dilution Of Precision), HDOP (Horizontal Dilution Of Precision), and VDOP (Vertical Dilution Of Precision) are compared in (

**a**–

**d**), respectively.

**Figure 9.**Percentage of Galileo constellation achieved positioning solutions in the YEL2 location excluding (blue bars) and including (red bars) the Milena (E14) and Doresa (E18) satellites for the E1, E5a, E5b, and E5 Galileo signal. The analysis was carried out on 1,728,000 epochs.

**Figure 10.**Scatter plot of the E1, E5a, E5b, and E5 single-point position error reported in (

**a**–

**d**). Blue and red markers represent errors when the solution was obtained by excluding or including the measurements coming from the Milena (E14) and Doresa (E18) satellites, respectively. The solution was achieved by using broadcast ephemeris.

**Figure 11.**E1, E5a, E5b, and E5 single-point position vertical error time series reported in (

**a**–

**d**). Blue and red markers represent errors when the solution was obtained by excluding or including the measurements coming from the Milena (E14) and Doresa (E18) satellites, respectively. The solution was achieved by using broadcast ephemeris.

**Figure 12.**Density histograms of the E1, E5a, E5b, and E5 single-point position coordinates’ error. Each line refers to a specific frequency: the first from above refers to the frequency E1, the second to E5a, the third to E5b, and the fourth to E5. Blue and red histograms were obtained excluding and including the measurements coming from the Milena (E14) and Doresa (E18) satellites, respectively. Solutions were achieved by using broadcast ephemeris.

**Figure 13.**Scatter plot of the E1, E5a, E5b, and E5 single-point position error reported in (

**a**–

**d**). Blue and red markers represent errors when the solution was obtained by using excluding and including the measurements coming from the Milena (E14) and Doresa (E18) satellites, respectively. Solutions were achieved by using precise SP3 ephemeris.

**Figure 14.**E1, E5a, E5b, and E5 single-point position time series of the vertical error reported in (

**a**–

**d**). Blue and red markers represent errors when the solution was obtained by excluding or including the measurements coming from the Milena (E14) and Doresa (E18) satellites, respectively. The solution was achieved by using precise ephemeris.

**Figure 15.**Density histograms of the E1, E5a, E5b, and E5 single-point position coordinates’ error. Each line refers to a specific frequency: the first from above refers to the frequency E1, the second to E5a, the third to E5b, and the fourth to E5. Blue and red histograms were obtained excluding and including the measurements coming from the Milena (E14) and Doresa (E18) satellites, respectively. The solution was achieved by using precise ephemeris.

**Figure 16.**Orbital error of the Milena (E14) satellite plotted versus time. The ticks on the x-axis are spaced 86,400 s (equal to one day); in this way, each tick corresponds to a day.

**Figure 17.**Orbital error of the Doresa (E18) satellite plotted versus time. The ticks on the x-axis are spaced 86,400 s (equal to one day); in this way, each tick corresponds to a day.

**Figure 18.**Analysis of the causes of the largest position errors. The time series of errors on the east, north, and vertical coordinates are represented in the first, second, and third row, respectively. The fourth row shows the orbital errors of the E14 (first and third columns) and E18 (second column) satellites. Finally, the fifth row shows the time series of HDOP (blue), VDOP (red), and the number of visible satellites (yellow). Each column shows the data related to the same time interval.

**Table 1.**Galileo satellite orbital parameters. IOV, In-Orbit Validation; FOC, Full Operational Capability.

Satellite | Semi-Major Axis (km) | Eccentricity | Inclination (deg) | Orbital Period (h) |
---|---|---|---|---|

IOV and FOC | 29,599.8 | 0.000 | 56.0 | 14.08 |

E14 and E18 | 27,977.6 | 0.162 | 49.850 | 12.97 |

**Table 2.**RMS comparison between two scenarios (including or excluding the Milena (E14) and Doresa (E18) satellites) analyzed. Broadcast ephemeris was used. DRMS, Distance Root Mean Squared.

Freq. | DRMS Excl. | Vert. RMS Excl. | DRMS Incl. | Vert. RMS Incl. |
---|---|---|---|---|

E1 | 1.21 | 2.74 | 1.95 | 3.97 |

E5a | 2.21 | 5.80 | 2.38 | 6.48 |

E5b | 1.91 | 4.66 | 2.45 | 5.77 |

E5 | 1.85 | 4.82 | 2.38 | 5.71 |

**Table 3.**RMS comparison between two scenarios (including or excluding the Milena (E14) and Doresa (E18) satellites) analyzed. Precise ephemeris used.

Freq. | DRMS Excl. | Vert. RMS Excl. | DRMS Incl. | Vert. RMS Incl. |
---|---|---|---|---|

E1 | 0.97 | 2.23 | 0.94 | 2.06 |

E5a | 2.08 | 5.56 | 1.60 | 5.45 |

E5b | 1.55 | 4.06 | 1.53 | 4.12 |

E5 | 1.59 | 4.39 | 1.53 | 4.28 |

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**MDPI and ACS Style**

Robustelli, U.; Pugliano, G.
Galileo Single Point Positioning Assessment Including FOC Satellites in Eccentric Orbits. *Remote Sens.* **2019**, *11*, 1555.
https://doi.org/10.3390/rs11131555

**AMA Style**

Robustelli U, Pugliano G.
Galileo Single Point Positioning Assessment Including FOC Satellites in Eccentric Orbits. *Remote Sensing*. 2019; 11(13):1555.
https://doi.org/10.3390/rs11131555

**Chicago/Turabian Style**

Robustelli, Umberto, and Giovanni Pugliano.
2019. "Galileo Single Point Positioning Assessment Including FOC Satellites in Eccentric Orbits" *Remote Sensing* 11, no. 13: 1555.
https://doi.org/10.3390/rs11131555