# A Galileo IOV assessment: measurement and position domain

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## Abstract

The European GNSS, Galileo, is currently in its in-orbit validation (IOV) phase where four satellites are finally available for computing the user position. In this phase, the analysis of the measurements and position velocity and time (PVT) obtained from the IOV satellites can provide insight into the potentialities of the Galileo system. A methodology is suggested for the analysis of the Galileo IOV pseudorange and pseudorange rates collected from the E1 and E5 frequencies. Several days of data were collected and processed to determine figures of merit such as root mean square and maximum errors of the Galileo observables. From the analysis, it emerges that Galileo is able to achieve better accuracy than GPS. A thorough analysis of the PVT performance is also carried out using broadcast ephemerides. Galileo and GPS PVTs are compared under similar geometry conditions showing the potential of the Galileo system.

### Keywords

Accuracy Galileo In-orbit validation IOV Multi-frequency Position velocity and time PVT Precise orbits Pseudorange Pseudorange rate## Introduction

Galileo, the European Global Navigation Satellite System (GNSS), is currently in its in-orbit validation (IOV) phase, and four satellites are finally available for computing the user position. The availability of the Galileo quartet allows researchers to investigate the potentiality of the Galileo system and extend previous results based on the signals broadcast by the Galileo in-orbit validation element (GIOVE) experimental satellites. More specifically, although the two GIOVE satellites did not allow the computation of the user position, it was possible to test the performance of new acquisition and tracking algorithms designed to fully exploit the benefits of the new Galileo signals. GIOVE satellites also allowed researchers to assess the ranging capabilities of future Galileo signals (Angrisano et al. 2012) and provided a significant experience for the design of next-generation Galileo satellites.

The first two IOV satellites were launched in October 2011, whereas the satellite quartet required for positioning was completed 1 year after, in October 2012. In the same year, GIOVE-A and GIOVE-B were decommissioned. The four IOV satellites transmit signals on E1, E5 and E6 bands, and Galileo-only positioning has been possible since March 2013, when the European Space Agency (ESA) started disseminating valid Galileo ephemerides. Although Galileo ephemerides are still broadcast in a discontinuous way and without warranty, they allow position computation using the sole Galileo signal-in-space (SIS). Since March 2013, several research groups reported successful Galileo-only positioning including the authors (Angrisano et al. 2013).

Despite the race to demonstrate Galileo-only positioning, limited analysis has been performed to evaluate the accuracy of the measurements broadcast from Galileo satellites. In particular, ranging capabilities of the IOV satellites can be assessed employing the precise orbits determined using the approach described in (Steigenberger et al. 2011) and available from ftp://cddis.gsfc.nasa.gov/pub/gps/products/mgex. These orbits, the availability of ionospheric corrections and a professional receiver placed in a surveyed location can be used to determine figures of merits such as the root mean square (RMS) and the maximum error of the Galileo observables, i.e., pseudoranges (PR) and PR rates (Angrisano et al. 2013).

A methodology is suggested for the analysis of the Galileo IOV PRs and PR rates collected from the E1BC and E5a frequencies. The methodology is an extension of the techniques developed in (Angrisano et al. 2012) and employed to characterize the PRs of GIOVE satellites. With respect to (Angrisano et al. 2012), the following elements of innovation have been introduced: Precise ephemerides are used to obtain a more accurate satellites position, and global ionospheric maps (GIM) are adopted to compute the ionospheric delay. Finally, the analysis is extended to PR rates and to E5a observables.

Several hours of data were collected using a Septentrio PolarRxS receiver and used to characterize the quality of Galileo observables. From the analysis, it emerges that Galileo measurements have accuracies comparable with those of GPS, showing the potential of the European GNSS.

It is noted that, although several groups focused on Galileo-only or combined Galileo-GPS positioning, no result has been published on the accuracy of IOV measurements. These results along with the methodology proposed are the main contributions of this paper. In addition to this, the benefits of combined GPS-Galileo positioning are also highlighted and some considerations on Galileo-only location are provided. More specifically, results obtained using Galileo broadcast ephemerides are also analyzed.

The analysis presented here is an extension of the conference contribution (Angrisano et al. 2013) published by the authors. With respect to the conference paper, a more thorough analysis of the IOV measurements and Galileo position have been performed, including results from the E5a band which was not previously considered. Additional analysis, using single differences (SD), has also been carried out to investigate the contribution of thermal noise. Moreover, the sample results presented were obtained considering a different GPS week from the one provided in (Angrisano et al. 2013). For this reason, the results presented in the following are complementary to those analyzed in (Angrisano et al. 2013).

The navigation states and the methodology developed for the analysis are described in the “Methodology” Section. The experimental setup adopted is detailed in the third section, and experimental results relative to the Galileo observables are described in the fourth section. Galileo PVT performance is discussed in the PVT analysis section, and some conclusions are finally drawn in the last section.

## Methodology

In this section, a detailed description of the methodology proposed is provided. Two different approaches are adopted for the position and the measurement domain analyses. First, the methodology used to evaluate the performance of Galileo single-point positioning is described, and then the multi-constellation approach is illustrated. In the second part of the section, the methodology for evaluating the measurement accuracy is proposed.

### Position domain

*ρ*is the PR measurement;

*d*is the satellite-receiver distance;

*cdt*

_{ u }is the receiver clock offset scaled by the speed of light

*c;*and

*ɛ*

_{ ρ }contains the residual errors after atmospheric and satellite-related corrections (Hoffmann-Wellenhof et al. 1992, Kaplan and Hegarty 2006, IS-GPS-200 2004)

*ρ*

^{.}is the PR rate measurement obtained from Doppler; \(\dot{d}\) is the geometric distance rate of change; \(c\dot{d}t_{u}\) is the receiver clock drift scaled by the speed of light; and \(\varepsilon_{{\dot{\rho }}}\) accounts for residual errors.

*cdt*

_{GAL}

^{GPS}and \(c\dot{d}t_{\text{GAL}}^{\text{GPS}}\) are the bias and drift between GPS time and GST, respectively. Note that also the PR and PR rate models (1) need to be modified in order to account for additional clock terms. In particular, when Galileo measurements are considered,

*cdt*

_{GAL}

^{GPS}and \(c\dot{d}t_{\text{GAL}}^{\text{GPS}}\) are added to the PR and PR rate models, respectively. Models (2) and (3) will be used to compute and analyze Galileo-only and combined GPS-Galileo navigation solutions, and the flow chart of the algorithms developed is shown in Fig. 2.

In this approach, all the measurements are used to estimate the clock unknowns, providing a better estimation of such parameters. The user position and velocity can also be used to determine true geometric distances and distance rates which, in turn, can be adopted to evaluate PR and PR rate errors along with the clock estimates and precise corrections available from ftp://cddis.gsfc.nasa.gov/pub/gps/products/mgex. A detailed representation of the technique adopted for the evaluation of PR and PR rate errors is depicted in Fig. 2. A more detailed explanation of the methodology adopted can be found in (Angrisano et al. 2013).

*cdt*

_{sv}and \(c\dot{d}t_{\text{sv}}\) are the satellite clock bias and drift;

*cT*

_{GD}is the time group delay scaled by the speed of light;

*cdt*

_{ r }is the relativistic correction;

*cdt*

_{sag}and \(c\dot{d}t_{\text{sag}}\) are the Sagnac effect corrections;

*d*

_{ I }is the ionospheric correction computed using GIM; and

*d*

_{ T }is the tropospheric correction computed using the Hopfield model; a combined GPS/Galileo navigation algorithm is developed in order to compute the clock biases and drifts and to remove them from the raw measurements.

*cdt*

_{ u }

^{GAL}and \(c\dot{d}t_{u}^{\text{GAL}}\) are the bias and the drift between receiver time and GST. E5a raw PR and PR rate measurements are corrected for the satellite clock errors, relativistic effects, the Sagnac and atmospheric effects as for E1. After computing the corrected PRs and PR rates, their residual error is defined as:

*d*and \(\dot{d}\) are obtained computing satellites position and velocity starting from the satellite ephemeris and the known receiver position.

Since most of the error sources related to the signal propagation have been sensitively reduced, PR and PR rate errors only contain residual biases due to the signal and its transmission.

*ρ*

^{ R1}and

*ρ*

^{ R2}are the PRs from the two receivers;

*cdt*

_{ R1−R2}is the difference between the two receiver clock, and

*ɛ*

_{ SD }is the residual error.

*cdt*

_{ R1−R2}is estimated using all the satellites available, and it is removed to analyze the residual error,

*ɛ*

_{ SD }. Note that single differencing removes all the common systematic errors.

## Experimental setup

In order to collect Galileo and GPS observables, a Javad RingAnt-G3T was mounted on the rooftop of the European Microwave Signature Laboratory (EMSL) in the Joint Research Centre (JRC) premises in Ispra, Italy. The EMSL, which is the highest building in the area was selected in order to minimize the amount of multipath received by the antenna.

The antenna was then fed to a Septentrio PolarRxS receiver able to simultaneously collect GPS, GLONASS and Galileo measurements on several GNSS bands. Both Galileo E1, tracked considering the BOC(1,1) modulation, and E5a signals are considered, and a comparison between measurements from the two frequencies is provided. A second Septentrio PolarRxS receiver was used for SD processing.

In order to verify the hypothesis of absence of multipath, data collected using the PolarRxS receiver were processed using the translating, editing and quality checking (TEQC) software (Estey and Meertens 1999). TEQC allows the analysis of the impact of multipath and ionospheric disturbances at a given site. With respect to multipath, a metric is obtained by combining PR and carrier phase measurements. Large and correlated values of this metric indicate the presence of multipath. In this case, the observed multipath metric assumes low values supporting the hypothesis of reduced multipath.

The result presented below was obtained using a Delay Lock Loop (DLL) bandwidth equal to 0.25 Hz. The same processing parameters were used for GPS and Galileo. The phase lock loop (PLL) bandwidth was set to 15 Hz for all the signals. The integration time was set to 10 ms (default value in the Septentrio PolarRxS receiver).

The position of the antenna was carefully surveyed using double difference carrier phase positioning. This information was in turn used to compute *d* and \(\dot{d}\).

With this calibrated setup, it was possible to collect several days of data which were used for the characterization of Galileo observables discussed in the following.

## Experimental results: Galileo observables

*C*/

*N*

_{0}). For the satellite elevation, a mask angle of ten degrees is adopted, whereas for the

*C*/

*N*

_{0}, values, lower than 35 dB-Hz are discarded.

*C*/

*N*

_{0}increase; the colored bars represent the mean of the errors, while the standard deviation (STD) is represented by the black lines. The mean error reaches a maximum value of 0.50 m for the IOV with PRN 19. The error statistics for the four IOVs are summarized in Table 1.

IOV E1BC PR error statistics

PRN | Max (m) | RMS (m) |
---|---|---|

11 | 2.12 | 0.31 |

12 | 1.86 | 0.35 |

19 | 2.47 | 0.37 |

20 | 2.29 | 0.35 |

*C*/

*N*

_{0}.

As for the PR, the SD error behavior of the four IOVs is similar; RMS value decreases passing from 14 to 5 cm increasing the *C*/*N* _{0}. Note that the RMS value of the SD error has been normalized by a factor \(\sqrt 2\) to account for the noise amplification due to the pseudorange differencing. Figure 4 quantifies the thermal noise contribution to the total RMS error. This contribution is less than a quarter of the total error budget.

*C*/

*N*

_{0}.

*C*/

*N*

_{0}increase. The error mean reaches a maximum value of 0.0162 m/s for IOV with PRN 11 with a STD 0.0125 m/s. The error statistics for the four IOVs are summarized in Table 2.

E1BC IOV PR rate error statistics

PRN | Max (m/s) | RMS (m/s) |
---|---|---|

11 | 0.0911 | 0.010 |

12 | 0.0955 | 0.011 |

19 | 0.0741 | 0.009 |

20 | 0.0946 | 0.008 |

The maximum error varies from 0.0741 m/s, for satellite 19, to 0.0955 m/s, for satellite 12; the RMS values are similar for all satellites with a difference of less than 2 mm/s.

*C*/

*N*

_{0}in Fig. 6.

*C*/

*N*

_{0}.

GPS (L1) and Galileo (E1BC) PR error statistics

System | Max (m) | RMS (m) |
---|---|---|

GPS | 4.49 | 0.84 |

Galileo | 2.47 | 0.34 |

From Table 3, it clearly emerges that Galileo PR errors are smaller than those of GPS. The results obtained are in line with the experimental results presented by (Engel 2008) on GIOVE-B signals and theoretically predicted by (Irsigler et al. 2004) and (Betz 1999).

*C*/

*N*

_{0}in Fig. 7.

GPS (L1) and Galileo (E1BC) PR rate error statistics

System | Max (m/s) | RMS (m/s) |
---|---|---|

GPS | 0.2772 | 0.0101 |

Galileo | 0.0955 | 0.0098 |

The main improvement in PR rate error is related to the maximum error, which is reduced to 9 cm/s from the 27 cm/s observed in the GPS case.

E1BC and E5a PR Error Statistics

Frequency | Max (m) | RMS (m/s) |
---|---|---|

E1 | 2.47 | 0.34 |

E5a | 3.80 | 0.49 |

Despite the theoretical superiority of the E5a signal, performance similar to that of the E1BC signal was observed; the maximum PR error is reduced by more than one meter when moving from E5a to E1BC. The RMS error is reduced by 15 cm. This degradation of the E5a signal was not expected, but a similar phenomenon was observed by (Simsky et al. 2008) and (Simsky et al. 2007) for GIOVE-A measurements. The cause of this slight degradation could be the presence of residual ionospheric errors which are 1.8 times larger on E5a than on E1 (Rodriguez et al. 2004).

The same analysis was performed for the PR rate errors, and the results obtained are shown in Fig. 9.

E1BC and E5a PR rate error statistics

Frequency | Max (m/s) | RMS (m/s) |
---|---|---|

E1 | 0.0955 | 0.010 |

E5a | 0.1097 | 0.011 |

The advantages of E1BC in this case are less evident; the maximum PR rate error is reduced only by 1 cm/s, and the RMS value passes from 10 mm/s to 11 mm/s.

## PVT analysis

In order to analyze Galileo-only positioning performance, broadcast ephemerides are used. The Galileo single-point solution is at first compared with the solution obtained using GPS-only measurements. Then the benefits of the inclusion of Galileo measurements are evaluated computing a combined solution using GPS and Galileo together. Position and velocity performance is analyzed in terms of RMS and maximum error for horizontal and vertical components.

One week of data (GPS week 1744) were used for PVT analysis; data were collected at 1 Hz rate. Note that the week considered is different from the one adopted in (Angrisano et al. 2013), which analyzed data from GPS week 1725. For this reason, the results presented here are complementary to those analyzed in (Angrisano et al. 2013).

In order to perform a fair comparison between GPS and Galileo, similar geometry conditions are considered and the GPS satellite geometry is artificially degraded. In particular, the following approach is adopted. The Galileo-only solution and its satellite geometry are evaluated. GPS satellites are then progressively excluded such that a geometry value similar to the Galileo one is obtained. This process is repeated for each epoch analyzed. The parameter selected to quantify the geometry is the horizontal dilution of precision (HDOP); hence, a fair comparison between the two systems is possible for the horizontal component.

In order to present a fair comparison, the two solutions are analyzed in the same epochs, i.e., during those epochs when the four Galileo satellites are available.

From Fig. 11, it is possible to observe that the Galileo horizontal position error (blue line) is higher than the GPS one (red line) only during the initial phase when the HDOP is higher than 3. This error corresponds to the linear trend observed in Fig. 10 where the Galileo estimated position is far away from the central cloud corresponding to the correct position.

GPS limited DOP and Galileo horizontal position error statistics

Configuration | Max (m) | Mean (m) |
---|---|---|

GPS limited DOP | 38.57 | 6.03 |

Galileo | 51.71 | 3.99 |

From Table 7, it emerges that in average Galileo provides a significant reduction in the position error. In particular, the mean position error is reduced from 6 m to 4 m. The maximum Galileo error is determined by the linear trend discussed above and is essentially due to a poor geometry. For this reason, the Galileo maximum position error exceeds the corresponding GPS value.

*ρ*

_{IF}is the Iono-free observable;

*f*

_{1}and

*f*

_{5}are the E1 and E5a center frequencies; and

*ρ*

_{1}and

*ρ*

_{5}are the PRs from E1 and E5a.

Horizontal and vertical position error statistics for E1, E5a and Iono-free combination

Configuration | Horizontal | Vertical | ||
---|---|---|---|---|

Max (m) | Mean (m) | Max (m) | Mean (m) | |

Single frequency E1 | 51.71 | 3.99 | 59.54 | 5.36 |

Single frequency E5a | 49.56 | 4.68 | 57.37 | 6.19 |

Iono-free E1/E5a | 57.87 | 3.88 | 64.76 | 5.48 |

In order to evaluate the benefits of the inclusion of Galileo measurements, a combined solution is performed using GPS and Galileo measurements according to the methodology outlined in Fig. 1. The performance of the multi-constellation solution is compared with the GPS-only case, and the comparison is carried out in the position domain in terms of mean and maximum error for both horizontal and vertical components.

Horizontal and vertical position error statistics for GPS, GPS/Galileo combination

Configuration | Horizontal | Vertical | ||
---|---|---|---|---|

Max (m) | Mean (m) | Max (m) | Mean (m) | |

GPS | 14.12 | 2.94 | 14.78 | 3.50 |

GPS/Galileo | 11.06 | 2.85 | 14.23 | 3.48 |

The inclusion of the Galileo observations contributes to a reduction in the maximum error for both horizontal and vertical components; the maximum horizontal error is reduced by 3 m passing from 14 m in GPS-only case to 11 m for the multi-constellation case.

### Velocity solution

Horizontal and vertical velocity error statistics for GPS limited DOP, Galileo E1 and E5a

Configuration | Horizontal | Vertical | ||
---|---|---|---|---|

Max (m/s) | Mean (m/s) | Max (m/s) | Mean (m/s) | |

GPS limited DOP | 0.30 | 0.019 | 1.78 | 0.024 |

Galileo E1 | 0.43 | 0.046 | 0.50 | 0.042 |

Galileo E5a | 0.52 | 0.049 | 0.56 | 0.042 |

From Table 10, it clearly emerges that the three configurations are characterized by similar performance and the differences are of cm/s order. The significant degradation in the vertical component of the GPS velocity solution is due to the rejection of satellites fundamental for the vertical geometry.

As for the position, in order to evaluate the benefits of the inclusion of Galileo PR rate measurements, a combined solution is performed using GPS and Galileo observables according to the methodology outlined in Fig. 1. The performance of the multi-constellation configuration is compared with the GPS-only case. The comparison is carried out in the velocity domain in terms of mean and maximum error for both horizontal and vertical components.

Horizontal and vertical velocity error statistics for GPS and GPS\Galileo

Configuration | Horizontal | Vertical | ||
---|---|---|---|---|

Max (m/s) | Mean (m/s) | Max (m/s) | Mean (m/s) | |

GPS | 0.105 | 0.008 | 0.098 | 0.002 |

GPS\Galileo | 0.085 | 0.008 | 0.066 | 0.001 |

From Table 11, it emerges that the two configurations are characterized by similar performance, and the differences are of mm/s order for the mean values, whereas the inclusion of the Galileo measurements reduces the maximum error for both horizontal and vertical components.

## Conclusions

The quality of Galileo PRs and PR rates on the E1BC and E5a frequencies was analyzed using precise ephemerides and GIM. The contribution of the thermal noise was isolated using a SD approach.

The performance of Galileo single-point positioning was investigated using broadcast ephemerides, and a comparison between the E1BC and E5a solutions was carried out in the position/velocity domain.

The performance of GPS was used as a term of comparison, and similar geometry conditions were considered; for a fair comparison, the GPS HDOP was degraded to match the Galileo one.

The benefits of the inclusion of Galileo measurements in single-point positioning were studied, comparing the performance of GPS/Galileo multi-constellation with respect to the GPS-only case, for both horizontal and vertical components. Hence, a complete analysis was performed in the measurement and position domains.

The analysis in the PR domain demonstrates that the measurements from the four IOVs are characterized by similar accuracies: for E1BC, the PR RMS error varies from 0.31 to 0.37 m and the maximum error is of metric order. The analysis on the E1BC and E5a demonstrates that the E5a signal has performance similar to that of the E1BC signal.

For the PR rates, similar conclusions were obtained: The four IOVs provide similar measurement accuracies, and differences are of mm/s order. Differences between E1 and E5a measurements are less evident than in the PR case. When compared to GPS, the Galileo PR errors are reduced by almost 50 %.

The advantages of the European GNSS clearly emerge in terms of maximum and RMS errors, suggesting that the improved structure of Galileo signals allows a GNSS receiver to extract less noisy measurements. Note that for the analysis, the same processing parameters were used for GPS and Galileo signals.

In the position domain, the comparison between Galileo and GPS with limited HDOP demonstrates the advantage of Galileo: The mean error is reduced of 2 m in the position domain, whereas in the velocity domain, the considered configurations are characterized by similar performance with differences lower than 2 cm/s.

A Iono-free solution was also computed using PRs from E1 and E5a. As expected, this solution leads to a reduction in the mean error. Finally, when combining measurements from GPS and Galileo, it was shown that the maximum positioning error is only slightly reduced with respect to the GPS-only case.

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