IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,

vol. 61, no. 12,

December

2014

1967

Calibration of Galileo Signals for Time Metrology Pascale Defraigne, Wim Aerts, Giancarlo Cerretto, Elena Cantoni, and Jean-Marie Sleewaegen Abstract—Using global navigation satellite system (GNSS) signals for accurate timing and time transfer requires the knowledge of all electric delays of the signals inside the receiving system. GNSS stations dedicated to timing or time transfer are classically calibrated only for Global Positioning System (GPS) signals. This paper proposes a procedure to determine the hardware delays of a GNSS receiving station for Galileo signals, once the delays of the GPS signals are known. This approach makes use of the broadcast satellite inter-signal biases, and is based on the ionospheric delay measured from dual-frequency combinations of GPS and Galileo signals. The uncertainty on the so-determined hardware delays is estimated to 3.7 ns for each isolated code in the L5 frequency band, and 4.2 ns for the ionosphere-free combination of E1 with a code of the L5 frequency band. For the calibration of a time transfer link between two stations, another approach can be used, based on the difference between the common-view time transfer results obtained with calibrated GPS data and with uncalibrated Galileo data. It is shown that the results obtained with this approach or with the ionospheric method are equivalent.

I. Introduction

G

lobal navigation satellite system (GNSS) signals are classically used for accurate timing and time transfer. To that aim, the GNSS receiver is connected to the local clock, and the synchronization difference between the local clock and the GNSS time scale is determined from the pseudorange measurements. GNSS has been used since the 1980s for time transfer [1]. Only the Global Positioning System (GPS) constellation has been used during the last 25 years, with some experiments based on Global Navigation Satellite System (GLONASS) measurements (e.g., [2], [3]). Two new constellations are already partially available, the Chinese system Beidou and the European system Galileo; the present article concerns the use of Galileo for timing and time transfer. GNSS measurements can be exploited for timing only if the electrical delay affecting the signal between the antenna phase center and the internal timing reference of the receiver is accurately known. To determine the synchronization difference between the local clock connected to the receiver and the GNSS time scale, the time bias between the receiver internal clock and the local clock must be known as well. These station hardware delays must be

Manuscript received July 23, 2014; accepted September 30, 2014. P. Defraigne and W. Aerts Jr. are with the Royal Observatory of Belgium, Brussels, Belgium (e-mail: [email protected]). G. Cerretto and E. Cantoni are with the Istituto Nazionale di Ricerca Metrologica (INRIM), Torino, Italy. J.-M. Sleewaegen is with Septentrio Satellite Navigation, Leuven, Belgium. DOI http://dx.doi.org/10.1109/TUFFC.2014.006649 0885–3010

determined through a calibration procedure. To this end, two techniques have been considered to date: the relative calibration, using true GNSS signals, and the absolute calibration based on the use of simulated GNSS signals. The principle of the absolute calibration is to inject simulated GNSS signals into the receiver/antenna, and to determine the hardware delays from the time differences between the injected signals and the measurements provided by the receiver/antenna. Complete descriptions of the method can be found, e.g., in [4]–[6] and references therein. This kind of calibration claims a very high accuracy of, e.g., 0.4 ns for the receiver single-frequency GPS codes [7], but it requires the use of complex equipment not existing in most timing laboratories. Moreover, this method does not allow determination of the hardware delays of already operational receiving chains that may not be interrupted. The relative calibration technique is therefore preferred for operational stations. It is based on a comparison of pseudorange measurements collected by the local receiving chain and an already calibrated reference receiving chain traveling from laboratory to laboratory [8]. In each laboratory, the local and the reference stations are connected to the same clock and installed in co-location, so that all the perturbations—except the multipath—are the same for both stations, and the differential hardware delays are directly determined from the difference of the pseudoranges measured by the two receiving chains, and corrected for the distance between the two antennas. The relative calibration can also be applied to a link for which an independent calibrated time transfer technique exists. The hardware delays for the link are in that case determined from the difference between the GNSS time transfer solution and the independent calibrated time transfer solution. This is classically done for calibration of two-way satellite time and frequency transfer links with respect to the GPS links [9] or GLONASS link with respect to the GPS links [10]. However, to access the time scales disseminated by the system, i.e., UTC and the system time (GPS time or Galileo System Time in the present case), the knowledge of station hardware delays of the receiving station is necessary, so a link calibration cannot be used in that case. Absolutely calibrated reference stations currently exist only for GPS. This paper proposes an approach to determine the hardware delays of Galileo signals from the known GPS hardware delays, using some ionospheric measurements. This approach is developed in the next section. It is then applied to three different GNSS stations in Section III; two stations are located in Brussels at the Royal Observatory of Belgium, and the third station is located

© 2014 IEEE

1968

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,

vol. 61, no. 12,

December

2014

[11] induces a delay of electromagnetic signals, which can be written at the first order as

Fig. 1. GNSS station hardware delays.

in Torino, at the INRIM Time and Frequency/RadioNavigation Laboratories. The results of the Galileo time transfer link calibrated using ionosphere measurements are also compared with those obtained when the Galileo link is calibrated with respect to the GPS link. Section IV presents the uncertainty budget on the proposed calibration method. In Section V, the station hardware delay of the GPS signal C5 is computed using the ionospheric measurements from signals broadcast by the GPS satellites of Block IIF, and the results are compared with the hardware delays found for Galileo E5a, i.e., the same frequency and the same modulation as GPS C5. The conclusions are finally drawn in Section VI.

II. Calibration for Galileo Signals The station hardware delays to be considered for GNSS timing and time transfer are represented in Fig. 1. They can be separated into two categories: the electrical delays of the GNSS signal from their arrival at the antenna to the receiver internal measurement latching (also called internal clock), and the synchronization difference between the internal clock and the external clock driving it. The GNSS signal delay contributors are the antenna (δA), the antenna cable (δCA), and the receiver (δR). The antenna cable delay is the same for all the GNSS signals, whereas the delays in the antenna and in the receiver are frequency dependent. In a differential calibration, two of those delays are generally considered together [8] as a global delay, namely δ = δA + δR. If the receiver internal clock, i.e., the latching point for the measurements, is the same for all the satellites belonging to the different constellations, the relation between the external clock and the receiver internal clock is also the same for all the satellites and all the signals. It is composed of the clock cable delay (δCC) and the offset between the internal clock and the input connector for the 1 pulse per second (1 PPS) signal coming from the external clock (δC). For a GNSS station already calibrated for the GPS signals, only the antenna and receiver delays for Galileo signals should therefore be determined. The approach we propose here is based on the measurement of the ionospheric delays in the GNSS signals, which can be obtained from the combination of dual-frequency signals and their associated hardware delays. The ionospheric refraction

I (f ) =

1 STEC 40.3  2 [in seconds], (1) c f

where c is the velocity of light, f is the signal frequency, and STEC is the slant total electron content (TEC), i.e., the integrated electron content inside a cylinder of 1 m2 along the signal path inside the ionosphere (see Fig. 2). STEC is expressed in units of 1016 electrons/m2. The difference of measurements of two GNSS signals of different frequencies, but arriving along the same path, contains only the frequency-dependent effects, i.e., the ionospheric delays and the station and satellite hardware delays. These differences therefore give access to the ionospheric delay of each frequency as explained, e.g., in [12]:



I (f i ) =

f j2  1  (Pj − Pi ) − (δPj − δPi ) rec f i − f j2  c 2

 − (δPj − δPi ) sat  , 

(2)

where Pi is the pseudorange measured on the frequency fi, and δPi is the hardware delay on the signal Pi, in seconds, either in the satellite (subscript sat) or in the stations (subscript rec). It must be noted here that only differential hardware delays between signals of different frequencies appear in the ionospheric measurement (2) so that only the receiver and antenna delays enter into the game here, as all other hardware delays are the same for the frequencies fi and fj. The differential hardware delays also called differential code biases (DCB) are classically determined as by-product in the computation of ionospheric TEC map, but only for signals of a given constellation. DCBs are so provided, e.g., by the IGS between GPS P1 and P2 for each satellite and a selection of stations [12]. Recently, Montenbruck et al. [13] also provided DCB for Galileo E1 to E5x (x = a, b, or blank for AltBoc) for the four IOV satellites and for the stations taking part to the IGS multi-GNSS experiment MGEX [14]. However, all these DCBs are given as relative values. Indeed, only the differences between satellite and station DCBs appear in the observation (2) so that no absolute DCB can be determined and some of them must be fixed, the other being determined relative to this fixed DCB. It is generally preferred to fix the average of the DCBs of the constellation to zero [15]. The relation between the DCBs and the differential hardware delays is therefore

DCB sat(i, j ) = (δPj − δPi ) sat − K ij

(3) DCB rec(i, j ) = (δPj − δPi ) rec − K ij ,

where Kij is the average of the (δPj − δPi)sat over the constellation. The satellite differential code biases are also broadcast in the navigation messages via the total group delay (TGD)

defraigne et al.: calibration of galileo signals for time metrology

for GPS P1 and P2 and the broadcast group delay (BGD) for Galileo E1 to E5a and E1 to E5b. The BGD(E1, E5a) is broadcast within the Galileo navigation message FNAV, in which the satellite clocks correspond to the ionospherefree combination of E1 and E5a, and the BGD(E1, E5b) is broadcast within the Galileo navigation message INAV, in which the satellite clocks correspond to the ionosphere-free combination of E1 and E5b. However, these are not directly the DCBsat but correspond to the DCBsat multiplied by the ratio of squared frequencies. Furthermore, the TGDs or BGDs transmitted by the satellites are based either on absolute calibration of the satellite hardware delays before launch, or on the code measurements collected by some absolutely calibrated GNSS station on ground. They represent therefore directly the true difference between the satellite hardware delays of the two signals multiplied by the ratio of squared frequencies. As a consequence, the relation between TGD (or BGD) and DCBsat is f j2 (DCB sat(i, j ) + K ij ) f i − f j2 (4) f j2 (δPj − δP Pi ) sat. =− 2 f i − f j2

TGD  or  BGD  = −

1969

Fig. 2. Schematic view of GPS and Galileo satellites suffering the same ionospheric delay at the same time.



I (f1, GPS) =

f 22  1  (P2 − P1) − (δP2 − δP1) rec f12 − f 22  c (5)  − (δP2 − δP1) sat  , 

where (δP1)rec and (δP2)rec are known from calibration, and f 22/(f12 − f 22) (δP2 − δP1)sat is the satellite TGD available from the navigation message. The corresponding equation for Galileo is

2

Whereas the DCBrec provided by the IGS are only provided for pairs of signals of a given constellation, we propose here to determine absolute station inter-system delays using the ionosphere measurements based on a GPS and a Galileo satellite of which signals travel the same ionospheric path at the same time as illustrated in Fig. 2, and hence to determine the station hardware delays of the Galileo signals from the known station GPS hardware delays and the known satellite hardware delays of GPS satellites (TGDs) and of Galileo satellites (BGDs). Galileo and GPS both share the same carrier of 1575.42 MHz in the L1 frequency band. Although the code modulation is slightly different, we can suppose that the receiver hardware delays of the codes GPS P1 and Galileo E1 are equal. An uncertainty of 1 ns is however considered, and was confirmed in [16], [17] through absolute calibration of the receiver PolaRx4. The equality of GPS P1 and Galileo E1 delays can be assumed for the antenna as well, because the antenna RF filters are typically wider than the receiver RF filters. The hardware delays of Galileo signals in the L5 frequency band can therefore be determined from ionospheric measurements of both GPS and Galileo signals using (2), once the station GPS differential hardware delay (δP2 − δP1)rec is known and the satellite TGDs/BGDs are known for both GPS and Galileo satellites. Indeed, the GPS L1 frequency signals and the Galileo E1 frequency signals should suffer exactly the same ionospheric delay when passing simultaneously through the ionosphere using the same path. These delays are given by (2) applied to the GPS and Galileo frequencies. For GPS, this is

f 52x f12 − f 52x

1  (E 5x − E 1) − (δE 5x − δE 1) rec  c  − (δE E 5x − δE 1) sat  ,  (6) I (f1, Galileo) =

where E1 and E5x are the pseudorange measurements, and f 52x /(f12 − f 52x )(δE5x − δE1)sat is the satellite BGD. The BGDs presently broadcast by Galileo for the 4 IOV satellites are however not the absolute BGDs, but have been translated to have a zero average. In the future, Galileo will also broadcast the absolute BGDs but in the meantime, we used for this study the absolute BGDs determined by absolute calibration of the four IOV satellites before launch, and kindly provided by the ESA. Furthermore, no BGD (E1, E5) is available. It is, however, possible to get an estimation using the DCBsat computed by the IGS in the frame of the MGEX campaign [14]. These DCBsat are also referred to a zero average so that they can be only used differentially. The BGD (E1, E5) can then be obtained as BGD(E 1, E 5) =

f 52  f12 − f 52a  BGD(E 1, E 5a)ESA f12 − f 52  f 52a + DCB sat(E 1, E 5)MGEX (7)  − DCB sat(E 1, E 5a)MGEX  . 

Using pairs of GPS and Galileo satellites appearing in the same direction, hence crossing the ionosphere following a same path as illustrated in Fig. 2, we have I1(GPS) = I1(Galileo), so that by combining (5) and (6), we can solve for δE5x, i.e., the station hardware delay on the Galileo signals E5a, E5b, and E5 AltBoc:

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vol. 61, no. 12,

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2014

f 52x f2 1  δE 5x,rec = 2 5x 2  (E 5x − E 1) + δE 1,rec  2  − f 5x f1 − f 5x  c

f 22  1  (P2 − P1) − (δP2 − δP1) rec  2 2  c  f1 − f 2  + BGD(E 1, E 5x ) − TGD, (8) −

in which we consider, as explained before, δE1 = δP1. III. Application to Selected GNSS Stations The technique just explained has been applied to three different GNSS stations dedicated to time transfer and already calibrated for GPS signals: BRUX and ZTB3, located in Brussels, Belgium, and INR5, located in Torino, Italy. All stations are connected to a local realization of UTC, namely UTC(ORB) for BRUX and ZTB3 and UTC(IT) for INR5. BRUX is used both for the IGS network and for time transfer to the international atomic time (TAI). The hardware delays of BRUX for GPS P1 and P2 were determined during a BIPM calibration campaign [18]. ZTB3 was calibrated differentially with respect to BRUX. INR5 was calibrated differentially with respect to the co-located station IENG, also driven by UTC(IT), and which was calibrated in a previous BIPM calibration campaign [19]. The three receivers used are Septentrio PolaRx4TR, so that we can make the assumption that the hardware delays of Galileo E1 is within one nanosecond of the hardware delay for P1, as explained previously. Both the station and the link calibration are investigated in this section. A. Station Calibration In a first step, we determined the ionospheric delays using pseudorange measurements on GPS P1 and P2, and on Galileo E1 and E5x, all except E5x corrected for the hardware delays; a first smoothing was applied in a similar way as in the CGGTTS procedure [20], using a modified version of the RINEX-CGGTTS software [21] using satellite tracks of 5 min, i.e., the results for the ionospheric delays are the midpoint of a linear fit over 5 min of 30-s data. This corresponds to the column MSIO in the CGGTTS files. The hardware delays δE5a, δE5b, and δE5 were then computed from the difference between the ionospheric delays measured on GPS and Galileo satellites in simultaneous view with angular separations less than 10°, 5°, and 2°. Fig. 3 presents the results obtained for the station BRUX. We can observe that all three data sets provide the same average at a 50 ps level, with different standard deviations. Depending on the geometry of both GPS and Galileo constellations, the number of occurrences of GPS/ Galileo satellite pairs in a same direction is variable, and the standard deviation when using a maximum of 2° for the angular separation of the satellites can be better than

Fig. 3. δE5a as obtained in the station BRUX with GPS and Galileo satellites in simultaneous view with angular separations less than 10°, 5°, and 2°.

when using a maximum of 5°, as is the case of the first four months of Fig. 3, or worse as is the case in the last three months because of the low number of points. To avoid the necessity of using several months of data for the calibration, there is clearly an advantage of using the maximum angular separation of 5°. Using angular separation up to 10°, however, always presents a larger standard deviation. From the results presented in Fig. 3, we can conclude that hardware delay for BRUX is 58.1 ns, and is stable during the whole period investigated. To detect a possible systematic effect related to the different Galileo satellites, we plotted in Fig. 4 the results obtained with and angular separation less than 5°, but for each Galileo satellite separately. As seen from Fig. 4, there is a very good agreement between the results of the four satellites, with a peak-topeak difference of only 0.7 ns. We have then applied the same procedure for E5b, using the BGDs transmitted in the INAV message, and for the E5 AltBoc using the BGD determined from FNAV BGD and the MGEX DCB as in (7). The results are given in Table I. The same calibration procedure has also been applied to the two other GNSS stations dedicated to time transfer,

Fig. 4. δE5a as obtained for the station BRUX with pairs of GPS and Galileo satellites in simultaneous view with an angular separation less than 5°, plotted separately for each Galileo satellite.

defraigne et al.: calibration of galileo signals for time metrology

1971

TABLE I. Hardware Delays (in Nanoseconds) of BRUX, ZTB3 (Receiver + Antenna), and INR5 (Receiver + Cable + Antenna) as Determined in this Study for the Galileo Signals in the E5 Frequency Band. E1 E5b E5 − E5b E5a − E5b

BRUX

ZTB3

INR5

Manufacturer

53.9 46.3 3.8 11.6

58.8 54.9 5.7 10.0

241.3 238.5 3.3 11.9

1.7 8.7

INR5 and ZTB3, and equipped with the same type of receiver as in BRUX, but a different antenna. The hardware delays determined for the Galileo signals are presented in Table I, where the differential delays between the three signals in the L5 frequency band are also reproduced. Because the three stations are equipped with the same receiver model, the differences for (E5x − E5y) are expected to be very close for BRUX, ZTB3, and INR5, which is indeed confirmed by the results of Table I. These values are also in good agreement with the nominal interfrequency biases (IFB) variation provided by the receiver manufacturer (see Fig. 5). The difference with the nominal values from the manufacturer are attributed to unit-to-unit variations (±3 ns), and to the fact that the manufacturer values only account for the receiver contribution, whereas our measured hardware delays include the contribution of the antenna. B. Comparison With the Link Calibration The knowledge of station hardware delays for a particular station is useful for the access to the time scales disseminated by the system, i.e., UTC and the system time (GPS time or Galileo System Time in the present case). Calibration is also important when the GNSS are used to compare accurately remote time scales connected to GNSS

Fig. 6. Differences between the CV results obtained with GPS calibrated data and Galileo data calibrated using the ionosphere measurements. The Galileo results were computed using the ionosphere-free combination of E1 and E5a (top), of E1 and E5b (middle), and E1 and E5 AltBoc (bottom).

receivers. When such a time link is already calibrated with GPS, the Galileo solution can be calibrated differentially with respect to the GPS solution. The advantage of such an approach with respect to calibration of individual stations, as done here, is that the uncertainty on the TGDs and BGDs has no impact in this case. Considering the calibrated GPS link for UTC(IT)-UTC(ORB) based on the receivers BRUX and INR5, we can therefore determine the hardware delay for the Galileo link. To quantify the agreement between the calibration method presented in the previous section and the link calibration, we present in Fig. 6 the differences between the GPS link and the Galileo link in which the calibration results of previous section have been introduced. Both GPS and Galileo links are based on the broadcast satellite orbits and clocks, and the common view approach. The differences obtained for the three ionosphere-free combinations of Galileo signals of E1 and one signal in the E5 frequency band are all lower than 0.5 ns. It must be noted that a large difference would not have been expected because the same TGD and BGD values were used for the calibration of both stations, and their effects somehow cancel when making the link between the two stations. However, the uncertainty budget on the link can be different when the calibration is performed on the link or on the isolated stations, as will be shown in the next section. IV. Uncertainty Budget

Fig. 5. Nominal interfrequency biases (IFB) variation as provided by the receiver manufacturer (receiver contribution only). The IFB has been measured by injecting a calibrated reference signal into the receiver at various carrier frequencies. The corresponding values in nanoseconds can be obtained by dividing the y-axis labels by 0.3.

The accuracy of a clock comparison result is given by the combined uncertainty U, type A, and type B uncertainties. The type-A uncertainty uA contains the random effects associated with the short- and long-term measurement noise, whereas the type-B uncertainty uB results from the calibration of the equipment used for the clock

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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,

vol. 61, no. 12,

December

2014

TABLE II. Uncertainty Budget (in Nanoseconds) for the Galileo Calibration Based on the GPS Calibration and the Ionosphere Measurements. 1-σ Uncertainty  f2−f2 1 f 2 − f 52x f 22  (E − E 1) − 1 (P2 − P1)  + 1 2 5x (BGD − TGD) 2 2 2  c  5x f 5x f1 − f 2 f 5x

1.0

δE1,rec

2.3

δE1,rec − δP1,rec f 22

f12 − f 22

f12

− f 52x

f 52x

1.0 (δP2 − δP1) rec

Global bias on Galileo Global bias on GPS

f12 − f 52x BGD f 52x

f12 − f 52x TGD f 52x

2.4 0.6 0.6

Total uncertainty on δE5x

3.7

Total uncertainty on δE5x − δE1

2.7

comparison. This section therefore aims at estimating uB, i.e., the uncertainty on the hardware delay estimated with the ionospheric method proposed in this paper. Using the expression of the E5x hardware delay given by (8), we reproduce in Table II the uncertainty on each term and the quadratic sum considered as the global uncertainty on the hardware delays so-determined. • For the combination of the measurements (E5x − E1) and (P2 − P1), we consider the standard deviation of the results presented in Fig. 3 for a separation angle lower than 5°, i.e., 1.0 ns. This also contains the random part of the uncertainties on the TGDs and BGDs, but not a possible bias on all the Galileo satellite BGDs or on all the GPS satellite TGDs; the possibility of such a bias must be considered separately. • For δE1,rec we use the uncertainty on δP1,rec known from the BIPM calibration, i.e., 2.3 ns [20], to which we add a possible difference of maximum 1 ns between the P1 and E1 hardware delays. • The uncertainty on (δP2 − δP1)rec from BIPM calibration is 2 ns. To determine the uncertainty associated with a possible bias affecting the broadcast TGDs of all the GPS satellites, we proceeded as follows. It is well known that some bias can exist in these quantities, because of some variations of the hardware delay of the receivers used for their determination, between two calibration processes [23]. We therefore considered determining their correctness from the comparison of the broadcast TGDs with what can be deduced from calibrated stations from the TAI network. Several IGS stations co-located with time laboratories, calibrated within a BIPM campaign during the last 8 years and regularly monitored were used: OPMT, IENG, BRUX, SYDN, WTZA, and PTBB. The DCBrec for (P1 − P2) determined by the IGS analysis center CODE of these stations for April 2014 were then compared with the calibration results of the stations. An offset of 5.3 ns was found with a standard deviation of 0.6 ns. Because

the CODE DBCs are based on a zero-mean constraint, this offset corresponds to the average of all the satellite and station DCBs for the period investigated. We therefore converted the DCBsat into TGDs using (4) with K = 5.3 ns. A very good agreement was then found with the broadcast TGD, as shown in Fig. 7: the average of the differences between the broadcast TGDs and those computed using CODE DCBs and the set of 6 calibrated IGS stations is only −0.16 ns. This confirms a very small bias in the broadcast TGDs of all the GPS satellites. We considered an uncertainty on this bias equal to 0.8 ns, i.e., the standard deviation on the results of the six calibrated stations added to the bias of 0.16 ns. For the Galileo BGDs, we considered the same uncertainty on the BGDs used as for the GPS TGDs. We however verified the stability of the true satellite differential hardware delays using the corresponding DCBsat computed by the IGS from the MGEX campaign. These are presented in Fig. 8, together with the broadcast BGDs. Because both are based on a zero-average constraint, they

Fig. 7. Comparison (up) and differences (bottom) between the broadcast TGDs and those reconstructed from the DCBsat using the calibrations of six stations participating to both the IGS and TAI networks.

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1973

TABLE III. Uncertainty Budget (in Nanoseconds) for the Galileo Calibration Based on the Link Calibration With Respect to the GPS Solution. 1-σ Uncertainty δP1,rec f 22 (δP2 − δP1) rec 2 f1 − f 22

Fig. 8. BGDs of the Galileo satellites for the whole period.

give the same absolute values. However, a much larger scatter of the broadcast values appeared, because of the network used, which is presently less than 20 Galileo sensor stations [24], whereas the MGEX DCBsat values are derived from a network of about 80 stations. Some deviation of the average BGD appears for satellites E11 and E20 in March 2014 (around MJD 56720), but not in the DCBs computed by CODE. This deviation is most probably due to some data issue in the network used by the ESA. Looking at the MGEX DCBsat results, a very good stability of the satellite differential hardware delays can, however, be observed. Finally, all these considerations lead to a resulting uncertainty of 3.7 ns on the E5x receiver hardware delays determined from known GPS hardware delays using the ionospheric delay measurements on GPS and Galileo signals traveling the same path through the ionosphere. Table II also proposes the uncertainty on δE5x − δE1x, which is necessary to determine the uncertainty on the timing solutions based on the ionosphere-free combination of E1 and E5x, which will be denoted E3x hereafter. Indeed, this combination can be expressed as [22]

E 3x = E 1 +

f 52x (E 5x − E 1) (9) f12 − f 52x

which allows a distinction to be made between the contributions common to both signals (i.e., cable delays, internal-external clock offset) and the receiver and antenna contributions which are frequency dependent. As in (8), where δE5x − δE1 is obtained when passing the term in δE1 in the left-hand side, the uncertainty on δE5x − δE1 is computed from the quadratic sum of all the terms of Table II except the two terms giving the uncertainty on δE1. The uncertainty on the clock solution determined from the ionosphere-free combination E3x is then the quadratic sum of the uncertainties on each of the two terms, which gives here uB(E3x) = 4.2 ns, so that the uB uncertainty for a link between two stations calibrated individually is equal to 5.9 ns. The uncertainty of the link calibration, in parallel, is given by the combination of the uB uncertainties on P3 in

Station 1

2.3

Station 2

2.3

Station 1

3.1

Station 2

3.1

CV(E3x) − CV(P3)

1.2

Total uB for the E3x link

5.6

the two stations, determined using (9) applied to P3, and the noise of the differences between the CV solutions in GPS P3 and Galileo E3x. These are reproduced in Table III, and result in an uncertainty of 5.6 ns for the link calibration. It must be noted that the link calibration discussed here is based on the initial GPS calibration of the two stations which were calibrated relatively to a reference receiver provided by the BIPM. The GPS link itself was not calibrated via a link calibration as proposed, e.g., in [25]. If such a GPS link calibration exists with an uncertainty σ, then the uncertainty on the link calibration for Galileo signals would be σ 2 + 1.44. V. Calibration of GPS C5 Delays In parallel to the calibration for Galileo signals, it is also possible to determine the hardware delays of GPS C5 for satellites of Block-IIF emitting in the three frequency bands. The GPS C5 signal uses exactly the same frequency and modulation as E5a, so that the station hardware delays for these two signals are exactly equal. We therefore tested the retrieval of the δE5a while computing the δC5 from the ionospheric delay measurement based either on the (P1, P2) combination [Eq. (5)] or on the (P1, C5) combination, which is



I (f1, GPS) =

f 52  1  (C 5 − P1) − (δC 5 − δP1) rec f12 − f 52  c (10)  − (δC 5 − δP1) sat  , 

GPS tested in June 2013 a first emission of the CNAV message, including the intersignal correction (ISC), i.e., differential group delays for all satellites of Blocks IIRM and IIF. Since May 1, 2014, this transmission became continuous while still in test phase, and updated only occasionally. Among others, the CNAV message contains the ISC between P1 and C5. Using the equality between (5) and (10) for each epoch of observation of the four satellites, we determined δC5. Fig. 9 presents the results obtained with BRUX using only observations above an elevation of 65°, which allows a reduction, as much as pos-

1974

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,

Fig. 9. Results for δC5 for the station BRUX obtained with five Block-IIF GPS satellites. Each point corresponds to the average of measurements above 65° during a pass of the satellite.

sible, of the impact of multipath appearing mainly at low elevation. Because δC5 is the station hardware delay, its value must be the same whatever the satellite on which the measurement has been made. A different value can, however, be observed when computed from the different satellites. This difference can only find its origin in an uncertainty in the broadcast group delays for P1 − C5 ISC because the TGDs have been shown to agree at less than 1 ns peak to peak in previous section. However, because the CNAV transmission is still in validation phase at the time of writing, we can expect some improvement in their quality in the coming months, and hence the validation of Galileo calibration for E5a with the GPS Block IIF satellites should exhibit better performance in the future. This validation is nonetheless really promising, because when using the results of May 2014 and June 2014 and ignoring the PRN 01 results which seem really problematic, the hardware delay of C5 is found in very good agreement with the result obtained for Galileo E5a. This provides a good validation of the calibration method proposed in the paper. VI. Conclusion This paper proposed a procedure to determine the hardware delays of a GNSS receiving station (antenna + receiver) for Galileo signals, once the delays of the GPS signals are known. This approach makes use of the broadcast satellite intersignal biases, and is based on the ionospheric delay measured from dual-frequency combinations of GPS and Galileo signals. The results show that using Galileo and GPS satellites appearing with a separation angle less than 5° provide a good compromise between the number of data and their noise to determine the Galileo station hardware delays from the GPS hardware delays. When used for the determination of the synchronization difference between the local clock and either the Galileo System Time, or the UTC broadcasted by Galileo, the uncertainty on the E5x (x = a, b, or blank) Galileo signal hardware delays has been estimated to 3.7 ns, and the uncertainty on the hardware delays for the ionosphere-free combination of E1 and E5x to 4.2 ns. When used for time transfer between two stations calibrated in the same way,

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the systematic uncertainty on the link is therefore theoretically multiplied by 2, i.e., 5.9 ns. When a time link is already calibrated with GPS, the Galileo solution can also be calibrated differentially with respect to the GPS solution. From the comparison with the calibration based on the ionospheric measurements, it was shown that both techniques agree within 0.5 ns and have a similar uncertainty, which is equal to 5.6 ns for the link calibration. Finally, the calibration method based on ionospheric measurements was also applied to GPS satellites emitting in the L5 frequency to retrieve the hardware delay of the GPS signal C5 from the known hardware delays for P1 and P2. The GPS C5 signal is using exactly the same frequency and modulation as E5a, so that the station hardware delays for these two signals are exactly equal. It was demonstrated, using the preliminary CNAV messages, that the values obtained for δC5 and δE5a using the method proposed in this paper agree within 1 ns.

Acknowledgments The authors thank the IGS community for the availability of their DCB products used in the present study.

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Pascale Defraigne received her Ph.D. degree in physics from the Université Catholique de Louvain (UCL), Belgium, in 1995. She is now head of the Time Laboratory at the Royal Observatory of Belgium. She is also actively involved in the activities of the Galileo Time Validation Facility and chairs the working group on GNSS Time Transfer of the Consultative Committee of Time and Frequency.

1975 Wim Aerts received the M.Sc. and Ph.D. degrees in electrical engineering from the Katholieke Universiteit Leuven, Belgium, in 2009. He focused on antenna research, ranging from arrays for satellite communication to sensors for cryptographic electromagnetic side channel analysis. Currently, he is a research engineer at the Royal Observatory of Belgium, managing the precise timing facility and the Belgian GNSS stations of the EUREF and IGS networks or dedicated to time transfer. Wim Aerts is a guest professor at the K.U. Leuven with an engineering course on analog and digital telecommunications.

Giancarlo Cerretto has a degree in telecommunication engineering and a Ph.D. degree in metrology, both achieved at the Politecnico di Torino. He is now working with the Italian Metrology Institute (INRIM) as a scientist, involved in the Institute’s Time and Frequency and RadioNavigation Laboratories’ maintenance and development activities. He is currently involved in the development of the European navigation system Galileo.

Elena Cantoni received a degree in physics and a Ph.D. degree in science and high technology at the University of Torino, Italy. Her early studies were devoted to cosmic ray physics, working on advanced data analysis of extensive air showers at the KASCADE-Grande Experiment. Currently, she works on time transfer techniques at INRIM’s Optical Division and she is involved in the Galileo project and in the INRIM Time and Frequency Laboratory’s institutional activities

Jean-Marie Sleewaegen is responsible for the GNSS signal processing, system architecture, and technology development at Septentrio Satellite Navigation. He received his M.Sc. and Ph.D. degrees in electrical engineering from the University of Brussels. He received the Institute of Navigation (ION) Burka award in 1999.