7.4 GIOVE-B special case
7.4.1 Phase meter comparisons
PHM and RAFS are compared through the CMCU unit. CMCU phase meter comparison of the RAFS against the PHM as reference on Figure 7.7 presents the phase meter comparison and Allan deviation between the nominal PHM and the hot redundant RAFS for 25th-27th December 2009, when the fractional frequency offset between both clocks crossed the zero offset. This result does not allow us to draw conclusions on the PHM as the RAFS noise is higher than the PHM and the harmonic effect (1E-13), but it confirms the good thermal control at RAFS location, since a clear signal is observed without harmonic contribution.
(a)Phase Meter comparison on GIOVE-B between RAFS and PHM
(b)Allan Deviation from phase meter Fig. 7.7: GIOVE-B on board PHM-RAFS phase meter comparison
7.4.2 Orbit residual
The harmonic observed on GIOVE-B clocks is the only one not explained by the sensitivity of the AFS or by group delay variations. This satellite is further investigated hereafter.
The current harmonic in the apparent clock behaviour observed on GIOVE-B was accurately predicted before the satellite launch by preliminary studies. The harmonic effect was also ex-pected and associated to an orbit residual of 10 cm (or 0.3 ns) linked to a limited number of sensor stations. The predicted Allan deviation in [26, picture 6] is similar to the one observed in orbit in Figure 6.23
In Section 6.3.6 it was explained how the orbit accuracy depends on the number of mea-surements and therefore on the number of stations. It remains the possibility to attribute some or most of the clock harmonic to the orbit residual. In order to increase the orbit accuracy two options have been studied. First, together with the L-Band measurement, periods with a
larger number of SLR measurements have been used in the adjustment with almost no weight (de-weighted) and in a posterior run with weights in accordance with the measurement stan-dard deviation in order to look for any improvement of the results. Second, additional CONGO stations have been added to the estimation and processed with NAPEOS.
For the first approach using SLR data, two different software packages have been applied:
GIOVE-M (run by GMV) and BAY-PAF (Bernese run by Astrium). The Figure 7.8 shows the detrended clock phase estimated by Astrium-Germany using BAY-PAF with weighted (black) and de-weighted (red) the SLR measurements. Up to 46 SLR measurements were included in this five days arc for 7-11 December 2008 (doy 342-346), coming from 5 stations. Both software recover the same harmonic for each run with some reduction in the amplitude. A consistent reduction of the fluctuation between 24% and 54% occurs for GMV and Astrium estimates when SLR observations are weighted in the process.
(a)Phase (b)Amplitude spectrum
Fig. 7.8: GIOVE-B (PHM) phase clock obtained with and without weighting the SLR measurements for 11-15 December 2008 (first and last 12h disregarded). Source: Astrium Germany
The second approach consists of increasing the number of observations by additional stations, since as considered in previous Section 6.3.6 the precision depends on the number of stations.
A common period of GESS (13) and CONGO (8) stations have been processed together by ESOC with the NAPEOS software, amounting for a total of 21 stations. The data covers a period of 28 days from mid August 2009 to mid September 2009 ahead the eclipse season for GIOVE-B. Figure 7.9 presents the phase evolution and the spectra of the signal. Two different solutions have been estimated : GESS+CONGO network and only with GESS stations. The clock from each solution plus the difference have been detrended per day and stacked. Two harmonics are recovered by both solutions with a main component of 0.43 ns amplitude on the orbit period (14.0865 hours) and a secondary component of 0.11 ns on the half orbit period (7.04324 hours). The clearer spectrum is obtained with all the stations while some spectral
7.4 GIOVE-B special case
0 1 2 3 4 5 6 7 8 9 10
0 0.1 0.2 0.3 0.4 0.5
Orbit [cycles]
Amplitude [nanoseconds]
1.gess
2.gess+CONGO Sol.1 − Sol.2
Fig. 7.9: GIOVE-B (PHM) FFT with GONGO and GESS Networks
leakage is obtained with only the GESS solution. The components have the same period with slightly different amplitude between the solutions. The second solution with the higher number of stations reduce the harmonic amplitude and also the residuals of the clocks overlapping, although not as much as expected from Section 6.3.6 study with IGS stations.
The difference between the two solutions with both methodologies shows a clear pattern and fluctuation, even if each apparent clock is noisier. Even if the two harmonic components can-cel out in the difference a large amount of energy remains with components at the frequency around one orbit cycle. Nevertheless, both methodologies show an improvement by including more measurements in the estimation.
An additional indication of the limited accuracy of the orbit due to the limited number of mea-surements derives from the arc length used in the estimation. While 1 day arcs is the typical duration in IGS processing, up to five days length have been identified as the most suitable length in GIOVE mission from the quality of the RMS difference between one day overlapping arcs. The same arc length has later been used by ESOC and DLR for GIOVE estimations. In case 5 days arcs estimation is used to improve the orbit, some ’butterfly’ or ’bath-tub’ effects are observed at the borders with larger differences between the weighted and deweighted solutions and it becomes necessary to extract only the 1 day central arc.
Some interesting feature of the harmonic is the slight difference (+2 m 50 s) between the harmonic (14.0865 h) and orbit period (14.03916 h±5 s) estimated by:
T2
a3 = 4π
GME [7.5]
with the mean semi-major axis transmitted in the navigation message during the analyzed time
(a=29545305.8). Beside further discarding the temperature as root cause of the harmonic, the difference could provide some indication about its origin. Similar differences (+1 min) have also been reported for GPS satellites [150], however this is a particular interesting analysis to be performed with PHM clocks due to the less noise signal and the low probability of temperature effects in the apparent clock.
In summary, any data addition by arc length increase, SLR data or sensor station, improves the orbit quality and decreases the harmonic amplitude. This fact indicates that some orbit residual still exists in the apparent clock affecting the harmonics amplitude. Additionally, a difference (+2 m 50 s) between the harmonic and orbit period exist which could help to identify its origin.
7.4.3 Argument of latitude dependency on SRP
After the harmonic origin has been finally attributed to the orbit accuracy, now the final question is what in the orbit estimation generates this orbit period dependency. One possibility could be the SRP model coefficients estimated together with the orbit.
The instantaneous Solar Radiation Pressure (SRP) is an inertial acceleration component due to direct solar radiation pressure upon the satellite. This forceaSRP needs to be included in the equations of motion of the satellite as explained in Section 5.3.2. In GIOVE mission the POD is performed using an empirical SRP model (Equation 7.6 presented in [136]) based on [23] with additional harmonics in all three directions with a total of 9 parameters ,
aSRP= D0eD+DceDcos(u) +DseDsin(u)+
Y0eY+YceYcos(u) +YseYsin(u)+
B0eB+BceBcos(u) +BseBsin(u)
[7.6]
whereeD is the unit vector satellite-Sun, positive towards to Sun,eY is the unit vector along the spacecraft’s solar-panel, positive following the definition of the satellite reference frame, andeB is the unit vector which completes the right handed system. Figure 7.10 shows the reference frame used for the empirical SRP model. The empirical parameters of the model to be estimated are D0, Dc, Ds, Y0, Yc, Ys, B0, Bc and Bs. An additional second harmonic model, where 15 parameters are estimated, were tested in GIOVE mission with good results.
Nonetheless, a generally observed improvement was not always consistent between the arcs and it was recommended to be reviewed when more stations will be available [50].
The main accelerationD0eD, along the Sun-Satellite direction, represents most of the SRP acceleration, since the rest of the terms take values of around 1% or less of the magnitude of the main component. The model contains two harmonic functions of the argument of latitudeu along the three directions.
7.4 GIOVE-B special case
Fig. 7.10: Reference frame for the empirical SRP model. Source: [136]
0 1 2 3 4 5 6
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6 0.8
1x 10−9
Orbit Angle [Rad]
seconds
Fig. 7.11: Harmonic as function of argument of latitude angle
The apparent clock harmonic is correlated with the argument of latitude angle as depicted in Figure 7.11. The figure has been obtained after a day by day by detrending the phase data and plotting each orbit versus the argument of latitude. Additionally, the independent clock estimations by the GGSP consortium did not agree only for the PHM (previous Figure 7.1(e)).
The SRP model used by each analysis center for each estimation was slightly different what could justify also the disagreement observed in the clock. Both facts indicate an inaccuracy of the SRP model as the most likely cause of the harmonic observed in GIOVE-B PHM clock.
Nevertheless, it must be highlighted that SRP modelling suffers from an observability prob-lem due to the reduced coverage (along and across components are difficult to observe) and therefore, independently of the model being used, the data quality is the main driver for a cor-rect satellite dynamic predictability. This hypothesis will be confirmed for Galileo IOV satellites once enough IGS stations become available to compute the orbit with sufficient accuracy. As an indication, IGS analysis centers use in average around 100 stations for the estimation of GPS satellite orbits.
The period for Figure 7.11 has been selected during eclipse season when the SRP estimation is less accurate due to the lower beta angle, as acknowledged in [12]. Each epoch used for the clock phase comes from an average of 48 different estimations using a moving arc estimation of 48 hours with one hour step between the arcs. All other periods outside eclipse present a clear correlation with the argument of latitude. The effect of temperature being excluded, it has been selected to additionally demonstrate how the PHM allows the identification of orbit modelling errors.