Empirical Correction Model for Galileo Clock Estimates 2014 - PS11... · Center for Orbit...
1
Empirical Correction Model for Galileo Clock Estimates Peter Steigenberger, Oliver Montenbruck Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen, Germany [email protected] Introduction Several authors like Montenbruck et al. (2012), Prange et al. (2014), Hackel et al. (2014), and Montenbruck et al. (2014) al- ready demonstrated systematic errors in clock estimates of the passive hydrogen masers (PHMs) onboard GIOVE-B and the Galileo In-Orbit Validation (IOV) satellites. These errors are, e.g., visible as a clear dependence of Satellite Laser Ranging (SLR) residuals on the elevation of the Sun above the orbital plane indicating deficiencies in the orbit modeling. They also show up as a prounounced bump in the Allan deviation (ADEV), see Figure 1. 10 2 10 3 10 4 10 5 10 -15 10 -14 10 -13 10 -12 Integration time [s] Allan Deviation E19 10 2 10 3 10 4 10 5 10 -15 10 -14 10 -13 10 -12 Integration time [s] Allan Deviation E20 COM GFM GRM TUM F IGURE 1: Allan deviation of the Galileo clocks estimates of the MGEX analysis centers Centre National d’Etudes Spatiales/Collecte Localisation Satellites (CNES/CLS, MGEX abbreviation GRM), Center for Orbit Determination in Europe (CODE, MGEX abbreviation COM), Deutsches Geo- ForschungsZentrum (GFZ, MGEX abbreviation GFM), Technische Universität München (TUM, MGEX abbreviation TUM). We use Galileo orbits computed within the Multi-GNSS EXper- iment (MGEX) of the International GNSS Service (IGS) and SLR observations provided by the International Laser Ranging Service (ILRS) for the estimation of a simple clock correction model. As an example, the results of the Galileo orbits of the Center for Orbit Determination in Europe (CODE, MGEX abbreviation COM, Prange et al., 2014) are used here. Galileo SLR Residuals All Galileo satellites are equipped with retro reflector arrays and they are observed by the tracking stations of the ILRS on a regu- lar basis. Systematic errors in the SLR residuals depend on the geometry of Earth, Sun, and the satellite as shown in Figure 2. F IGURE 2: Elevation of the Sun above the orbital plane β and Earth-satellite-Sun elongation angle γ . The dependence of the SLR residuals on the elevation of the Sun above the orbital plane β is plotted in Figure 3. The scatter of the residuals clearly depends on the β -angle with the smallest scatter during periods with a large absolute value of β . -30 -20 -10 0 10 20 30 SLR residuals [cm] Jun Aug Oct Dec Feb Apr Jun Aug Oct -90 -60 -30 0 30 60 90 β-angle [°] 2012 2013 F IGURE 3: SLR residuals of the E11 COM orbits. In addition the elevation of the Sun above the orbital plane β is plotted. The grey-shaded areas indicate the eclipse periods. The SLR residuals also show a dependence w.r.t. the Earth- satellite-Sun angle γ as illustrated in Figure 4: • The orbit determined from GNSS microwave observations is shifted away from the Sun compared to the orbit as seen by SLR. • The SLR residuals are in general positive when the satellite is on the bright side and negative when the satellite is on the dark side of the Earth. • A mean bias of about −5 cm shifts the residuals in addition. • The reason for this systematics is most probably related to SRP mismodeling issues due to its clear dependency on the geometry of Sun, Earth, and satellite. 0 45 90 135 180 -40 -20 0 20 40 SLR Residuals [cm] γ [°] E11 0 45 90 135 180 -40 -20 0 20 40 SLR residuals [cm] γ [°] E12 F IGURE 4: SLR residuals of Galileo E11 and E12 plotted versus the Earth-satellite-Sun angle γ . Galileo Clock Performance Systematic effects are also visible in the satellite clock estimates. Figure 5 shows a 3-dimensional Allan deviation plot with time on the third axis. The ADEVs at long integration times show a clear time dependence and vary between 2 · 10 −15 and 4 · 10 −14 . The minimum values around day 115/2013 coincide with the maxi- mum β -angle, see Figure 3. F IGURE 5: Allan deviation of Galileo E11 clock estimates as a function of time. The gray shaded areas indicate the eclipse seasons. Empirical Clock Correction Model Based on the γ -dependence of the SLR residuals shown in Fig- ure 4 a simple empirical clock correction model has been esti- mated: • A cubic function depending on γ was fitted to the SLR residu- als. • SLR residuals with γ< 25 ◦ and an absolute value larger than 25 cm were excluded from the estimation. The ADEVs computed from the Galileo E11 clock estimates cor- rected with the empirical model are shown in Figure 6. Com- pared to Figure 5 the time-dependence of the ADEV is signifi- cantly reduced by empirically correcting orbital errors. F IGURE 6: Allan deviation of Galileo E11 clock estimates as a function of time after applying the empir- ical correction. The gray shaded areas indicate the eclipse seasons. However, during the eclipse periods indicated by gray rectan- gles additional bumps at 3,000 s are introduced and the ADEV during periods with high β -angles around day 115/2013 is also degraded. Figure 7 shows daily E11 Allan deviations of the raw COM clock solution as well as corrected with the empirical model. The eclipse seasons have been excluded due to the deficiencies of the model shown above. For integration times up to 4,000 s the observed ADEV follows a 10 −12 / √ τ relation indicating white frequency noise of the PHM. 10 2 10 3 10 4 10 5 10 -15 10 -14 10 -13 10 -12 Allan Deviation Integration time [s] E11 10 2 10 3 10 4 10 5 10 -15 10 -14 10 -13 10 -12 Allan Deviation Integration time [s] E11 F IGURE 7: Daily Allan deviations of the COM Galileo E11 clock solution outside the eclipse season without (left) and with (right) empirical clock correction model applied. The blue line represents an Allan deviation of 10 −12 / √ τ for τ< 4, 000 s and 1.6 · 10 −14 for τ> 4, 000 s. For integration times larger than 4,000 s the observed ADEV tends to be constant on average at a value of 1.6 · 10 −14 . This value may comprise residual orbit determination errors as well as possible thermal bias variations in the signal generation and should be considered as an upper threshold for the true PHM clock performance outside the eclipse region. Conclusions • An empirical correction model for Galileo clock estimates has been derived from SLR residuals. • The model significantly reduces the bump in the Allan devia- tion for time periods with small β -angle. • During periods with a large absolute value of the β -angle an even better performance of the apparent clock can be achieved as the orbit errors are minimal, see Figure 5. • Further refinement of the Galileo IOV orbit modeling will be required to further reduce the amplitude of 1-CPR and 2-CPR harmonics and to better isolate the actual clock behavior from other effects at the respective correlation times. Further Reading Hackel, S., Steigenberger, P., Hugentobler, U., Uhlemann, M., Montenbruck, O., 2014. Galileo orbit determination using combined GNSS and SLR observations. GPS Solutions online first, doi: 10.1007/s10291-013-0361-5. Montenbruck, O., Steigenberger, P., Khachikyan, R., Weber, G., Langley, R. B., Mervart, L., Hugentobler, U., 2014. IGS-MGEX: Preparing the ground for multi-constellation GNSS science. Inside GNSS 9 (1), 42–49. Montenbruck, O., Steigenberger, P., Schönemann, E., Hauschild, A., Hugentober, U., Dach, R., Becker, M., 2012. Flight characteri- zation of new generation GNSS satellite clocks. Navigation, Journal of the Institute of Navigation 59 (4), 291–302. Prange, L., Dach, R., Lutz, S., Schaer, S., Jäggi, A., 2014. The CODE MGEX orbit and clock solution. In: Willis, P. (Ed.), IAG Potsdam 2013 Proceedings. International Association of Geodesy Symposia. Springer, accepted for publication. DLR f¨ ur Luft- und Raumfahrt Deutsches Zentrum German Aerospace Center IGS Workshop 2014 > Pasadena, USA
Transcript of Empirical Correction Model for Galileo Clock Estimates 2014 - PS11... · Center for Orbit...
Empirical Correction Model for Galileo Clock EstimatesPeter Steigenberger, Oliver Montenbruck
Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen, Germany
IntroductionSeveral authors like Montenbruck et al. (2012), Prange et al.(2014), Hackel et al. (2014), and Montenbruck et al. (2014) al-ready demonstrated systematic errors in clock estimates of thepassive hydrogen masers (PHMs) onboard GIOVE-B and theGalileo In-Orbit Validation (IOV) satellites. These errors are,e.g., visible as a clear dependence of Satellite Laser Ranging(SLR) residuals on the elevation of the Sun above the orbitalplane indicating deficiencies in the orbit modeling. They alsoshow up as a prounounced bump in the Allan deviation (ADEV),see Figure 1.
102
103
104
105
10−15
10−14
10−13
10−12
Integration time [s]
Alla
n D
evia
tion
E19
102
103
104
105
10−15
10−14
10−13
10−12
Integration time [s]
Alla
n D
evia
tion
E20
COMGFM
GRMTUM
FIGURE 1: Allan deviation of the Galileo clocks estimates of the MGEX analysis centers CentreNational d’Etudes Spatiales/Collecte Localisation Satellites (CNES/CLS, MGEX abbreviation GRM),Center for Orbit Determination in Europe (CODE, MGEX abbreviation COM), Deutsches Geo-ForschungsZentrum (GFZ, MGEX abbreviation GFM), Technische Universität München (TUM, MGEXabbreviation TUM).
We use Galileo orbits computed within the Multi-GNSS EXper-iment (MGEX) of the International GNSS Service (IGS) andSLR observations provided by the International Laser RangingService (ILRS) for the estimation of a simple clock correctionmodel. As an example, the results of the Galileo orbits ofthe Center for Orbit Determination in Europe (CODE, MGEXabbreviation COM, Prange et al., 2014) are used here.
Galileo SLR ResidualsAll Galileo satellites are equipped with retro reflector arrays andthey are observed by the tracking stations of the ILRS on a regu-lar basis. Systematic errors in the SLR residuals depend on thegeometry of Earth, Sun, and the satellite as shown in Figure 2.
FIGURE 2: Elevation of the Sun above the orbital plane β and Earth-satellite-Sun elongation angle γ.
The dependence of the SLR residuals on the elevation ofthe Sun above the orbital plane β is plotted in Figure 3. Thescatter of the residuals clearly depends on the β-angle with thesmallest scatter during periods with a large absolute value of β.
−30
−20
−10
0
10
20
30
SLR
res
idua
ls [c
m]
Jun Aug Oct Dec Feb Apr Jun Aug Oct−90
−60
−30
0
30
60
90
β−an
gle
[°]
2012 2013
FIGURE 3: SLR residuals of the E11 COM orbits. In addition the elevation of the Sun above the orbitalplane β is plotted. The grey-shaded areas indicate the eclipse periods.
The SLR residuals also show a dependence w.r.t. the Earth-satellite-Sun angle γ as illustrated in Figure 4:
• The orbit determined from GNSS microwave observations isshifted away from the Sun compared to the orbit as seen bySLR.
• The SLR residuals are in general positive when the satelliteis on the bright side and negative when the satellite is on thedark side of the Earth.
• A mean bias of about −5 cm shifts the residuals in addition.
• The reason for this systematics is most probably related toSRP mismodeling issues due to its clear dependency on thegeometry of Sun, Earth, and satellite.
0 45 90 135 180−40
−20
0
20
40
SLR
Res
idua
ls [c
m]
γ [°]
E11
0 45 90 135 180−40
−20
0
20
40
SLR
res
idua
ls [c
m]
γ [°]
E12
FIGURE 4: SLR residuals of Galileo E11 and E12 plotted versus the Earth-satellite-Sun angle γ.
Galileo Clock PerformanceSystematic effects are also visible in the satellite clock estimates.Figure 5 shows a 3-dimensional Allan deviation plot with time onthe third axis. The ADEVs at long integration times show a cleartime dependence and vary between 2 ·10−15 and 4 ·10−14. Theminimum values around day 115/2013 coincide with the maxi-mum β-angle, see Figure 3.
FIGURE 5: Allan deviation of Galileo E11 clock estimates as a function of time. The gray shaded areasindicate the eclipse seasons.
Empirical Clock Correction ModelBased on the γ-dependence of the SLR residuals shown in Fig-ure 4 a simple empirical clock correction model has been esti-mated:
• A cubic function depending on γ was fitted to the SLR residu-als.
• SLR residuals with γ < 25◦ and an absolute value larger than25 cm were excluded from the estimation.
The ADEVs computed from the Galileo E11 clock estimates cor-rected with the empirical model are shown in Figure 6. Com-pared to Figure 5 the time-dependence of the ADEV is signifi-cantly reduced by empirically correcting orbital errors.
FIGURE 6: Allan deviation of Galileo E11 clock estimates as a function of time after applying the empir-ical correction. The gray shaded areas indicate the eclipse seasons.
However, during the eclipse periods indicated by gray rectan-gles additional bumps at 3,000 s are introduced and the ADEVduring periods with high β-angles around day 115/2013 is alsodegraded.
Figure 7 shows daily E11 Allan deviations of the raw COM clocksolution as well as corrected with the empirical model. Theeclipse seasons have been excluded due to the deficiencies ofthe model shown above. For integration times up to 4,000 s theobserved ADEV follows a 10−12/
√τ relation indicating white
frequency noise of the PHM.
102
103
104
105
10−15
10−14
10−13
10−12
Alla
n D
evia
tion
Integration time [s]
E11
102
103
104
105
10−15
10−14
10−13
10−12
Alla
n D
evia
tion
Integration time [s]
E11
FIGURE 7: Daily Allan deviations of the COM Galileo E11 clock solution outside the eclipse seasonwithout (left) and with (right) empirical clock correction model applied. The blue line represents anAllan deviation of 10−12/
√τ for τ < 4, 000 s and 1.6 · 10−14 for τ > 4, 000 s.
For integration times larger than 4,000 s the observed ADEVtends to be constant on average at a value of 1.6 · 10−14. Thisvalue may comprise residual orbit determination errors as wellas possible thermal bias variations in the signal generation andshould be considered as an upper threshold for the true PHMclock performance outside the eclipse region.
Conclusions• An empirical correction model for Galileo clock estimates hasbeen derived from SLR residuals.
• The model significantly reduces the bump in the Allan devia-tion for time periods with small β-angle.
• During periods with a large absolute value of the β-anglean even better performance of the apparent clock can beachieved as the orbit errors are minimal, see Figure 5.
• Further refinement of the Galileo IOV orbit modeling will berequired to further reduce the amplitude of 1-CPR and 2-CPRharmonics and to better isolate the actual clock behavior fromother effects at the respective correlation times.
Further ReadingHackel, S., Steigenberger, P., Hugentobler, U., Uhlemann, M., Montenbruck, O., 2014. Galileo orbit determination using combinedGNSS and SLR observations. GPS Solutions online first, doi: 10.1007/s10291-013-0361-5.
Montenbruck, O., Steigenberger, P., Khachikyan, R., Weber, G., Langley, R. B., Mervart, L., Hugentobler, U., 2014. IGS-MGEX:Preparing the ground for multi-constellation GNSS science. Inside GNSS 9 (1), 42–49.
Montenbruck, O., Steigenberger, P., Schönemann, E., Hauschild, A., Hugentober, U., Dach, R., Becker, M., 2012. Flight characteri-zation of new generation GNSS satellite clocks. Navigation, Journal of the Institute of Navigation 59 (4), 291–302.
Prange, L., Dach, R., Lutz, S., Schaer, S., Jäggi, A., 2014. The CODE MGEX orbit and clock solution. In: Willis, P. (Ed.), IAGPotsdam 2013 Proceedings. International Association of Geodesy Symposia. Springer, accepted for publication.
DLR fur Luft- undRaumfahrt
DeutschesZentrum
GermanAerospaceCenter IGS Workshop 2014 > Pasadena, USA
