orbit determination of Low Earth Orbiters Impact of the ... · Astronomical Institute, University...
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AIUB ESA LPS-929 ESA Living Planet Symposium 2016 9 - 13 May 2016, Prague, Czech Republic D. Arnold 1 , C. Dahle 1,2 , A. Jäggi 1 , G. Beutler 1 , U. Meyer 1 1 Astronomical Institute, University of Bern, Bern, Switzerland 2 GFZ German Research Centre for Geosciences, Potsdam, Germany Poster compiled by Daniel Arnold, May 2016 Astronomical Institute, University of Bern, Bern [email protected] Impact of the ionosphere on GPS-based precise orbit determination of Low Earth Orbiters Introduction Deficiencies in gravity fields derived from the orbital trajectories of Low Earth Orbiting (LEO) satellites determined by GPS-based Pre- cise Orbit Determination (POD) were identified in recent years. The precise orbits of the Gravity Field and Steady-State Ocean Circula- tion Explorer (GOCE) mission are, e.g., severely affected by an in- creased position noise level over the geomagnetic poles and spuri- ous signatures along the Earth’s geomagnetic equator. This is illus- trated in Figure 1, showing the carrier phase residuals of a reduced- dynamic orbit determination for GOCE in meters, binned to the ionospheric piercing points at 450 km altitude (Jäggi et al., 2015a). The degradation of the orbits directly maps into the gravity fields recovered from these orbits. Figure 1: Carrier phase residuals of reduced-dynamic GOCE POD (in m). Systematic signatures along the geomagnetic equator are visible. The same problems are evident, as well, for the on-going ESA mis- sions Swarm and Sentinel. They are related to a disturbed GPS signal propagation through the Earth’s ionosphere. While this might indicate that the GPS observation model and/or the data pre- processing need to be improved, there is now strong evidence that receiver-specific tracking problems under difficult ionospheric con- ditions play an important role. GPS and ionosphere The propagation of a microwave signal of frequency f emitted by GPS satellites is dispersively affected by the free electrons in the Earth’s ionosphere: Δρ ion = ± C X 2 Ef -2 + O(f -3 ) , (1) where Δρ ion is the path delay due to the ionosphere, C X /2 ≈ 40 m 3 s -2 and E = R N e (ρ)dρ is the line-of-sight total electron con- tent (TEC), obtained by integrating the electron density N e along the ray path. The negative sign in Eq. (1) refers to the phase advance (phase observations), the positive sign to the group delay (code ob- servations), respectively. • GPS satellites emit microwave signals at two frequencies (f 1 = 1575.42 MHz and f 2 = 1227.60 MHz) and the ionosphere-free linear combination L if =(f 2 1 L 1 - f 2 2 L 2 )/(f 2 1 - f 2 2 ) of the two original carrier phase observations L 1 and L 2 eliminates the ionospheric refraction proportional to f -2 . • The terms O(f -3 ) are called higher-order ionospheric (HOI) corrections. They are not eliminated by forming L if . Their modeling requires the knowledge of the electron density and the magnetic field along the ray path (Hoque et al., 2008). • All orbit and gravity field solutions presented here were ob- tained by using only the ionosphere-free linear combination. In Jäggi et al. (2015a) some attempts were made to mitigate ionosphere-induced problems in GOCE POD by means of HOI modeling, but the success was marginal. • The dynamics of the ionosphere can be directly derived from the GPS data by forming the so-called geometry-free linear combination L gf = L 1 - L 2 , which, up to a carrier phase am- biguity, corresponds to the ionospheric refraction. Figure 2 (left) shows Swarm-A carrier phase residuals of two days with comparable orbit-Sun geometry (day 15/111: local time of as- cending arc ∼ 17 h, day 15/233: local time of descending arc ∼ 18 h), but with substantially different mean TEC in die Earth’s ionosphere, see Figure 2 (right). Note that the ionospheric disturbances are usu- ally largest for the evening hours local time. -50 -40 -30 -20 -10 0 10 20 30 40 50 -80 -60 -40 -20 0 20 40 60 80 Phase residuals [mm] Geographical latitude [deg] Ionosphere-free phase residuals Swarm-A Day 15/111 Day 15/233 10 15 20 25 30 35 40 45 001 032 060 091 121 152 182 213 244 274 305 335 Mean TEC [TECU] Day of year 2015 Figure 2: Left: carrier phase residuals of reduced-dynamic Swarm-A POD for days 15/111 (21-Apr-2015) and 15/233 (21-Aug-2015). Right: daily mean TEC as derived by the Center for Orbit Determination in Europe (CODE). The two vertical lines mark the days 15/111 and 15/233. 1 TECU ≡ 10 16 electrons/m 2 . Polar regions Figure 3 (left) shows the time derivative dL gf /dt computed from the observations of the Swarm-A receiver to one GPS satellite (G05) during 15.6 minutes when Swarm-A was at high latitudes φ (from -60.0 ◦ to -87.4 ◦ back to -60.0 ◦ ). From minute 1304 (φ = -76.2 ◦ ) onwards the ionospheric refraction shows massive high-frequency variations, resulting in a higher noise also in the L if phase residuals. They are most probably scintillation. -5 -4 -3 -2 -1 0 1 2 3 4 5 1300 1302 1304 1306 1308 1310 1312 1314 [cm], [cm/s] Minute of day 14/353 L if dL gf /dt 0 2 4 6 8 10 12 14 16 001 032 060 091 121 152 182 213 244 274 305 335 Daily RMS(dL gf /dt) [mm] Day of year 2015 Swarm-A Swarm-B Swarm-C Figure 3: Left: time derivative of geometry-free linear combination L gf (red, char- acterizing rate of change of ionospheric refraction) and ionosphere-free carrier phase residuals (green) for Swarm-A (kinematic POD) passing the south pole on day 14/353 (19-Dec-2014). Right: daily RMS of dL gf /dt over all GPS satellites for polar passes (|φ| > 60 ◦ ). Such passes are very common for GPS observations gathered by spaceborne receivers at high latitudes. Figure 3 (right) shows the daily RMS values of dL gf /dt for all Swarm satellites and for polar passes. Note the clear correlation with the daily mean TEC in Fig- ure 2 (right). Equatorial regions While scintillation-like features of dL gf /dt do occur also at low lat- itudes, the more important phenomena are slower variations of dL gf /dt with larger amplitudes. This is illustrated in Figure 4. Figure 4: Geographically binned RMS of dL gf /dt for Swarm-A. Left: the full signal dL gf /dt is shown. Right: only the highpass part of dL gf /dt is shown (a Gauss filter of width 100 s was used to filter each pass), indicating the geographical locations of scintillation-like features. The latter also appear for equatorial crossings, but the large RMS for low latitudes in the left plot is mainly due to the deterministic behavior shown in Figure 5 (left). Figure 5 (left) shows an equatorial pass (from 30 ◦ to -30 ◦ geograph- ical latitude) for Swarm-A on November 1, 2014. -6 -4 -2 0 2 4 6 8 198 200 202 204 206 208 210 212 0 2 4 6 8 10 [cm], [cm/s] Number of satellites Minute of day 14/305 dL gf /dt L if Num. sat. ΔR 0 5 10 15 20 25 30 35 001 032 060 091 121 152 182 213 244 274 305 335 Daily RMS(dL gf /dt) [mm] Full signal Swarm-A Swarm-B Swarm-C 0 1 2 3 4 5 6 7 8 9 001 032 060 091 121 152 182 213 244 274 305 335 Daily RMS(dL gf /dt) [mm] Day of year 2015 Highpass filtered signal Figure 5: Left: Swarm-A passing the equator on day 14/305 (01-Nov-2014) west of South America. Red: time derivative of geometry-free linear combination L gf (w.r.t. G04). Green: ionosphere-free carrier phase residuals of kinematic POD. Blue: num- ber of GPS satellites used for kinematic positioning. Magenta: difference between reduced-dynamic and kinematic Swarm-A orbit in radial direction. Right: daily RMS of dL gf /dt over all GPS satellites for equatorial passes (|φ| < 30 ◦ ). The top figure shows the full signal, the bottom plot only the highpass part. On minutes 204 (φ =4.9 ◦ ) and 210 (φ = -18.1 ◦ ) the difference be- tween the reduced-dynamic and the kinematic orbit shows short de- viations of several centimeters. Due to the stiffness of the reduced- dynamic orbit (6 minutes piecewise constant empirical accelerations were set up) these deviations have to be attributed to the kinematic orbit. They will be mapped into a gravity field solution recovered from these kinematic positions (see Fig. 8, left). Figure 6 shows that the GPS receivers on the GRACE satellites be- haves differently under similar ionospheric conditions. Figure 6: Number of missing GPS observations for GRACE-B (left) and Swarm-A (right) for March 2014. For these days the ascending arcs of GRACE-B and the de- scending arcs of Swarm-A passed the equator in the evening hours and the TEC was relatively high (38-44 TECU). While the Swarm receiver shows virtually no miss- ing observations, the GRACE receiver skips a significant number of observations along the geomagnetic equator. This is presumably one of the reasons why GPS- only GRACE gravity fields show no, or at least very much reduced spurious signals along the geomagnetic equator. Impact of tracking loop settings The bandwidth of the L 1 carrier loop was increased by 50 % (from 10 to 15 Hz) and the bandwidth of the L 2 carrier loop by 100 % (from 0.25 to 0.5 Hz) for • Swarm-C on 06-May-2015 (day 15/126) • Swarm-A on 08-Oct-2015 (day 15/281) • Swarm-B on 10-Oct-2015 (day 15/283). Figure 7 shows that the tracking loop changes mainly decrease the carrier phase residuals at high latitudes (compare Swarm-A and -C between days 126 and 281). Figure 7: Daily RMS values of L if phase residuals of kinematic POD for polar (top) and equatorial (bottom) passes. The three vertical lines indicate the days on which the tracking loop updates occurred. Original tracking loops Updated tracking loops Figure 8: Monthly gravity fields recovered from kinematic positions of Swarm-A (left) and Swarm-C (right) for June (top) and September (bottom) 2015. Geoid height differences of degree and order 90 solutions w.r.t. GOCO05S are shown, a 400 km Gauss filter was applied. Figure 8 shows that the tracking loop updates also help to substan- tially reduce the artifacts in the gravity field solution along the ge- omagnetic equator. In June and September 2015 Swarm-C had the updated settings, while Swarm-A was still at the old settings. Fig- ure 9 shows that the tracking loop update did not cause the receiver of Swarm-C to reject the data along the geomagnetic equator. We therefore conclude that this data was “corrupted” prior to the track- ing loop update! Figure 9: Number of missing GPS observations for Swarm-A (left) and Swarm-C (right) for September 2015. Similar picture for June 2015. Conclusions • Ionospheric disturbances have an important effect on GPS- based LEO POD and gravity field recovery, even when using the ionosphere-free linear combination. • The first time derivative of the geometry-free linear combina- tion L gf is used to characterize the behavior of the ionospheric refraction. For Swarm, scintillation-like features of dL gf /dt oc- cur mainly at high latitudes, while the equatorial crossings are characterized by large, but deterministic changes of dL gf /dt. • The variations of the ionospheric refraction over the equator induce systematic biases in the kinematic positions. They map into gravity fields recovered from these positions. While un- considered HOI modeling might play a certain role, receiver- specific tracking problems are likely the main cause of the degrada- tions. An increase of the Swarm tracking loop bandwidths sub- stantially reduces the traces of the geomagnetic equator in the gravity field solutions. • The increased tracking loop bandwidths also result in smaller L if residual noise at high latitudes. This might be in particular beneficial for space baselines determined for orbit and gravity field computations. References Hoque, M. M., and Jakowski, N. (2008) Estimate of higher order ionospheric errors in GNSS positioning. Radio Sci., 43, RS5008, doi:10.1029/2007RS003817 Jäggi, A., Bock, H., Meyer, U., Beutler, G., van den IJssel, J. (2015a) GOCE: assessment of GPS-only gravity field determination. J Geod 89:33-48, doi:10.1007/s00190-014- 0759-z Jäggi, A., Dahle, C., Arnold, D., Bock, H., Meyer, U., Beutler, G., van den IJssel, J. (2015b) Swarm kinematic orbits and gravity fields from 18 months of GPS data. Adv Space Res, 57(1), 218-233, doi:10.1016/j.asr.2015.10.035 Contact address Daniel Arnold Astronomical Institute, University of Bern Sidlerstrasse 5 3012 Bern (Switzerland) [email protected] source: https://doi.org/10.7892/boris.85133 | downloaded: 10.6.2020
Transcript of orbit determination of Low Earth Orbiters Impact of the ... · Astronomical Institute, University...
AIUB
ESA LPS-929ESA Living Planet Symposium 20169 - 13 May 2016, Prague, Czech Republic
D. Arnold1, C. Dahle1,2, A. Jäggi1, G. Beutler1, U. Meyer1
1Astronomical Institute, University of Bern, Bern, Switzerland2GFZ German Research Centre for Geosciences, Potsdam, Germany
Poster compiled by Daniel Arnold, May 2016Astronomical Institute, University of Bern, [email protected]
Impact of the ionosphere on GPS-based preciseorbit determination of Low Earth Orbiters
IntroductionDeficiencies in gravity fields derived from the orbital trajectories ofLow Earth Orbiting (LEO) satellites determined by GPS-based Pre-cise Orbit Determination (POD) were identified in recent years. Theprecise orbits of the Gravity Field and Steady-State Ocean Circula-tion Explorer (GOCE) mission are, e.g., severely affected by an in-creased position noise level over the geomagnetic poles and spuri-ous signatures along the Earth’s geomagnetic equator. This is illus-trated in Figure 1, showing the carrier phase residuals of a reduced-dynamic orbit determination for GOCE in meters, binned to theionospheric piercing points at 450 km altitude (Jäggi et al., 2015a).The degradation of the orbits directly maps into the gravity fieldsrecovered from these orbits.
Figure 1: Carrier phase residuals of reduced-dynamic GOCE POD (in m). Systematicsignatures along the geomagnetic equator are visible.
The same problems are evident, as well, for the on-going ESA mis-sions Swarm and Sentinel. They are related to a disturbed GPSsignal propagation through the Earth’s ionosphere. While thismight indicate that the GPS observation model and/or the data pre-processing need to be improved, there is now strong evidence thatreceiver-specific tracking problems under difficult ionospheric con-ditions play an important role.
GPS and ionosphereThe propagation of a microwave signal of frequency f emitted byGPS satellites is dispersively affected by the free electrons in theEarth’s ionosphere:
∆ρion = ±CX
2Ef−2 +O(f−3) , (1)
where ∆ρion is the path delay due to the ionosphere, CX/2 ≈40 m3s−2 and E =
∫Ne(ρ)dρ is the line-of-sight total electron con-
tent (TEC), obtained by integrating the electron densityNe along theray path. The negative sign in Eq. (1) refers to the phase advance(phase observations), the positive sign to the group delay (code ob-servations), respectively.
• GPS satellites emit microwave signals at two frequencies (f1 =1575.42 MHz and f2 = 1227.60 MHz) and the ionosphere-freelinear combination Lif = (f21L1 − f22L2)/(f21 − f22 ) of the twooriginal carrier phase observations L1 and L2 eliminates theionospheric refraction proportional to f−2.
• The terms O(f−3) are called higher-order ionospheric (HOI)corrections. They are not eliminated by forming Lif. Theirmodeling requires the knowledge of the electron density andthe magnetic field along the ray path (Hoque et al., 2008).
• All orbit and gravity field solutions presented here were ob-tained by using only the ionosphere-free linear combination.In Jäggi et al. (2015a) some attempts were made to mitigateionosphere-induced problems in GOCE POD by means of HOImodeling, but the success was marginal.
• The dynamics of the ionosphere can be directly derived fromthe GPS data by forming the so-called geometry-free linearcombination Lgf = L1 − L2, which, up to a carrier phase am-biguity, corresponds to the ionospheric refraction.
Figure 2 (left) shows Swarm-A carrier phase residuals of two dayswith comparable orbit-Sun geometry (day 15/111: local time of as-cending arc∼ 17 h, day 15/233: local time of descending arc∼ 18 h),but with substantially different mean TEC in die Earth’s ionosphere,see Figure 2 (right). Note that the ionospheric disturbances are usu-ally largest for the evening hours local time.
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Figure 2: Left: carrier phase residuals of reduced-dynamic Swarm-A POD for days15/111 (21-Apr-2015) and 15/233 (21-Aug-2015). Right: daily mean TEC as derivedby the Center for Orbit Determination in Europe (CODE). The two vertical lines markthe days 15/111 and 15/233. 1TECU ≡ 1016 electrons/m2.
Polar regionsFigure 3 (left) shows the time derivative dLgf/dt computed fromthe observations of the Swarm-A receiver to one GPS satellite (G05)during 15.6 minutes when Swarm-A was at high latitudes φ (from−60.0◦ to −87.4◦ back to −60.0◦). From minute 1304 (φ = −76.2◦)onwards the ionospheric refraction shows massive high-frequencyvariations, resulting in a higher noise also in the Lif phase residuals.They are most probably scintillation.
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Figure 3: Left: time derivative of geometry-free linear combination Lgf (red, char-acterizing rate of change of ionospheric refraction) and ionosphere-free carrier phaseresiduals (green) for Swarm-A (kinematic POD) passing the south pole on day 14/353(19-Dec-2014). Right: daily RMS of dLgf/dt over all GPS satellites for polar passes(|φ| > 60◦).
Such passes are very common for GPS observations gathered byspaceborne receivers at high latitudes. Figure 3 (right) shows thedaily RMS values of dLgf/dt for all Swarm satellites and for polarpasses. Note the clear correlation with the daily mean TEC in Fig-ure 2 (right).
Equatorial regionsWhile scintillation-like features of dLgf/dt do occur also at low lat-itudes, the more important phenomena are slower variations ofdLgf/dt with larger amplitudes. This is illustrated in Figure 4.
Figure 4: Geographically binned RMS of dLgf/dt for Swarm-A. Left: the full signaldLgf/dt is shown. Right: only the highpass part of dLgf/dt is shown (a Gauss filterof width 100 s was used to filter each pass), indicating the geographical locationsof scintillation-like features. The latter also appear for equatorial crossings, but thelarge RMS for low latitudes in the left plot is mainly due to the deterministic behaviorshown in Figure 5 (left).
Figure 5 (left) shows an equatorial pass (from 30◦ to−30◦ geograph-ical latitude) for Swarm-A on November 1, 2014.
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Figure 5: Left: Swarm-A passing the equator on day 14/305 (01-Nov-2014) west ofSouth America. Red: time derivative of geometry-free linear combination Lgf (w.r.t.G04). Green: ionosphere-free carrier phase residuals of kinematic POD. Blue: num-ber of GPS satellites used for kinematic positioning. Magenta: difference betweenreduced-dynamic and kinematic Swarm-A orbit in radial direction. Right: daily RMSof dLgf/dt over all GPS satellites for equatorial passes (|φ| < 30◦). The top figureshows the full signal, the bottom plot only the highpass part.
On minutes 204 (φ = 4.9◦) and 210 (φ = −18.1◦) the difference be-tween the reduced-dynamic and the kinematic orbit shows short de-viations of several centimeters. Due to the stiffness of the reduced-dynamic orbit (6 minutes piecewise constant empirical accelerationswere set up) these deviations have to be attributed to the kinematicorbit. They will be mapped into a gravity field solution recoveredfrom these kinematic positions (see Fig. 8, left).Figure 6 shows that the GPS receivers on the GRACE satellites be-haves differently under similar ionospheric conditions.
Figure 6: Number of missing GPS observations for GRACE-B (left) and Swarm-A(right) for March 2014. For these days the ascending arcs of GRACE-B and the de-scending arcs of Swarm-A passed the equator in the evening hours and the TEC wasrelatively high (38-44 TECU). While the Swarm receiver shows virtually no miss-ing observations, the GRACE receiver skips a significant number of observationsalong the geomagnetic equator. This is presumably one of the reasons why GPS-only GRACE gravity fields show no, or at least very much reduced spurious signalsalong the geomagnetic equator.
Impact of tracking loop settingsThe bandwidth of the L1 carrier loop was increased by 50 % (from10 to 15 Hz) and the bandwidth of the L2 carrier loop by 100 % (from0.25 to 0.5 Hz) for
• Swarm-C on 06-May-2015 (day 15/126)
• Swarm-A on 08-Oct-2015 (day 15/281)
• Swarm-B on 10-Oct-2015 (day 15/283).
Figure 7 shows that the tracking loop changes mainly decrease thecarrier phase residuals at high latitudes (compare Swarm-A and -Cbetween days 126 and 281).
Figure 7: Daily RMS values of Lif phase residuals of kinematic POD for polar (top)and equatorial (bottom) passes. The three vertical lines indicate the days on whichthe tracking loop updates occurred.
Original tracking loops Updated tracking loops
Figure 8: Monthly gravity fields recovered from kinematic positions of Swarm-A(left) and Swarm-C (right) for June (top) and September (bottom) 2015. Geoid heightdifferences of degree and order 90 solutions w.r.t. GOCO05S are shown, a 400 kmGauss filter was applied.
Figure 8 shows that the tracking loop updates also help to substan-tially reduce the artifacts in the gravity field solution along the ge-omagnetic equator. In June and September 2015 Swarm-C had theupdated settings, while Swarm-A was still at the old settings. Fig-ure 9 shows that the tracking loop update did not cause the receiverof Swarm-C to reject the data along the geomagnetic equator. Wetherefore conclude that this data was “corrupted” prior to the track-ing loop update!
Figure 9: Number of missing GPS observations for Swarm-A (left) and Swarm-C(right) for September 2015. Similar picture for June 2015.
Conclusions• Ionospheric disturbances have an important effect on GPS-
based LEO POD and gravity field recovery, even when usingthe ionosphere-free linear combination.
• The first time derivative of the geometry-free linear combina-tion Lgf is used to characterize the behavior of the ionosphericrefraction. For Swarm, scintillation-like features of dLgf/dt oc-cur mainly at high latitudes, while the equatorial crossings arecharacterized by large, but deterministic changes of dLgf/dt.
• The variations of the ionospheric refraction over the equatorinduce systematic biases in the kinematic positions. They mapinto gravity fields recovered from these positions. While un-considered HOI modeling might play a certain role, receiver-specific tracking problems are likely the main cause of the degrada-tions. An increase of the Swarm tracking loop bandwidths sub-stantially reduces the traces of the geomagnetic equator in thegravity field solutions.
• The increased tracking loop bandwidths also result in smallerLif residual noise at high latitudes. This might be in particularbeneficial for space baselines determined for orbit and gravityfield computations.
ReferencesHoque, M. M., and Jakowski, N. (2008) Estimate of higher order ionospheric errors
in GNSS positioning. Radio Sci., 43, RS5008, doi:10.1029/2007RS003817Jäggi, A., Bock, H., Meyer, U., Beutler, G., van den IJssel, J. (2015a) GOCE: assessment
of GPS-only gravity field determination. J Geod 89:33-48, doi:10.1007/s00190-014-0759-z
Jäggi, A., Dahle, C., Arnold, D., Bock, H., Meyer, U., Beutler, G., van den IJssel, J.(2015b) Swarm kinematic orbits and gravity fields from 18 months of GPS data.Adv Space Res, 57(1), 218-233, doi:10.1016/j.asr.2015.10.035
Contact addressDaniel ArnoldAstronomical Institute, University of BernSidlerstrasse 53012 Bern (Switzerland)[email protected]
source: https://doi.org/10.7892/boris.85133 | downloaded: 10.6.2020
