Assessment of GPS Observables for
Gravity Field Recovery from GRACE
Adrian Jäggi
24th IUGG General Assembly, 02-13 July, Perugia
Astronomisches Institut, Universität Bern
Recovery from LEO hl-SST Data (1)
Kinematic Orbit Positions
Pseudo-Observations with
Covariance Information
Accelerometer Data
(not used)
Set-Up of an Orbit Determination Problem by Least-Squares
- computation of the observation equations for each daily arc by numerical integration
(estimated parameters: SH coefficients, arc-specific parameters, e.g., initial conditions and pulses)
- construction of the normal equations for each daily arc
Manipulation of Normal Equation Systems
- manipulation and subsequent pre-elimination of arc-specific parameters
(e.g., constraining or downsampling of pulses)
- accumulation of the daily normal equations into weekly, monthly, and yearly systems
- regularization of SH coefficients
(not used so far)
- inversion of the resulting normal equation systems
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Astronomisches Institut, Universität Bern
Recovery from LEO hl-SST Data (2)
CHAMP Kinematic Orbits
1 year of data (DOY 071, 2002 – DOY 070, 2003)
Jäggi, A., G. Beutler, H. Bock, U. Hugentobler 2006: Kinematic and highly reduced-dynamic LEO orbit
determination for gravity field estimation, in Dynamic Planet – Monitoring and Understanding a
Dynamic Planet with Geodetic and Oceanographic Tools , edited by C. Rizos and P. Tregoning, pp.
354-361, Springer.
GRACE Kinematic Orbits
1 year of data (DOY 001, 2003 – DOY 365, 2003)
Jäggi, A., U. Hugentobler, H. Bock, G. Beutler 2007: Precise Orbit Determination for GRACE Using
Undifferenced or Doubly Differenced GPS Data, Advances in Space Research, in press, available online
at http://dx.doi.org/10.1016/j.asr.2007.03.012.
GRACE Kinematic Baselines
55 days of data (DOY 243, 2003 – DOY 297, 2003)
Jäggi, A., U. Hugentobler, H. Bock, G. Beutler 2007: Precise Orbit Determination for GRACE Using
Undifferenced or Doubly Differenced GPS Data, Advances in Space Research, in press, available online
at http://dx.doi.org/10.1016/j.asr.2007.03.012.
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Astronomisches Institut, Universität Bern
Recovery from LEO hl-SST Data (3)
Difference w.r.t. EIGEN-GL04C
Observations:
30s positions
Data Period:
1 year
Accelerometer:
not used
Pulses:
15min
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Astronomisches Institut, Universität Bern
Recovery from LEO hl-SST Data (4)
Cumulative Geoid Height Differences
(in cm) w.r.t. EIGEN-GL04C
GPS Smp:
30s
Pos Smp:
30s
L. Prange et al.
Gravity Field Determination at the AIUB –
The Celestial Mechanics Approach
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Astronomisches Institut, Universität Bern
GPS Carrier Phase hl-SST Observables (1)
L1
carrier phase measurement on P1 channel
(λ = 19.0 cm)
L2
carrier phase measurement on P2 channel
LA
carrier phase measurement on C/A channel
(λ = 24.4 cm)
(λ = 19.0 cm, σ(LA) < σ(L1) for BlackJack receivers)
The ionosphere-free observable may be formed as
L3 = α1*L1+α2*L2
or
L3‘ = α1*LA+α2*L2
L3‘ is better for BlackJack receivers w.r.t. the noise
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Astronomisches Institut, Universität Bern
GPS Carrier Phase hl-SST Observables (2)
Difference w.r.t. EIGEN-GL04C
Observations:
30s positions
Data Period:
1 year
Accelerometer:
not used
Pulses:
15min
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Astronomisches Institut, Universität Bern
GRACE Carrier Phase hl-SST Observables (1)
Reduced-Dynamic
(DD,
float)
fixed)
Reduced-Dynamic
(ZD)
KBR RMS:
10.90mm
6.38
0.88
mm
Kinematic
Kinematic
Kinematic
(DD,
(DD,(ZD)
fixed)
float)
KBR RMS:
20.50mm
15.91
4.41
mm
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Astronomisches Institut, Universität Bern
GRACE Carrier Phase hl-SST Observables (2)
Difference w.r.t. EIGEN-GL04C
Observations:
varied
Data Period:
55d
Accelerometer:
not used
Pulses:
15min
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Astronomisches Institut, Universität Bern
GRACE Carrier Phase hl-SST Observables (3)
Difference w.r.t. EIGEN-GL04C
Observations:
30s pos. diff.
Data Period:
55d
Accelerometer:
not used
Pulses:
15min
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Astronomisches Institut, Universität Bern
GRACE Carrier Phase hl-SST Observables (4)
“normal”
KBR RMS:
14.41 mm
5.78 mm
“time-differenced”
KBR RMS:
6.10 mm
6.10 mm
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Astronomisches Institut, Universität Bern
Conclusions
Gravity Field Recovery from CHAMP and GRACE hl-SST
data has successfully been initiated at the AIUB.
General
•Results are comparable with others
LA vs. L1
•LA should be used for the recovery
•No improvement for low degrees
Single Satellites
vs.
Space Baseline
•Small benefit for very high degrees
•Low degrees have to be improved
•Ambiguity Resolution hardly helps
•Affects expectations, e.g., for SWARM
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Astronomisches Institut, Universität Bern