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Assessment of GPS Observables for Gravity Field Recovery from GRACE

This study discusses the setup of an orbit determination problem using least-squares and the computation of observation equations for each daily arc. It also explores the manipulation of normal equation systems and the recovery of gravity field from LEO.hl-SST data.

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Assessment of GPS Observables for Gravity Field Recovery from GRACE

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  1. Assessment of GPS Observables forGravity Field Recovery from GRACE Adrian Jäggi 24th IUGG General Assembly, 02-13 July, Perugia

  2. 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 Recovery from LEO hl-SST Data (1) Kinematic Orbit Positions Pseudo-Observations with Covariance Information Accelerometer Data (not used) Accelerometer Data (not used) • 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

  3. 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.

  4. 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

  5. L. Prange et al. Gravity Field Determination at the AIUB – The Celestial Mechanics Approach Recovery from LEO hl-SST Data (4) Cumulative Geoid Height Differences (in cm) w.r.t. EIGEN-GL04C GPS Smp: 30s Pos Smp: 30s

  6. carrier phase measurement on P2 channel (λ = 24.4 cm) L2 carrier phase measurement on C/A channel (λ = 19.0 cm, σ(LA) < σ(L1) for BlackJack receivers) LA The ionosphere-free observable may be formed as L3 = α1*L1+α2*L2 or L3‘ = α1*LA+α2*L2L3‘ is better for BlackJack receivers w.r.t. the noise GPS Carrier Phase hl-SST Observables (1) L1 carrier phase measurement on P1 channel (λ = 19.0 cm)

  7. 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

  8. Reduced-Dynamic (DD, float) Reduced-Dynamic (DD, fixed) Reduced-Dynamic (ZD) KBR RMS: 10.90 mm KBR RMS: 6.38 mm KBR RMS: 0.88 mm Kinematic (DD, float) Kinematic (DD, fixed) Kinematic (ZD) KBR RMS: 20.50 mm KBR RMS: 15.91 mm KBR RMS: 4.41 mm GRACE Carrier Phase hl-SST Observables (1)

  9. GRACE Carrier Phase hl-SST Observables (2) Difference w.r.t. EIGEN-GL04C Observations: varied Data Period: 55d Accelerometer: not used Pulses: 15min

  10. 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

  11. “time-differenced” KBR RMS: 6.10 mm 6.10 mm GRACE Carrier Phase hl-SST Observables (4) “normal” KBR RMS: 14.41 mm 5.78 mm

  12. General • Results are comparable with others LA vs. L1 • LA should be used for the recovery • No improvement for low degrees • Small benefit for very high degrees • Low degrees have to be improved • Ambiguity Resolution hardly helps • Affects expectations, e.g., for SWARM Single Satellites vs. Space Baseline Conclusions Gravity Field Recovery from CHAMP and GRACE hl-SST data has successfully been initiated at the AIUB.

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