Stochastic Modeling of GOCE Gravitational Tensor Invariants
The aim of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) Mission is to provide global and regional models of the Earth’s time-averaged gravity field and of the geoid with high spatial resolution and accuracy. The approach based on the rotational invariants of the gravitational tensor constitutes an independent alternative to conventional analysis methods. Due to the colored noise characteristic of individual gradiometer observations, the stochastic model assembly of the rotational invariants is a highly challenging task on its own. In principle, the invariants’ variance-covariance (VC) information can be deduced from the gravitational gradients (GG) by error propagation. But the huge number of gradiometer data and the corresponding size of the VC matrix prohibit this approach. The time series of these invariants, however, display similar stochastic characteristics as the gravitational gradients. They can thus be decorrelated by means of numerical filters. A moving-average (MA) filter of order 50 has been estimated and a filter cascade (high-pass and MA filters) has been developed. This filter cascade has been implemented in the decorrelation of the GOCE tensor invariant observation model.
KeywordsPower Spectral Density Gravity Gradient Colored Noise Gravity Field Model Stochastic Characteristic
We gratefully acknowledge the financial support of the BMBF (Bundesministerium für Bildung und Forschung) and the DFG (Deutsche ForschungsGemeinschaft). Within the GEOTECHNOLOGIEN programme. Furthermore, we kindly acknowledge helpful support in the estimation of the filter by W.-D. Schuh and I. Krasbutter.
- Baur O, Sneeuw N, Cai J, Roth M (2010) GOCE data analysis: realization of the invariants approach in a high performance computing environment. In: Proceedings of the ESA living planet symposium, Bergen, Norway, 28 June-2 July, 2010, ESA SP-686Google Scholar
- Brockmann JM, Kargoll B, Krasbutter I, Schuh W-D, Wermuth M (2010) GOCE Data analysis: from calibrated measurements to the global earth gravity field. In: Flechtner F, Gruber T, Guntner A, Mandea M, Rothacher M, Schone T, Wickert J (eds) System earth via geodetic-geophysical space techniques, advanced technologies in earth sciences, Springer, Berlin, pp 213–229Google Scholar
- Brockwell PJ, Davis RA (2002) Introduction to time series and forecasting, 2nd edn. Springer, New YorkGoogle Scholar
- Cai J, Baur O, Sneeuw N (2010) GOCE gravity field determination by means of rotational invariants: first experiences, GEOTECHNOLOGIEN Science Report Nr. 17, Observation of the system earth from space, pp 62–69Google Scholar
- Hamming RW (1989) Digital filters, 3ed edn. Prentice Hall, New JerseyGoogle Scholar
- Krasbutter I, Brockmann JM, Kargoll B, Schuh W-D (2010) Stochastic model refinements for GOCE gradiometry data, GEOTECHNOLOGIEN Science Report Nr. 17, Observation of the system earth from space, pp 70–76Google Scholar
- Oppenheim AV, Schafer RW (1999) Discrete-time signal processing, Pearson; 2nd edn. Prentice Hall, New JerseyGoogle Scholar
- Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh W-D, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geod 85:819–843. doi: 10.1007/s100190-011-0467-x CrossRefGoogle Scholar
- Rummel R (1986) Satellite gradiometry. In: Sünkel H (ed) Mathematical and numerical techniques in physical geodesy, Lecture notes in earth sciences, 7. Springer, Berlin, pp 317–363. doi: 10.1007/BFb0010135
- Schuh W-D (1996) Tailored numerical solutions strategies for the global determination of the Earth’s gravity field, Mitteilungen der Universität Graz 81Google Scholar
- Schuh W-D, Brockmann JM, Kargoll B, Krasbutter I (2010) Refinement of the stochastic model of GOCE scientific data and its effect on the in-site gravity field solution. In: Proceedings of ESA living planet symposium, Bergen, Norway, 28 June - 2 July 2010, ESA SP-686Google Scholar
- Siemes C (2008) Digital filtering algorithms for decorrelation within large least squares problems. Ph.D. thesis, Institute of Geodesy and Geoinformation, University of Bonn, BonnGoogle Scholar