171 research outputs found
From the time-wise to space-wise GOCE observables
No full textThe observables of the GOCE three-axis gradiometer are taken in time, along the orbit and, in the timewise proposal, filtered to stay in the measurement bandwidth, i.e. in the frequency interval between 0.005 and 0.1Hz. As a consequence, the resulting “observable" is a convolution of the original data stream with a time-wise weighting kernel. In other words, we cannot assume that the observations are point-wise evaluations of any function and so, in a spacewise approach, any averaging or interpolating operation to obtain gridded spatial data has little sense. The problem is therefore to model correctly the observational functionals, including the correlation along the orbit. This can be done by exploiting theWiener filter theory, using the prior knowledge of a geopotential model and the power spectral density (PSD) of the measurement error. A numerical simulation from the EGM96 model (degrees between 50 and 300) is performed, showing that the along track Wiener filter produces Trr spatialized observables with an error standard deviation of the order of 5 mE. A covariance function of the estimation error is also provided by the Wiener filter theory. The use of these filtered observables in a space-wise approach allows for the reconstruction of the gravity field in terms of spherical harmonics up to degree 200.Key words. Satellite gradiometry, space-wise approach, measurement bandwidth, Wiener filte
On the combination of high-resolution and satellite-only global gravity models
No full textThe issue of combining high-resolution gravity models, based on observations taken on the Earth surface, with those derived from satellite-only observations is of increasing importance, due to the new data provided by gravity satellite missions, CHAMP, GRACE and GOCE. The paper addresses this issue with a twofold purpose. On the one hand, it is an attempt to discuss and assess general concepts, well known in literature, such as achievable resolution, regularization in the least-squares sense or in an infinite dimensional setup, combination criteria, symmetry and block diagonal structures. In particular, as for the symmetry question, a well-defined result, generalizing known facts, is derived. On the other hand, the outcomes of the general discussion are specifically applied to the combination of a high-resolution model (e.g. EGM08) with a GOCE gravity model estimated by the so-called space-wise approach. Small numerical examples are developed to clarify the property of the proposed solution
GOCE: la gradiometria dallo spazio per la determinazione del campo della gravità terrestre
No full textGOCE (Gravity field and steady-state Ocean Circulation Explorer) ha rappresentato una missione di grande successo dell’Agenzia Spaziale Europea. Lanciato nel marzo 2009, il satellite ha avuto una durata ben superiore a quella inizialmente prevista, terminando nel novembre 2013. E’ stata la prima missione di gradiometria dallo spazio e ha permesso di mappare il campo gravitazionale terrestre con un livello di accuratezza e risoluzione mai raggiunti in precedenza a partire da soli dati da satellite. Dal 2010 sono stati rilasciati numerosi modelli di gravità ottenuti da dati GOCE, calcolati da diversi gruppi di ricerca a livello europeo. Il gruppo di geodesia spaziale del Politecnico di Milano è (unico in Italia) uno dei dieci gruppi dedicati all’analisi dei dati GOCE e alla produzione di modelli globali del geoide
Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis
No full textCollocation is widely used in physical geodesy. Its application requires to solve systems with a dimension equal to the number of observations, causing numerical problems when many observations are available. To overcome this drawback, tailored step-wise techniques are usually applied. An example of these step-wise techniques is the space-wise approach to the GOCE mission data processing. The original idea of this approach was to implement a two-step procedure, which consists of first predicting gridded values at satellite altitude by collocation and then deriving the geo-potential spherical harmonic coefficients by numerical integration. The idea was generalized to a multi-step iterative procedure by introducing a time-wise Wiener filter to reduce the highly correlated observation noise. Recent studies have shown how to optimize the original two-step procedure, while the theoretical optimization of the full multi-step procedure is investigated in this work. An iterative operator is derived so that the final estimated spherical harmonic coefficients are optimal with respect to the Wiener–Kolmogorov principle, as if they were estimated by a direct collocation. The logical scheme used to derive this optimal operator can be applied not only in the case of the space-wise approach but, in general, for any case of step-wise collocation. Several numerical tests based on simulated realistic GOCE data are performed. The results show that adding a pre-processing time-wise filter to the two-step procedure of data gridding and spherical harmonic analysis is useful, in the sense that the accuracy of the estimated geo-potential coefficients is improved. This happens because, in its practical implementation, the gridding is made by collocation over local patches of data, while the observation noise has a time-correlation so long that it cannot be treated inside the patch size. Therefore, the multi-step operator, which is in theory equivalent to the two-step operator and to the direct collocation, is in practice superior thanks to the time-wise filter that reduces the noise correlation before the gridding. The criteria for the choice of this filter are investigated numerically
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