Satellite gradiometry using a satellite pair

Abstract

Providing global and high-resolution estimates of the Earth's gravity field and its temporal variations with unprecedented accuracy is the primary science objective of the GRACE mission. These twin satellites are the second spacecraft of the type gravity field dedicated missions which have realized satellite to satellite tracking in the low-low mode(SST-LL). The preceding spacecraft is the low orbiting CHAMP satellite which has substantiated the high-low mode satellite to satellite tracking concept(SST-HL).

Observing inter-satellite range and range rate by the K-band Ranging System (KBR) with the highest possible accuracy is the superiority of GRACE over CHAMP. Nevertheless, LL-configuration can be combined with the HL-concept implemented in CHAMP to provide a much higher sensitivity. The line of sight (LOS) acceleration differences between the twin satellites and a Taylor expansion of the gravitational tensor components of the barycenter of the satellites, called gradiometry approach afterward, are two outcomes of the two concepts combination. Global gravity field determination in terms of spherical harmonic coefficients can be preformed using the LOS acceleration differences directly. However, full implementation of the other observable is neither possible nor required. On the other hand, being satisfied just with the applicable form of the observable corresponding to linear combination of the components of the tensor, causes linearization error. Unfortunately, contribution of this systematic error to the estimated coefficients is considerable. Therefore, the observable should be either modified or expanded at least up to third order to lower the effect of the neglected terms. Herein, the modified form of the observable will be employed due to complexity of cubic term expansion for full gravitational potential expansion. One possible modification is replacing the gravitational potential and all corresponding quantities with the incremental ones. Low-degree (up to 30) coefficients can be perfectly estimated by just using an incremental quantity corresponding to an ellipsoidal reference field. Due to simplicity of the cubic term of the expansion for an ellipsoidal reference field, a mixed linear-cubic approximation of the observable can be applied for low-degree harmonic coefficients estimation as well. Both of them yield the same numerical results. However, a reasonable accuracy can not be achieved in the higher degree (n>30) coefficients estimation with the aforementioned modification. An incremental potential correspond with a spheroidal reference field of the degree l (l>2) can be utilized instead. Redefinition of the reference field leads to an acceptable accuracy in the higher degree estimated coefficients. Another alternative is using a mixed equation in which mathematical models of the acceleration difference and the linear combination of the gravitational radient tensor elements types are considered for low-degree (n<l) and higher degree (n>l) harmonics respectively. It's equivalent to removing the contribution of a spheroidal reference field of the degree l to the observations as a deterministic trend of the measurements. Implementation of these modifications results much the same accuracy as the other approach yields.

For better understanding of the commission error behavior, the simulated observations are contaminated with a simulated Gaussian random noise sequence. Its contribution to the estimated coefficients with respect to other errors are analyzed. Besides, aliasing/omission error, the dominant degradation factor and its contribution to the estimated coefficients are studied. The numerical analysis indicates that overestimating the coefficients and weeding out the higher degree harmonics as the affected terms seems to be one of the possible strategies for minimizing the aliasing. The Gradiometry approach takes more CPU time as compared to the LOS acceleration differences. It is due to the second order derivatives of the potential calculation besides the first order derivatives which is common to both approaches. In contrast, the observable in gradiometry approach is a one-point function while the other observable is a two-point function. Therefore, in space-wise approach and local gravity field determination (i.e. local geoid), the gradiometry approach would be preferable to the other. In addition, the tensor elements indicate curvature of the gravitational potential which directly corresponds to geometry of the field.