Basic aspects of geopotential field approximation from satellite-to-satellite tracking data

The satellite-to-satellite tracking (SST) problems are characterized from m athematical point of view. Uniqueness results are formulated. Moreover, the basic relations are developed between (scalar) approximation of the earth' s gravitational potential by 'scalar basis systems' and (vectorial) approxi mation of the gravitational field by 'vectorial basis systems'. Finally, th e mathematical justification is given for approximating the external geopot ential field by finite linear combinations of certain gradient fields (for example, gradient fields of multi-poles) consistent to a given set of SST d ata. Copyright (C) 2001 John Wiley & Sons, Ltd.