Gravity Field Approximations Using Inertial Survey Systems

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Abstract
Inertial survey systems can be used to determine changes in the anomalous gravity vector. The underlying principle and the resulting estimation procedures are discussed in this paper. The analysis of the measuring procedure shows that the observed quantities are dependent on the second-order gradients of the anomalous potential. Thus, the usual representation by the first-order gradients does not adequately model the measurements. The model proposed in this paper considers theoretical as well as practical requirements. The estimation of gravity field changes is done by optimal filtering. The time-dependent system of differential equations representing the system errors is augmented by a set of parameters that model the anomalous gravity vector as a position-dependent quantity. This leads to a nonlinear estimation problem. Quasilinearization is discussed as one of the possible solutions. The first-order approximation of this solution is a linear estimation problem and thus can be compared to the filtering methods used in present day systems. Questions of implementation are discussed and some open problems are outlined.

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