On the initialization of the sensitivity matrix in variational equations
Tóm tắt
We address a claim frequently raised by one author that determination of Earth’s gravity field by satellite observations using traditional methods is mathematically flawed. Specifically, attention is drawn to the practice of setting to zero the initial sensitivity matrix in the variational equations for force model parameters. It is asserted that this would lead to mathematical contradictions. In this paper we establish necessary and sufficient conditions for the initial sensitivity matrix to be zero—conditions that are well founded and accepted worldwide in classical satellite-based determinations of the gravity field. To claim otherwise is shown to be without basis. We inspect a proposed counterexample, and find it, too, requires zero initialization of the sensitivity matrix. In addition, we review proofs and derivations from a classic textbook that also confirm zero initialization. In a numerical exercise, perfect, synthetic data for the central force problem are processed with standard procedures, and results confirm the validity of zero initialization of the sensitivity matrix.
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