Definition
Least-squares collocation (LSC) is one important method for the solution of the partial differential equation for the determination of the anomalous gravity potential (disturbing potential).
Introduction
The difference T = W-U is denoted the anomalous gravity potential . W is the gravity potential and U is a suitable reference potential which includes the same centrifugal potential as W. T therefore becomes a harmonic function , i.e., it satisfies the Laplace equation outside the masses of the Earth. (The contribution of the Moon and the planets, as well as of the atmosphere, will not be discussed here.) The determination of (approximations to) T is thus equivalent to the solution of a partial differential equation. The following discussion will be limited to the solution in 3 dimensions. For 2 dimensions see Forsberg (1984).
One of the methods for the solution of the partial differential equation in the form of an approximation to Tis the method of least-squares...
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References and Reading
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Tscherning, C.C. (2015). Least-Squares Collocation. In: Grafarend, E. (eds) Encyclopedia of Geodesy. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_51-1
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DOI: https://doi.org/10.1007/978-3-319-02370-0_51-1
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