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How to Compute Interval Inclusions of Geodetic Coordinates from Interval Inclusions of Cartesian Coordinates

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Reliable Computing

Abstract

In satellite geodesy the position of a point P is usually determined by computing its coordinate vector x with respect to an earth-fixed Cartesian coordinate system S. S is chosen such that a rotational ellipsoid E, closely approximating the surface of the earth, has normal form with respect to S. Since the geodetic coordinates of P with respect to E (ellipsoidal latitude ϕ, ellipsoidal longitude λ, and ellipsoidal height h) describe the location of P with respect to the surface of the earth much better than x, a frequently appearing problem is to compute ϕ, λ, and h from x.

In practice this problem is solved by iterative methods, the convergence properties of which are not analyzed in detail but for which fast (numerical) convergence is observed for points near to E.

In the present paper a theoretically well founded new method is developed, working for all P having a unique nearest point in E.

In addition it will be shown that the new method can be implemented such that interval inclusions for ϕ, λ, and h can be computed from interval inclusions of the components of x.

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Heindl, G. How to Compute Interval Inclusions of Geodetic Coordinates from Interval Inclusions of Cartesian Coordinates. Reliable Computing 3, 421–435 (1997). https://doi.org/10.1023/A:1009953605448

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  • DOI: https://doi.org/10.1023/A:1009953605448

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