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Trilateration Algorithm for Cartesian to Geodetic Conversion

Goal: The Trilateration Algorithm is a new geometrical solution for the conversion of Cartesian coordinates (X,Y,Z) in ECEF into Ggodetic coordinates (B,L,h).

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Ahmed Hamdi Mansi
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Heuristic Algorithm to Compute Geodetic Height (h) from Ellipse Equation
Mohamed Eleiche
added 2 research items
This research introduces and presents a new algorithm named “Trilateration Algorithm” to compute the Geodetic coordinates (ϕ, λ, h) of any point (P), given its Cartesian coordinates (xp, yp, zp) in reference to the geodetic ellipsoid. The algorithm is based on the new “Seta-Point Theorem” in the meridian plan, which defines a new deterministic Twin-Point (P0) for any point (P). From such a Twin-Point (P0), a single iteration solution is processed to achieve highly-accurate values for (ϕ, h) using a relatively simple and deterministic computational algorithm which is both valid and stable for all values of (ϕ, h). The proposed solution was tested on a sample of 4277 points. The mean error value of the computed latitude is -2.291E-10 arc-second and the mean error value of the computed height is 3.96E-8 mm.
The transformation of Cartesian coordinates (xp, yp, zp) of a point (P) into their geodetic equivalent (φ, λ, h) in reference to the geodetic ellipsoid, is an essential requirement in geodesy. There are many well-known algorithms solving this transformation in closed-form, approximate or iterative approaches. This paper presents a new algorithm named “Trilateration Algorithm” for this transformation. It is based on the new “Seta-Point Theorem” in the meridian plan, which defines a new deterministic Twin-Point (P0) for the point (P). From the Twin-Point (P0), a single iteration solution is processed to achieve highly-accurate values for (φ, h) in a relatively simple and deterministic computation algorithm which is valid and stable for all values of (φ, h). The proposed solution was tested on a sample of 4277 points that cover all possible cases of point (P). The produced maximum absolute error in latitude is (0.000 0026″) and (0.000 476 mm) in height, computed from first iteration.
Mohamed Eleiche
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GUI for the application
 
Mohamed Eleiche
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Mohamed Eleiche
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The Trilateration Algorithm is a new geometrical solution for the conversion of Cartesian coordinates (X,Y,Z) in ECEF into Ggodetic coordinates (B,L,h).