4.4 3D Geodetic Model

Once the angular observations have been corrected for the deflection of the vertical, it is a simple matter to develop the mathematics for the 3D geodetic model. The reduced observations, i.e., the observables of the 3D geodetic model, are the geodetic azimuth c04-math-0471, the geodetic horizontal angle c04-math-0472, the geodetic vertical angle c04-math-0473 (or the geodetic zenith angle c04-math-0474), and the slant distance c04-math-0475. Geometrically speaking, these observables refer to the geodetic horizon and the ellipsoidal normal. The reduced horizontal angle is an angle between two normal planes, defined by the target points and the ellipsoidal normal at the observing station. The geodetic vertical angle is the angle between the geodetic horizon and the line of sight to the target.

We assume that the vertical angle has been corrected for atmospheric refraction. The model can be readily extended to include refraction parameters if needed. Thanks to the availability of GNSS systems, we no longer depend on vertical angle ...

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