What is the closest geometrical shape used to approximate the Earth in GPS observations?

The Earth's shape is best approximated by an ellipsoid when it comes to GPS observations. This is due to the fact that the Earth is not a perfect sphere; it has irregularities caused by its rotation and gravitational forces exerted by the mass distribution within the planet. An ellipsoid represents these variations more accurately by allowing for a bulge around the equator and flattening at the poles.

In GPS technology, which relies on precise calculations of distance and positioning, using a spheroid model (or ellipsoid) ensures better accuracy for determining locations on Earth. The mathematical equations and parameters used in GPS systems, like the WGS84 (World Geodetic System 1984), are based on an ellipsoidal model that takes into account the Earth's measured deviations from a perfect sphere.

The other geometrical shapes, such as a sphere, cylinder, or cube, do not reflect the Earth's true form and lack the necessary accuracy for the calculations performed in GPS systems. Therefore, given the need for precision in geospatial measurements, the ellipsoid is the appropriate choice for approximating the Earth's shape.