I have been reading the following article about radio navigation in general and GPS / GLONASS receiver design:
in which the author states the following about hyperbolic radionavigation:
Hyperbolic navigation systems were first implemented as ground-based navigation systems [...] Since the transmitters are located on the Earth's surface, the geometry of the problem does not allow a three-dimensional navigation. [...] To measure the altitude, one of the transmitters should be located above or below the user's receiver or at least out of the user's horizon plane.
I do not seem to be able to comprehend why this is the case. Even if the transmitters are located on the surface (e.g. Loran-C), the differences between reception times of signals from 4 transmitters would generate 3 rotational hyperboloids in 3D space, the intersection of which could be above (or below) surface.