In order to describe the umbrella inversion mode, which is characteristic of AB(3)-type molecules, we have introduced an alternative hyperspherical coordinate set based on a parametrization of Radau-Smith orthogonal vectors and have considered constraints which allow us to enforce the C-3 nu symmetry. Structural properties and electronic energies at equilibrium and barrier configurations have been obtained at MP2 and CCSD(T) levels of theory. Energy profiles have been calculated using the CCSD(T) method with an aug-cc-pVQZ basis set. The NH3 and H3O+ umbrella inversion levels are obtained by the hyperquantization algorithm for a one-dimensional calculation, using a specially defined hyperangle as the inversion coordinate. The results are compared with experimental and theoretical energy levels, in particular, with those obtained by calculations based on two-dimensional models. The emerging picture of the umbrella inversion based on this hyperangular coordinate compares favorably with respect to the usual valence-type description.