The inverse problem for time-harmonic acoustic wave scattering to recover a sound-soft obstacle from a
given incident field and the far field pattern of the scattered field is considered. We split this problem into two
subproblems; first to reconstruct the shape from the modulus of the data and this is followed by
employing the full far field
pattern in a few measurement points to find the location of the obstacle.
We extend a nonlinear integral equation approach for shape reconstruction from the modulus of the far field
data  to the three-dimensional case. It is known, see , that the location
of the obstacle cannot be reconstructed from only the modulus of the far field pattern since it is invariant under
translations. However, employing the underlying invariance relation
and using only few far field measurements in the backscattering direction we
propose a novel approach for the localization of the obstacle.
The efficient implementation of the method is described and the feasibility of the approach is illustrated by numerical