  In this paper, we consider the inverse problem of determining the location
and the shape of a sound-soft obstacle from the modulus of the far-field data
for a single incident plane wave. By adding a reference ball artificially to
the inverse scattering system, we propose a system of nonlinear integral
equations based iterative scheme to reconstruct both the location and the shape
of the obstacle. The reference ball technique causes few extra computational
costs, but breaks the translation invariance and brings information about the
location of the obstacle. Several validating numerical examples are provided to
illustrate the effectiveness and robustness of the proposed inversion
algorithm.
