  We are interested in the identification of a Generalized Impedance Boundary
Condition from the far--fields created by one or several incident plane waves
at a fixed frequency. We focus on the particular case where this boundary
condition is expressed with the help of a second order surface operator: the
inverse problem then amounts to retrieve the two functions $\lambda$ and $\mu$
that define this boundary operator. We first derive a global Lipschitz
stability result for the identification of $\ld$ or $\mu$ from the far--field
for bounded piecewise constant impedance coefficients and we give a new type of
stability estimate when inexact knowledge of the boundary is assumed. We then
introduce an optimization method to identify $\lambda$ and $\mu$, using in
particular a $H^1$-type regularization of the gradient. We lastly show some
numerical results in two dimensions, including a study of the impact of some
various parameters, and by assuming either an exact knowledge of the shape of
the obstacle or an approximate one.
