  In this paper, we study the inverse medium scattering problem to reconstruct
unknown inhomogeneous medium from far field patterns of scattered waves. In the
first part of our work, the linear inverse scattering problem was discussed,
while in the second part, we deal with the nonlinear problem. The main idea is
to apply the linear Kalman filter to the linearized problem. There are several
ways to linearize, which introduce two reconstruction algorithms. Finally, we
give numerical examples to demonstrate our proposed method.
