A Kalman filter solution of the inverse scattering problem with a rational reflection coefficient

This paper presents a new inverse scattering method for reconstructing the reflectivity function of symmetric two-component wave equations, or the potential of a Schrodinger equation, when the reflection coefficient is rational. This method relies on the so-called Chandrasekhar equations which implement the Kalman filter associated to a stationary state-space model. These equations are derived by using first a general layer stripping principle to obtain some differential equations for reconstructing a general scattering medium, and by specializing these recursions to the case when the probing waves have a state-space model.