Adaptive ensemble Kalman filter with extended sampling for inverse scattering problem with limited aperture data

In this paper, we are concerned with the inverse acoustic scattering problem of determining the position and shape of a sound-soft obstacle from the limited aperture far-field data. We propose the Adaptive Ensemble Kalman Filter (AEKF) combined with the extended sampling method (ESM) to recover the location and shape of the obstacle. Firstly, ESM is applied to identify the position of the obstacle based on the limited data. Then, the AEKF is employed to reconstruct the shape of the obstacle by adaptively updating the ensemble through a covariance adjustment guided by the Data Misfit Controller (DMC). Numerical examples are provided to demonstrate the effectiveness of the proposed method.