Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid obstacle using partial data. In the first step, the approximate location of the unknown obstacle is obtained by the extended sampling method. In the second step, the ensemble Kalman filter is employed to reconstruct the shape. The location obtained in the first step guides the construction of the initial particles of the ensemble Kalman filter, which is critical to the performance of the second step. Both steps are based on the same physical model and use the same scattering data. Numerical examples are shown to demonstrate the effectiveness of the proposed method.

当通常只有部分数据可用时，逆问题更具挑战性。在本文中，我们提出了一种结合扩展采样方法和集成卡尔曼滤波器的两步方法，以使用部分数据重建弹性刚性障碍物。第一步，通过扩展采样方法获得未知障碍物的大致位置。第二步，使用集成卡尔曼滤波器重建形状。第一步获得的位置指导集成卡尔曼滤波器初始粒子的构建，这对第二步的性能至关重要。这两个步骤都基于相同的物理模型并使用相同的散射数据。数值例子证明了所提出方法的有效性。