声波反散射问题的正则化集合卡尔曼方法  

A regularized ensemble Kalman method for acoustic inverse scattering problem

作　　者：郑祥 陈碟 ZHENG Xiang;CHEN Die(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]电子科技大学数学科学学院,四川成都611731

出　　处：《合肥工业大学学报（自然科学版）》2024年第7期971-978,共8页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金青年科学基金资助项目(11701070)。

摘　　要：集合卡尔曼滤波在处理反问题时存在稳定性不够、对初值集合依赖过大等不足,文章将集合卡尔曼滤波算法与正则化思想相结合处理声波反散射问题。在集合卡尔曼滤波框架中加入正则化思想,根据最大后验估计给出滤波过程的具体计算步骤,并进行仿真实验。仿真结果表明,该正则化集合卡尔曼滤波在处理声波反散射问题时滤波精度、稳定性都优于传统的集合卡尔曼滤波。Ensemble Kalman filter is not stable enough and depends too much on the set of initial values when processing the inverse problem.In this paper,ensemble Kalman filter algorithm and regularization idea are combined and applied to the acoustic inverse scattering problem.The regularization idea is introduced into the frame of ensemble Kalman filter,the specific calculation steps of filtering process are given based on maximum a posteriori estimate,and the numerical experiment is carried out.The numerical results show that the regularized ensemble Kalman filter is superior to the traditional ensemble Kalman filter in terms of filtering accuracy and stability in dealing with acoustic inverse scattering reconstruction.

关 键 词：反散射问题 贝叶斯理论 集合卡尔曼滤波 亥姆霍兹方程 正则化 

分 类 号：O241.8[理学—计算数学]