泰勒展开与交替投影最大似然结合的离网格DOA估计算法  

Off-grid DOA Estimation Algorithm Based on Taylor-expansion and Alternating Projection Maximum Likelihood

作　　者：刘帅[1] 许媛媛 闫锋刚 金铭[1] LIU Shuai;XU Yuanyuan;YAN Fenggang;JIN Ming(School of Information Science and Engineering,Harbin Institute of Technology(Weihai),Weihai 264209,China)

机构地区：[1]哈尔滨工业大学(威海)信息科学与工程学院,威海264209

出　　处：《电子与信息学报》2024年第8期3219-3227,共9页Journal of Electronics & Information Technology

基　　金：国家自然科学基金面上项目(62071144,62171150);泰山学者工程专项经费(tsqn202211087)。

摘　　要：针对最大似然DOA估计算法需要多维搜索、计算量大且面临着在网格估计的问题,该文提出一种基于泰勒展开的离网格交替投影最大似然算法。该方法首先利用交替投影将多维搜索转化为多个1维搜索,获得对应预设大网格的粗估计结果;再利用矩阵求导理论将1维代价函数在粗估计结果处进行2阶泰勒展开;最后通过对2阶泰勒展开求偏导并令导数等于零,求得离网参数的闭式解。与交替投影最大似然算法相比,该方法突破了搜索网格大小的限制,在保证算法精度的同时,有效减少了算法的在网格计算点数,提升了运算效率。仿真结果证明了该算法的有效性。According to the problem that the maximum likelihood DOA estimation algorithm requires multidimensional search,is computationally intensive,and there is a problem in grid estimation,an Off-grid alternating projection maximum likelihood algorithm based on Taylor expansion is proposed.Firstly,the alternating projection method is used to transform the multi-dimensional search into multiple one-dimensional searches to obtain the rough estimation results corresponding to the preset large grid.Then,the second-order Taylor expansion of the one-dimensional cost function at the rough estimation results is carried out by using the matrix derivation theory.Finally,by calculating the partial derivative of the second-order Taylor expansion and making the derivative equal to zero,the closed-form solution of the off-grid parameters is obtained.Compared with the alternating projection maximum likelihood algorithm,the proposed algorithm breaks through the limitation of the search grid size.It effectively reduces the number of points in the grid calculation of the algorithm while ensuring the accuracy of itself,and improves the operation efficiency.Simulation results show the effectiveness of the algorithm.

关 键 词：最大似然算法 交替投影 离网格 泰勒展开 

分 类 号：TN911.7[电子电信—通信与信息系统]