一种包含组合范数惩罚项的波达方向稀疏估计方法  

A sparse estimation method for DOA involving combined norm penalties

作　　者：李宝山 徐海文[2] 陈晨[2] 李凡 LI Bao-Shan;XU Hai-Wen;CHEN Chen;LI Fan(College of Air Traffic Management,Civil Aviation Flight University of China,Guanghan 618307,China;College of Science,Civil Aviation Flight University of China,Guanghan 618307,China;Research Base of Civil Aviation Flight Technology and Flight Safety,Civil Aviation Flight University of China,Guanghan 618307,China)

机构地区：[1]中国民用航空飞行学院空中交通管理学院,广汉618307 [2]中国民用航空飞行学院理学院,广汉618307 [3]中国民用航空飞行学院民航飞行技术与飞行安全科研基地,广汉618307

出　　处：《四川大学学报（自然科学版）》2024年第3期87-94,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科技厅项目(2021JDRC0080);中央高校基本业务费面上项目(J2021-058);国家自然科学基金民航联合基金重点项目(U2033213)。

摘　　要：波达方向(Direction of Arrival,DOA)估计是阵列观测数据研究领域的一个基本问题.对于观测数据服从复椭球对称分布的应用场景,现有的方法多采用l1-范数惩罚项来实现信号波达方向的稀疏估计,其中的l1-范数惩罚项仅考虑信号的稀疏性而没有考虑信号的多样性,从而造成这些估计方法一般将弱信号(具有较低功率的信号)略去,可能无法准确地估计弱信号的波达方向.为解决这个问题,本文通过引入一个组合范数惩罚项构建了一个新的估计(模型)方法,其中的组合范数惩罚项是l1-范数惩罚项与l2-范数平方惩罚项的线性组合,其组合系数(惩罚参数)互不相关,l2-范数平方惩罚项则可以保留弱信号的多样性.然后,本文基于Majorization-Minimization(MM)算法设计了模型的求解算法,并证明该方法是收敛的.数值实验表明,相较于那些基于l1-惩罚项的估计方法,本方法具有更高的精度.The estimation of direction of arrival(DOA)is a fundamental problem in array data analysis.In the scenarios where the received array data is complex elliptically symmetrically distributed,the mainstream of sparse DOA estimation methods apply the l1-norm penalty to exploit the sparsity of DOA.In these methods,the sparsity of signal is emphasized while the diversity of signal is unfortunately neglected.As a result,these methods have to overlook the weak signals(signals with low power).In this paper,we propose a novel penalized likelihood(model)method incorporating the combination of two norm penalties for the effective estimation of DOAs including both sparse and weak signals.The combination of norm penalties is a linear com‐bination of l1-norm penalty and l2-norm square penalty with independent combination coefficients(penalty parameters),where the l2-norm square penalty term can help preserve the diversity of signal.Under the Majorization-Minimization(MM)algorithm framework,we design an algorithm to solve the model and prove its convergence.Finally,it is shown by a numerical experiment that the new method has higher estimation accuracy comparing with the known methods.

关 键 词：阵列信号 波达方向 复椭球对称分布 惩罚似然估计 MM算法 

分 类 号：O29[理学—应用数学]