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
李宝山 1徐海文 2陈晨 2李凡3
作者信息
- 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
- 折叠
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.
Abstract
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 meth-ods,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 es-timation 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 pa-rameters),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 estima-tion 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Key words
Array signals/Direction of arrival/Complex elliptically symmetric distribution/Penalized likeli-hood estimation/MM algorithm引用本文复制引用
基金项目
四川省科技厅项目(2021JDRC0080)
中央高校基本业务费专项面上项目(J2021-058)
国家自然科学基金-中国民用航空总局联合资助重点项目(U2033213)
出版年
2024
国家科技期刊平台
NSTL
万方数据