基于核范数最小的正定Toeplitz填充算法及稀疏阵列解模糊应用  

Positive definite Toeplitz completion algorithm via nuclear norm minimization and ambiguity resolution for sparse array

作　　者：陈根华[1] 罗晓萱 CHEN Genhua;LUO Xiaoxuan(School of Information Engineering,Nanchang Institute of Technology,Nanchang 330099,China)

机构地区：[1]南昌工程学院信息工程学院,江西南昌330099

出　　处：《南昌工程学院学报》2020年第4期72-79,共8页Journal of Nanchang Institute of Technology

基　　金：国家自然科学基金资助项目(61401187);江西省教育厅科学技术研究项目(GJJ170990)。

摘　　要：稀疏阵列流形是模糊的,但当其差分伴随阵连续且完备时,可通过阵列协方差相关序列的Toeplitz变换实现疏阵列流形识别与解模糊。当伴随阵不连续完备时,需估计缺失相关项。本文将估计缺失相关项转换成Toeplitz填充优化问题,并提出核范数最小的正定Toeplitz填充算法。该算法先对最大熵约束下Toeplitz的正定性约束松弛为矩阵的迹为正,将其转换为核范数约束优化问题,并提出截断的均值奇异值门限法求解缺失相关项,最后实现最近邻准则下的正定Teoplitz填充。该算法适用于任意稀疏线阵流形解模糊,有效地提高填充的稳定性,降低了计算复杂度。仿真结果验证了算法的有效性、正确性和实时性。The sparse linear array manifold is ambiguous for its sub-Nyquist sampling.However,the manifold identification and ambiguity resolution could easily be achieved through the structured Toeplitz transform with its covariance lags when its difference coarray is consecutive and complete.But the missing covariance gaps should be estimated for ambiguity resolution when there are some missing lags in the difference coarray.The novel positive definite Toeplitz completion algorithm based on nuclear norm constraint is proposed for the estimation of the missing covariance gaps.Then Toeplitz completion is transformed into nuclear norm optimization through the positive trace relaxation of the positive definiteness under maximum entropy constraint.Therefore,the nuclear norm optimization problem is solved for the missing gaps using the mean-valued truncated singular value threshold algorithm.Subsequently the positive definite Toeplitz is computed by the alternating convex projection under the closest neighbor criterion.This allows fast and stable Toeplitz completion for the missing covariance gaps with arbitrary sparse linear array structure.Extensive simulation results demonstrate that the proposed algorithm is validate and has the better real-time performance.

关 键 词：正定Toeplitz填充 解模糊 核范数 差分伴随阵 稀疏阵列 

分 类 号：TN958[电子电信—信号与信息处理]