对称阵列中基于原子范数的远近场混合源定位

Atomic norm based high-resolution mixed near-field and far-field source localization for symmetric arrays

目前现有的基于子空间和压缩感知的远近场混合源定位方法受到了网格划分的制约。同时现有方法大多仅考虑均匀阵列,缺乏对稀疏阵列定位场景的研究。文中提出了一种基于稀疏对称阵列的无网格远近场信源定位方法。该方法首先建立一个四阶累积量矩阵,利用阵列对称性质消除距离参数的影响。再利用原子范数理论,建立基于低秩矩阵重构的半正定规划问题,并通过非凸优化方法进行模型求解。进而利用范德蒙分解定理得到角度的估计值。再通过一维搜索方法来得到近场信源距离的估计值。该方法在实现角度估计时无需网格划分,因此具有较高的估计精度。该方法还能实现对信源类型的自动判断以及角度和距离参数的自动配对。同时,该方法不仅适用于均匀阵列,还适用于具有对称结构的稀疏阵列,具有更加广泛的应用场景。文中还通过一系列仿真实验验证了所提算法的有效性。

Existing subspace based or compressive sensing based localization methods for near-field(NF)and far-field(FF)sources suffer from the grid mismatch effect.Moreover,most methods consider the uniform linear array(ULA)case rather than the sparse linear array(SLA)case.A gridless mixed FF and NF source localization method for symmetric SLAs is proposed.Firslyt,a fourth-order cumulant matrix is constructed and the range parameter by using the symmetric property is eliminated.Based on the atomic norm theory,a semidefinite programming(SDP)is formulated by using the low-rank matrix reconstruction and then solved by using a non-convex method.The directions-of-arrival(DOA)is retrieved by using the Vandermonde decomposition theorem.Finally,the range estimates are obtained from one-dimensional searching.The method does not require angle discretization in DOA estimation,thus having high estimate accuracy.The sources can be automatically classified as the FF or NF ones,and the DOA and range parameters can be automatically paired.Meanwhile,the method can be applicable for the ULAs and the symmetric SLAs.Simulation experiments verify the effectiveness of the method.