基于稀疏信号重构的阵元位置误差校正方法

A sparse signal reconstruction perspective for hydrophone array shape calibration

阵元位置误差的存在会严重影响水听器阵列的测向性能,为此在使用阵列之前需对该误差进行校正。针对这一需求,提出了一种对任意阵型适用的高精度阵元位置有源校正方法。结合远场阵列模型以及位置误差"有界"的特点,基于压缩感知理论,将阵元位置估计转化为对稀疏信号的重构过程,建立了阵元位置误差模型,构造了该模型下凸优化函数,并采用l_1-SVD(Singular Value Decomposition,SVD)方法进行求解,同时给出了物理解释和算法实施步骤。计算机仿真表明基于稀疏信号重构的校正方法性能明显高于子空间拟合算法,且性能接近相应克拉美罗下界,对于校正源方位误差有较强的容错能力,不受制于微小误差的假设以及初值的选取。该方法是一种可对阵列中的部分或全部阵元进行校正的高精度、稳健的有源校正算法。

The performance of array processing algorithms critically depends on the precise knowledge of the array shape. Calibration of array shape error must be obtained in advance. A high precision array shape calibration method using sources in known directions which can be applied to arbitrary array geometries is proposed. With the prior knowledge of the bound of senor location uncertainty, the problem of array shape estimation is transformed into the process of sparse signal reconstruction from multiple time measurements with overcomplete basis. A geometry error model combined with compressed sensing method is established. The convex objective function penalized by l1-norm aimed to enforce sparsity is efficiently solved in second-order cone（SOC） programming framework. The l1 SVD algorithm is used to summarize multiple time samples. The physical interpretation and algorithm implementation steps are also explained. Computer simulations indicate the effectiveness of the proposed method by comparing the estimator RMSE to the Cramer-Rao lower bound（CRLB）. Other advantages include high calibration precision, robustness to direction of calibration sources and not requiring accurate initialization.