阵元失效下基于Khatri-Rao积的高分辨测向方法

High-resolution DOA estimation method based on Khatri-Rao product in presence of element failure

摘要:

在雷达、声呐、深空通信等实际应用中，阵元的失效会造成检测性能下降，虚警率增加；在目标方位估计中，阵元失效会造成采样协方差矩阵的秩亏问题，使得基于子空间类的传统目标方位估计方法失效。针对存在阵元失效的均匀线列阵的目标方位估计问题，提出了一种基于Khatri-Rao(KR)积处理的阵列自由度恢复方法以及Toeplitz矩阵数据重构的高分辨DOA估计方法。首先对有损伤的阵列采样协方差矩阵进行KR积处理，将产生的冗余项进行平均处理, 处理后的阵列模型将重构阵列自由度，并将阵列孔径扩展为之前的2倍。该阵列模型等效为一确定噪声下的单快拍的相干源估计, 采用基于Toeplitz矩阵数据重构的方法来去相干，重构协方差，最后采用MUSIC方法进行方位估计。数值仿真表明该方法能有效解决均匀线列阵阵元失效下的自由度损失问题，提高阵列的目标方位估计性能，而且具有计算量小的优点。

Abstract:

An array freedom recovery method based on Khatri-Rao(KR) product and a high resolution estimation method based on Toeplitz matrix data reconstruction is proposed in order to resolve the array element failure of uniform linear array in DOA estimation. Firstly, the damaged sample covariance matrix is processed by KR product. The difference co-array conception is used to recover the degrees of freedom of array failure and double the array aperture. The processed model is equivalent to a coherent sources estimation problem of single snapshot under determined noise. Then, the Toeplitz matrix data reconstruction is used for the de-coherence of the sources. Finally, the DOA is estimated by traditional MUSIC method. Due to the exploitation of the reconstructed and extended virtual array aperture, the proposed method can estimate the DOA effectively in the failure of array element case. Numerical simulations demonstrate the effectiveness and low computational complexity of the proposed method.