基于改进二维ESPRIT-like算法的相干源方向角估计

Orientation angle estimation based on improved 2-D ESPRIT-like algorithm

针对用于二维十字相控阵的类旋转不变技术估计信号参数(ESPRIT-like)算法用于相干源方向角估计时存在仰角和方位角配对困难的问题,提出一种基于接收信号矩阵联合对角化的改进二维ESPRIT-like算法。首先,通过ESPRIT-like算法得到x和y方向自相关矩阵,并由其重构出对应的Toeplitz矩阵以去相干;然后对Toeplitz矩阵进行等效分解,得到去相干后x和y方向的等效接收信号矩阵;最后对等效接收信号矩阵进行矩阵联合对角化,实现相干源仰角和方位角自动配对,从而得到正确的信源方向估计结果。仿真结果表明,与改进前的算法相比,改进后的算法能够实现正确的方向角估计;与目前常用的基于空间平滑的二维多重信号分类(MUSIC)算法相比,在信噪比为30 d B时,该算法响应时间减少了79%左右,仰角和方位角分辨率分别提高了20%和40%左右,均方误差约为MUSIC算法角度误差的10%。

To deal with the mismatching between elevation and azimuth angles in orientation angle estimation of coherence signals by 2-D Estimating Signal Parameter via Rotational Invariance Techniques（ ESPRIT）-like algorithm designed for the two-dimensional cross-shaped MEMS（ Micro-Electro-Mechanical System） ultrasonic phased array,the improved 2-D ESPRITlike algorithm based on the joint diagonalization of receive signal matrices was proposed. Firstly,the correlation matrices along x and y axis were derived by the received signal matrices to reconstruct the Toeplitz matrices to decoherence correspondingly according to ESPRIT-like algorithm. Secondly,the Toeplitz matrices were decomposed equivalently to obtain the equivalent received signal matrices after decoherencing. Finally,the joint diagonalization was used to diagonalize the equivalent received signal matrices to realize the matching between elevation and azimuth angles and estimate the orientation angles correctly. The simulation results show that the improved algorithm can estimate the orientation angles correctly compared with the algorithm before being improved. In comparison with the commonly used 2-D MUltiple SIgnal Classification（ MUSIC） algorithm based on spatial smoothing,the response time of the proposed algorithm is decreased by 79%,the resolution of elevation and azimuth angles is increased by about 20% and 40% respectively,and the angle error is about 10% that of MUSIC algorithm when the SNR is 30 d B.