Multi-dimensional Vandermonde Structure Based DOD-DOA and Doppler Frequency Estimation for Bistatic MIMO Radar
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摘要: 针对双基地MIMO雷达收发角及多普勒联合频率估计问题，该文基于参数流型矩阵的多维范德蒙德结构特征，提出一种低运算量的3维参数联合估计算法。首先根据回波模型的多维结构特性构造3阶张量，并对其分别沿发射维、接收维和脉冲维切片得到3个等效矩阵；然后结合多维范德蒙德结构特征和等效矩阵的左奇异矩阵具有Khatri-Rao乘积结构特征，估计收发阵列流型矩阵和多普勒流型矩阵；最后通过Root-MUSIC算法估计收发角和多普勒频率。与现有算法相比，该算法显著改善了参数估计精度，在小脉冲数下，其运算量与旋转不变子空间算法(ESPRIT)相当。仿真实验验证了该算法的有效性。Abstract: In order to solve the problem of Direction Of Departure (DOD), Direction Of Arrival (DOA) and Doppler frequency estimation in bistatic MIMO radar, a low complexity method is proposed for joint estimation of the three parameters based on the multi-dimensional Vandermonde structure characteristic of the parameter manifold matrices. First, a third-order tensor is constructed according to the multi- dimensional structure of the echo model. Three equivalent matrices are obtained by cutting the tensor along transmit dimension, receive dimension and pulse dimension respectively. Then, combining the multi-dimensional Vandermonde characteristic with the Khatri-Rao product characteristic of the left-singular matrix of the equivalent matrix, transmit manifold matrix, receive manifold matrix and Doppler manifold matrix are estimated. Finally, the DOD, DOA and Doppler frequency are estimated by Root-MUSIC algorithm. Compared with the existence methods, the proposed algorithm improves obviously the estimation precision, and its computational cost is comparable to that of Estimation of Signal Parameters via Rotation Invariant Techniques (ESPRIT) method in small pulse number. The effectiveness of the proposed method is verified by simulation results.
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表 1 基于多维范德蒙德结构的参数估计算法步骤
输入：匹配滤波输出的回波信号式(3)。 输出：目标收发角和多普勒频率估计值。 步骤1 根据式(3)的回波模型构造3阶张量，对其做3维展开，得到式(4)的等效矩阵 ${{Y}}_1,{{Y}}_2,{{Y}}_3$； 步骤2 对 ${{Y}}_1$做奇异值分解，根据式(10)计算矩阵 ${{F}}$；对 ${{F}}$特征值分解，利用其特征值和式(11)估计发射流型矩阵 ${{\widehat{{A}}}_1}$； 步骤3 据式(12)和式(13)计算接收流型矩阵 ${{\widehat{{B}}}_1}$，根据式(14)计算多普勒流型矩阵 ${{\widehat{{C}}}_1}$； 步骤4 用 ${{Y}}_2$代替 ${{Y}}_1$，重复步骤2和步骤3，得到 ${\widehat {{A}}_2},{\widehat {{B}}_2},{\widehat {{C}}_2}$；当目标散射特性服从Swerling-I模型时，用 ${{Y}}_3$代替 ${{Y}}_1$，重复步骤2和步骤3，
得到 ${\widehat {{A}}_3},{\widehat {{B}}_3},{\widehat {{C}}_3}$；步骤5 求解式(15)，将误差剩余最小的一组作为最终流型矩阵的估计 $\widehat {{A}},\widehat {{B}},\widehat {{C}}$； 步骤6 采用Root-MUSIC算法处理步骤5得到的 $\widehat {{A}},\widehat {{B}},\widehat {{C}}$的每一列，估计收发角和多普勒频率。 
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