Novel angle estimation for bistatic MIMO radar using an improved MUSIC

In this article, we study the problem of angle estimation for bistatic multiple-input multiple-output (MIMO) radar and propose an improved multiple signal classification (MUSIC) algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation. The proposed algorithm obtains initial estimations of angles obtained from the signal subspace and uses the local one-dimensional peak searches to achieve the joint estimations of DOD and DOA. The angle estimation performance of the proposed algorithm is better than that of estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, and is almost the same as that of two-dimensional MUSIC. Furthermore, the proposed algorithm can be suitable for irregular array geometry, obtain automatically paired DOD and DOA estimations, and avoid two-dimensional peak searching. The simulation results verify the effectiveness and improvement of the algorithm.     

基于协方差差分的近场源定位参量估计

提出一种基于空间差分技术的近场源方位角和距离联合估计新算法.算法利用平稳噪声协方差矩阵关于主对角线对称的特点,构造近场源定位模型下的空间差分矩阵.推导并证明了该矩阵的谱分解特性,以此为基础确定噪声子空间,借助谱峰搜索实现定位参量估计.算法通过对消噪声分量有效降低了未知平稳噪声对定位精度的影响,同时避免了应用差分技术解决信源定位时出现的伪峰问题.均方根误差的仿真结果证明了算法的有效性.     

Unitary Subspace-Based Method for Angle Estimation in Bistatic MIMO Radar

In this paper, the issue of joint angle estimation for bistatic multiple-input multiple-output (MIMO) radar is investigated, and an algorithm for the joint estimation under real-valued computation is proposed. By utilizing the unitary transformation, the direction matrices and the data matrix are transformed to be real-valued ones. The direction of departure (DOD) can be estimated via the real-valued rotational invariance in the subspace, and the direction of arrival (DOA) can be obtained via the real-valued reduced-dimension function of multiple signal classification (MUSIC). The proposed algorithm utilizes both the signal and noise subspaces, requires no peak searching, and can achieve automatically paired estimations of the angles. Furthermore, it has better angle estimation performance than some existing methods. The simulation results verify the algorithmic effectiveness and robustness of the proposed algorithm.     

基于时间反转的MIMO雷达实值MUSIC算法

针对时间反转(TR)多输入多输出(MIMO)雷达多重信号分类(MUSIC)算法计算量庞大的问题,提出一种基于时间反转的MIMO雷达实值MUSIC算法。首先,通过采用降维思想对TR MIMO回波信号进行降维处理,来减少计算量;然后,为将协方差矩阵转化到实数域,构造酉变换矩阵进行实值变换;最后,分解出实值协方差矩阵的噪声子空间,构造谱函数估计信号波达角。相对于传统的MUSIC算法,该算法借助实值变换剔除了复数运算,极大地降低了计算量,而且不需要空间平滑降低阵列孔径就具有解相干的能力。仿真结果证实了算法的正确性。     

Blind DOA and polarization estimation for polarization-sensitive array using dimension reduction MUSIC

A novel blind direction-of-arrival (DOA) and polarization estimation algorithm for polarization-sensitive uniform linear array using dimension reduction multiple signal classification (MUSIC) is proposed in this paper. The proposed algorithm utilizes the signal subspace to obtain an initial estimation of DOA, then estimates more accurate DOA through a one-dimensional (1-D) local searching according to the initial estimation of DOA, and finally obtains polarization parameter estimation via the estimated polarization steering vectors. The proposed algorithm, which only requires a one-dimension local searching, can avoid the high computational cost within multi-dimensional MUSIC algorithm. The simulation results reveal that the proposed algorithm has better DOA and polarization estimation performance than both estimation of signal parameters via rotational invariance technique algorithm and trilinear decomposition algorithm. Furthermore, the proposed algorithm can be suitable for irregular array geometry, obtain automatically paired multi-dimensional parameter estimation, and avoid multi-dimensional searching. Simulation results verify the effectiveness of the proposed algorithm.     

Joint estimation of TOA and DOA in IR-UWB system using a successive propagator method

Impulse radio ultra-wideband (IR-UWB) ranging and positioning require accurate estimation of time-of-arrival (TOA) and direction-of-arrival (DOA). With receiver of two antennas, both of the TOA and DOA parameters can be estimated via two-dimensional (2D) propagator method (PM), in which the 2D spectral peak searching, however, renders much higher computational complexity. This paper proposes a successive PM algorithm for joint TOA and DOA estimation in IR-UWB system to avoid 2D spectral peak searching. The proposed algorithm firstly gets the initial TOA estimates in the two antennas from the propagation matrix, then utilises successively one-dimensional (1D) local searches to achieve the estimation of TOAs in the two antennas, and finally obtains the DOA estimates via the difference in the TOAs between the two antennas. The proposed algorithm, which only requires 1D local searches, can avoid the high computational cost in 2D-PM algorithm. Furthermore, the proposed algorithm can obtain automatically paired parameters and has better joint TOA and DOA estimation performance than conventional PM algorithm, estimation of signal parameters via rotational invariance techniques algorithm and matrix pencil algorithm. Meanwhile, it has very close parameter estimation to that of 2D-PM algorithm. We have also derived the mean square error of TOA and DOA estimation of the proposed algorithm and the Cramer-Rao bound of TOA and DOA estimation in this paper. The simulation results verify the usefulness of the proposed algorithm.     

一种快速DOA估计算法

MUSIC算法需要将天线阵列接收数据的协方差矩阵进行特征分解,并在全空域进行谱峰搜索。该算法具有很高的分辨力、估计精度及稳定性,但是运算量巨大,难以实时实现。通过对等距线阵特点及MUSIC算法的研究,提出了一种无需特征分解和在全空域进行谱峰搜索的快速算法,算法采取降维处理的方法快速估计信号子空间,然后根据基于阵列一次快拍的FFT算法粗略估计的局域信号空间进行谱峰搜索,从而有效降低了算法的计算量,理论分析和计算机仿真结果证明了该算法的有效性。     

IR-UWB 系统中基于 root-MUSIC 算法的 TOA 和 DOA 联合估计简

针对二维多重信号分类算法可以估计出系统的到达时间(TOA, time-of-arrival)和波达方向(DOA, direction- of-arrival)参数,但需要复杂度非常高的二维谱峰搜索这一问题,提出了IR-UWB系统中基于求根MUSIC(root-MUSIC)的TOA和DOA联合估计算法,该算法对接收信号的频域形式建模,先估计出TOA,然后由TOA的差值计算出DOA,从而实现TOA和DOA的联合估计。该算法不需谱峰搜索,可直接给出估计参数的闭式解,还可实现参数配对。还推导了参数估计的误差方差。仿真结果表明,该算法的参数估计性能明显优于矩阵束算法、传播算子算法以及基于旋转不变技术估计信号参数算法,并且非常接近于2D-MUSIC算法,但该算法的复杂度却远远低于2D-MUSIC算法。     

基于内插阵列变换的非圆信号MUSIC算法

针对非圆信号的波达方向(DOA)估计问题,提出一种基于内插阵列变换的非圆信号MUSIC算法(VIA-NC-MUSIC算法)。利用真实阵列流型与虚拟阵列流型之间的变换矩阵,将真实协方差矩阵变换为虚拟协方差矩阵,再对虚拟协方差矩阵进行奇异值分解(SVD),利用信号子空间与噪声子空间的正交性,得出算法的空间谱函数。仿真实验表明:存在阵元位置误差的情况下,新算法通过对阵元位置校准数据进行内插阵列变换(VIA),取得与阵元位置校准的非圆信号MUSIC算法(NC-MUSIC算法)相当的估计性能,保持了高估计精度、阵列扩展能力等优点。     

基于Toeplitz矩阵重构的相干信源二维DOA估计算法

针对空间相干信源的二维DOA估计问题,提出一种基于Toeplitz矩阵重构的新算法。采用垂直放置的L形阵列,通过对重构的Toeplitz矩阵进行特征分解,得到对应的噪声子空间,并用MUSIC算法进行有限次一维搜索,先后估计出俯仰角和相应的方位角。与空间平滑处理算法相比,不减少阵元的有效孔径,具有更强解相干能力,估计性能也优于后者。最后计算机仿真结果证实了算法的有效性和可行性。     

Computationally efficient DOA estimation for coprime linear array: a successive signal subspace fitting algorithm

ABSTRACT

In this paper, direction of arrival (DOA) estimation of multiple signals with coprime array is investigated and signal subspace fitting (SSF) method is linked to the coprime array, which achieves a better DOA estimation performance than the traditional uniform array. While the SSF method requires expensive computational cost in the case of multiple signals due to the multidimensional global angular searching, we propose a successive SSF (S-SSF) algorithm from a computationally efficient perspective. In the proposed algorithm, we employ rotational invariance and coprime property to obtain the initial estimates. Then, via a successive scheme, we transform the traditional multidimensional global angular searching problem into one-dimensional partial angular searching one. Consequently, the computational complexity has been significantly reduced. Specifically, the proposed S-SSF algorithm can obtain almost the same DOA estimation performance as SSF but with remarkably lower complexity. Finally, Cramer-Rao Bound (CRB) is provided and numerical simulations demonstrate the effectiveness of the proposed algorithm.     

一种基于Toeplitz矩阵重构的相干信源DOA估计算法

提出一种基于Toeplitz矩阵重构的相干信号源DOA估计算法。首先对各个阵元的接收数据与参考阵元（第一个阵元）的接收数据的相关函数进行排列,形成Hermitian Toeplitz矩阵,然后通过奇异值分解可以得到信号子空间和噪声子空间,从而实现相干信源的DOA估计。该算法在不减少阵列有效孔径的情况下,增加了可估计相干信号源数目,并在低信噪比条件下能够得到较好的估计性能,计算机仿真结果证实了算法的有效性。     

基于逼近噪声子空间的求根时延估计算法

多重信号分类(MUSIC)时延估计算法需要多径数估计,且其特征分解和谱峰搜索的计算复杂度较高。针对此问题,给出了一种基于逼近噪声子空间的求根时延估计算法。该算法利用协方差矩阵逆的高次幂逼近噪声子空间与其自身共轭转置的积,并构造多项式等式,以多项式求根的方式避免谱峰搜索,从而降低了计算复杂度。仿真结果表明,在无需多径数估计和复杂度低于MUSIC算法的条件下,所提算法的性能与MUSIC算法的性能相当,并且逼近克拉美罗界。     

一种新的信号子空间宽带测向算法

宽带信号测向是信号处理研究的难点课题之一,经典的旋转信号子空间（RSS）变换算法需要知道和真实来波方向接近的方向初始值。不合适的方向初始值将会降低估计器的收敛能力,引起估计偏差,从而使算法的估计精度受预估计的影响很大。本文提出的新算法首先推导出不同频段不同方向角的方向矢量之间的关系,然后再利用信号子空间、噪声子空间和阵列流型之间的关系构造一个特殊矩阵,最后通过求条件数来判断来波方向。所以新算法不需要构造聚焦矩阵,不需预知初始值,从而提高了算法的稳健性,降低了运算量,且新算法同时利用了信号子空间和噪声子空间,减少了噪声子空间扰动对算法精度的影响。计算机仿真验证了新算法的有效性。     

Two-dimensional DOA estimation for acoustic vector-sensor array using a successive MUSIC

This paper discusses the problem of two-dimensional (2D) direction of arrival (DOA) estimation for acoustic vector-sensor array, and derives a successive multiple signal classification (MUSIC) algorithm therein. The proposed algorithm obtains initial estimations of the azimuth and elevation angles obtained from the signal subspace, and uses successively one-dimensional local searches to achieve the joint estimation of 2D-DOA. The proposed algorithm, which requires the one-dimension local searches, can avoid the high computational cost within 2D-MUSIC algorithm. The proposed algorithm can obtain automatically-paired 2D-DOA estimation for acoustic vector-sensor array, and it has better DOA estimation performance than propagator method, estimation of signal parameters via rotational invariance technique algorithm and trilinear decomposition algorithm. Meanwhile, it has very close angle estimation to 2D-MUSIC algorithm. Furthermore, it is suitable for non-uniform linear arrays, works well for the sources with the same azimuth angle, and imposes less constraint on the sensor spacing, which does not have to be restricted within half-wavelength. We have also derived the mean-square error of DOA estimation of the proposed algorithm and the Cramer-Rao bound of DOA estimation. Simulation results verify the usefulness of the proposed algorithm.     

基于时频子空间分解的宽带线性调频信号DOA估计

针对具有时变方向向量的宽带线性调频信号,该文建立了基于短时Wigner-Ville分布(WVD)的空间时频分布矩阵,通过对各个空间时频矩阵的特征分解获得对应的信号子空间和噪声子空间,给出了基于时频子空间投影实现多个时频点综合估计信号DOA的算法。利用空间时频分布的前后向平滑解决了具有相同时频特性信号的均匀线阵DOA估计问题。算法不需要聚汇和插值等复杂的矩阵变换,精度较高,计算简便.仿真实验显示该算法性能显著优越于基于矩阵插值的宽带调频信号DOA估计算法.     

基于波束域的子空间正交性测试宽带DOA估计方法研究

投影子空间正交性测试(Test of Orthogonality of Projected Subspace:TOPS)算法通过测试宽带信号各频率点上噪声子空间和信号子空间之间的正交性对目标方位进行到达角估计(DOA:direction-of-arrival)。此算法对参考频点上的信号子空间的估计依赖性较大,因此存在较多伪峰,低信噪比条件下性能差等缺点。针对该问题,提出一种基于波束域的宽带DOA估计方法。该方法通过将阵列接收信号转换到波束域,在波束域中利用信号带宽内各频率分量的波束域方向向量与噪声子空间之间的正交关系构造判决向量,根据判决向量搜索空间谱的极大值对应的角度进行DOA估计。该方法不需要进行角度预估,避免了TOPS算法中常出现的伪峰,降低了信噪比分辨门限,减少了计算量,具有较好的估计效果。将该方法分别运用到均匀圆阵和线阵上,通过仿真对比和海试实验数据的处理,证明了本文所提方法的有效性。      

Propagator-based computationally efficient direction finding via low-dimensional equation rooting

Direction-of-arrival (DOA) estimation of multiple emitters with sensor arrays has been a hot topic in the area of signal processing during the past decades. Among the existing DOA estimation methods, the subspace-based ones have attracted a lot of research interest, mainly due to their satisfying performance in direction estimation precision and super-resolution of temporally overlapping signals. However, subspace-based DOA estimation methods usually contain procedures of covariance matrix decomposition and refined spatial searching, which are computationally much demanding and significantly deteriorate the computational efficiency of these methods. Such a drawback in heavy computational load of the subspace-based methods has further blocked the application of them in practical systems. In this paper, we follow the major process of the subspace-based methods to propose a new DOA estimation algorithm, and devote ourselves to reduce the computational load of the two procedures of covariance matrix decomposition and spatial searching, so as to improve the overall efficiency of the DOA estimation method. To achieve this goal, we first introduce the propagator method to realize fast estimation of the signal-subspace, and then establish a DOA-dependent characteristic polynomial equation (CPE) with its order equaling the number of incident signals (which is generally much smaller than that of array sensors) based on the signal-subspace estimate. The DOA estimates are finally obtained by solving the low-dimensional CPE. The computational loads of both the subspace estimation and DOA calculation procedures are thus largely reduced when compared with the corresponding procedures in traditional subspace-based DOA estimation methods, e.g., MUSIC. Theoretical analyses and numerical examples are carried out to demonstrate the predominance of the proposed method in both DOA estimation precision and computational efficiency over existing ones.     

加权伪噪声子空间投影的修正MUSIC算法

多重信号分类（multiple signal classification: MUSIC）方法通过计算搜索导向矢量与噪声或信号子空间的距离来估计波达方向,对采样协方差矩阵的依赖性较大。在小快拍或存在强弱临近信号条件下,采样协方差矩阵的估计值与真实值通常存在较大差异,导致估计的噪声或信号子空间发生畸变,严重恶化了MUSIC方法的波达角估计性能。针对该问题,本文提出采用加权伪噪声子空间投影的改进方法（称为wpnMUSIC）。该方法在修正数据相关矩阵的基础上估计与搜索导向矢量对应的伪噪声子空间并利用其在伪噪声子空间的投影值对MUSIC空间谱进行加权处理,在保持子空间处理方法高分辨能力的同时改善了对小快拍和强弱信号的稳健性。理论分析和仿真实验表明本文方法对强弱临近目标的分辨能力优于MUSIC方法。      

一种适用于小样本的迭代多重信号分类算法

当样本数不足时,由采样协方差矩阵特征分解得到的噪声子空间偏离其真实值,使得多重信号分类(MUSIC)算法目标角度(DOA)估计性能下降。为了解决这个问题,该文提出了一种迭代算法通过校正信号子空间来提高MUSIC算法性能。该方法首先利用采样协方差矩阵特征分解得到的噪声子空间粗略估计目标角度;其次基于信源的稀疏性和导向矢量的低秩特性,由上一步得到的目标角度以及其邻域角度对应的导向矢量构造一个新的信号子空间;最后通过解一个优化问题来校正信号子空间。仿真结果表明,该算法有效地提高了子空间估计精度。基于新的信号子空间实现MUSIC DOA估计可以使得性能得到改善,且在低样本数下改善尤为明显。