Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

A Novel CCA-NMF Whitening Method for Practical Machine Learning Based Underwater Direction of Arrival Estimation

Underwater direction of arrival(DOA)estimation has always been a very challenging theoretical and practical problem.Due to the serious non-stationary,non-linear,and non-Gaussian characteristics,machine learning based DOA estimation methods trained on simulated Gaussian noised array data cannot be directly applied to actual underwater DOA estimation tasks.In order to deal with this problem,environmental data with no target echoes can be employed to analyze the non-Gaussian components.Then,the obtained information about non-Gaussian components can be used to whiten the array data.Based on these considerations,a novel practical sonar array whitening method was proposed.Specifically,based on a weak assumption that the non-Gaussian components in adjacent patches with and without target echoes are almost the same,canonical cor-relation analysis(CCA)and non-negative matrix factorization(NMF)techniques are employed for whitening the array data.With the whitened array data,machine learning based DOA estimation models trained on simulated Gaussian noised datasets can be used to perform underwater DOA estimation tasks.Experimental results illustrated that,using actual underwater datasets for testing with known machine learning based DOA estimation models,accurate and robust DOA estimation performance can be achieved by using the proposed whitening method in different underwater con-ditions.

DOA estimation of high-dimensional signals based on Krylov subspace and weighted l_(1)-norm

With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direction of arrival(DOA)estimation due to the computational complexity of algorithms.Traditional subspace algorithms require estimation of the covariance matrix,which has high computational complexity and is prone to producing spurious peaks.In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements,this paper proposes a DOA estimation method based on Krylov subspace and weighted l_(1)-norm.The method uses the multistage Wiener filter(MSWF)iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace,further uses the measurement matrix to reduce the dimensionality of the signal subspace observation,constructs a weighted matrix,and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted l_(1)-norm to solve the target DOA.Simulation results show that the proposed method has high resolution under large array conditions,effectively suppresses spurious peaks,reduces computational complexity,and has good robustness for low signal to noise ratio(SNR)environment.

Combining Self-Organizing Map and Lipschitz Condition for Estimation in Direction of Arrival

There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.

Direction-of-arrival estimation for co-located multiple-input multiple-output radar using structural sparsity Bayesian learning

This paper addresses the direction of arrival （DOA） estimation problem for the co-located multiple-input multiple- output （MIMO） radar with random arrays. The spatially distributed sparsity of the targets in the background makes com- pressive sensing （CS） desirable for DOA estimation. A spatial CS framework is presented, which links the DOA estimation problem to support recovery from a known over-complete dictionary. A modified statistical model is developed to ac- curately represent the intra-block correlation of the received signal. A structural sparsity Bayesian learning algorithm is proposed for the sparse recovery problem. The proposed algorithm, which exploits intra-signal correlation, is capable being applied to limited data support and low signal-to-noise ratio （SNR） scene. Furthermore, the proposed algorithm has less computation load compared to the classical Bayesian algorithm. Simulation results show that the proposed algorithm has a more accurate DOA estimation than the traditional multiple signal classification （MUSIC） algorithm and other CS recovery algorithms.

Direction-of-arrival estimation based on direct data domain (D3) method

A direction-of-arrival （DOA） estimation algorithm based on direct data domain （D3） approach is presented. This method can accuracy estimate DOA using one snapshot modified data, called the temporal and spatial two-dimensional vector reconstruction （TSR） method. The key idea is to apply the D3 approach which can extract the signal of given frequency but null out other frequency signals in temporal domain. Then the spatial vector reconstruction processing is used to estimate the angle of the spatial coherent signal source based on extract signal data. Compared with the common temporal and spatial processing approach, the TSR method has a lower computational load, higher real-time performance, robustness and angular accuracy of DOA. The proposed algorithm can be directly applied to the phased array radar of coherent pulses. Simulation results demonstrate the performance of the proposed technique.

Direction of arrival estimation method based on quantum electromagnetic field optimization in the impulse noise

In order to resolve direction finding problems in the impulse noise,a direction of arrival(DOA)estimation method is proposed.The proposed DOA estimation method can restrain the impulse noise by using infinite norm exponential kernel covariance matrix and obtain excellent performance via the maximumlikelihood(ML)algorithm.In order to obtain the global optimal solutions of this method,a quantum electromagnetic field optimization(QEFO)algorithm is designed.In view of the QEFO algorithm,the proposed method can resolve the difficulties of DOA estimation in the impulse noise.Comparing with some traditional DOA estimation methods,the proposed DOA estimation method shows high superiority and robustness for determining the DOA of independent and coherent sources,which has been verified via the Monte-Carlo experiments of different schemes,especially in the case of snapshot deficiency,low generalized signal to noise ratio(GSNR)and strong impulse noise.Beyond that,the Cramer-Rao bound(CRB)of angle estimation in the impulse noise and the proof of the convergence of the QEFO algorithm are provided in this paper.

High-order extended coprime array design for direction of arrival estimation

Nonuniform linear arrays,such as coprime array and nested array,have received great attentions because of the increased degrees of freedom(DOFs)and weakened mutual coupling.In this paper,inspired by the existing coprime array,we propose a high-order extended coprime array(HoECA)for improved direction of arrival(DOA)estimation.We first derive the closed-form expressions for the range of consecutive lags.Then,by changing the inter-element spacing of a uniform linear array(ULA),three cases are proposed and discussed.It is indicated that the HoECA can obtain the largest number of consecutive lags when the spacing takes the maximum value.Finally,by comparing it with the other sparse arrays,the optimized HoECA enjoys a larger number of consecutive lags with mitigating mutual coupling.Simulation results are shown to evaluate the superiority of HoECA over the others in terms of DOF,mutual coupling leakage and estimation accuracy.

Polynomial-rooting based fourth-order MUSIC for direction-of-arrival estimation of noncircular signals

A polynomial-rooting based fourth-order cumulant algorithm is presented for direction-of-arrival（DOA） estimation of second-order fully noncircular source signals, using a uniform linear array（ULA）. This algorithm inherits all merits of its spectralsearching counterpart except for the applicability to arbitrary array geometry, while reducing considerably the computation cost.Simulation results show that the proposed algorithm outperforms the previously developed closed-form second-order noncircular ESPRIT method, in terms of processing capacity and DOA estimation accuracy, especially in the presence of spatially colored noise.

DIRECTION-OF-ARRIVAL ESTIMATION IN THE PRESENCE OF MUTUAL COUPLING BASED ON JOINT SPARSE RECOVERY

A novel Direction-Of-Arrival (DOA) estimation method is proposed in the presence of mutual coupling using the joint sparse recovery. In the proposed method, the eigenvector corresponding to the maximum eigenvalue of covariance matrix of array measurement is viewed as the signal to be represented. By exploiting the geometrical property in steering vectors and the symmetric Toeplitz structure of Mutual Coupling Matrix (MCM), the redundant dictionaries containing the DOA information are constructed. Consequently, the optimization model based on joint sparse recovery is built and then is solved through Second Order Cone Program (SOCP) and Interior Point Method (IPM). The DOA estimates are gotten according to the positions of nonzeros elements. At last, computer simulations demonstrate the excellent performance of the proposed method.

Direction-of-arrival estimation of quasi-stationary signals using two-level Khatri-Rao subspace and four-level nested array

The Khatri-Rao(KR) subspace method is a high resolution method for direction-of-arrival(DOA) estimation.Combined with 2q level nested array,the KR subspace method can detect O(N2q) sources with N sensors.However,the method cannot be applicable to Gaussian sources when q is equal to or greater than 2 since it needs to use 2q-th order cumulants.In this work,a novel approach is presented to conduct DOA estimation by constructing a fourth order difference co-array.Unlike the existing DOA estimation method based on the KR product and 2q level nested array,the proposed method only uses second order statistics,so it can be employed to Gaussian sources as well as non-Gaussian sources.By exploiting a four-level nested array with N elements,our method can also identify O(N4) sources.In order to estimate the wideband signals,the proposed method is extended to the wideband scenarios.Simulation results demonstrate that,compared to the state of the art KR subspace based methods,the new method achieves higher resolution.

Dynamic Direction of Arrival Estimation with an Unknown Number of Sources

Aiming at source number determination and direction of arrival(DOA) estimation under the case of time-varying source number,a method of DOA estimation with an unknown number of sources was proposed.Firstly,an algorithm based on crossvalidation technique was introduced to determine the number of sources.Then dynamic DOAs of source were estimated using an algorithm based on blind source separation(BSS) under the case that number of sources were unknown in advance and it was timevarying.The effectiveness of the proposed method was validated by simulation of time-invariant and time-varying numbers of source.Compared with other conventional methods,the proposed method has superior evaluation performances The proposed method can estimate m(the numbers of sensor) DOAs while other conventional methods estimate less than m DOAs.The R_(mse) of the proposed method in the case of low signal-to-noise ratio(SNR)(equal or lower than 30 dB) is smaller than 0.2 while R_(mse) of other conventional methods are greater than 0.8.

Ambiguity Resolution in Direction of Arrival Estimation with Linear Antenna Arrays Using Differential Geometry

Linear antenna arrays(LAs)can be used to accurately predict the direction of arrival(DOAs)of various targets of interest in a given area.However,under certain conditions,LA suffers from the problem of ambiguities among the angles of targets,which may result inmisinterpretation of such targets.In order to cope up with such ambiguities,various techniques have been proposed.Unfortunately,none of them fully resolved such a problem because of rank deficiency and high computational cost.We aimed to resolve such a problem by proposing an algorithm using differential geometry.The proposed algorithm uses a specially designed doublet antenna array,which is made up of two individual linear arrays.Two angle observation models,ambiguous observation model(AOM)and estimated observation model(EOM),are derived for each individual array.The ambiguous set of angles is contained in the AOM,which is obtained from the corresponding array elements using differential geometry.The EOM for each array,on the other hand,contains estimated angles of all sources impinging signals on each array,as calculated by a direction-finding algorithm such as the genetic algorithm.The algorithm then contrasts the EOM of each array with its AOM,selecting the output of that array whose EOM has the minimum correlation with its corresponding AOM.In comparison to existing techniques,the proposed algorithm improves estimation accuracy and has greater precision in antenna aperture selection,resulting in improved resolution capabilities and the potential to be used more widely in practical scenarios.The simulation results using MATLAB authenticates the effectiveness of the proposed algorithm.

Wideband direction-of-arrival estimation based on cubic spline function

A new direction-of-arrival （DOA） estimation algorithm for wideband sources is introduced, The new method obtains the output of the virtual arrays in the signal bandwidth using cubic spline function interpolation techniques. The narrowband high- resolution algorithm is then used to get the DOA estimation. This technique does not require any preliminary knowledge of DOA angles. Simulation results demonstrate the effectiveness of the method.

2-D Direction-of-arrival Estimation of Real-valued Sources

A new method is presented to estimate two-dimensional （2-D） Direction-of-Arrival （DOA） angles of narrowband real-valued signals impinging on a L-shape Arrays（LA）. The basic idea of the proposed method is to increase both the effective aperture size and the number of sensors by employing the conjugate invariance property of real-valued signals. Thus, the proposed method can provide a more precise DOA and detect more signals than the Cross-Correlation Matrix Method （CCMM）. Numerical simulation results are presented to support the theory.

基于二阶统计特性的方向向量估计算法的DOA估计

为了减小天线阵流形误差对波达方向(DOA)估计结果的影响,以及克服基于传统盲源分离算法的DOA估计算法不能应用于少通道测向设备的不足,提出一种基于2阶统计特性的方向向量估计算法的DOA估计算法。首先,根据确定性最大似然(DML)估计算法谱函数的特征,构造关于协方差矩阵的酉约束下的优化问题;然后,通过优化该问题获得各个单信号的实际方向向量;最后,将各个单信号的实际方向向量输入到空间谱算法中实现DOA估计。由于将多信号的DOA估计转化为多个单信号的DOA估计,因此在天线阵列流形存在误差时,所提算法比传统的DOA方法具有更好的DOA估计性能。由于所提算法仅需使用协方差矩阵,因此所提算法可应用于少通道测向设备。由仿真实验结果可知,在阵列流形存在误差以及测向设备为少通道测向设备时,与传统DOA方法相比,所提算法的DOA估计的准确度、抗扰度以及分辨率更高。

基于均匀圆阵的压制式相干干扰DOA估计算法

针对导航抗干扰中一般干扰信号波达方向(direction-of-arrival, DOA)算法无法在均匀圆阵上有效地估计含有相干干扰的信号来向问题,提出了一种基于虚拟线阵的协方差矩阵重构的MUSIC算法。该算法通过对均匀圆阵进行模式空间变换,形成虚拟线阵,将模式空间变换后的数据协方差矩阵的所有行进行Toeplitz重构,并将所有Toeplitz矩阵构造成一个新的等效的满秩数据协方差矩阵,以此来达到解相干的目的。结合在虚拟线阵上的MUSIC算法,并通过多谱峰搜索算法直接得到空间谱的谱峰位置,从而完成对干扰来向的DOA估计。经仿真验证,该算法在存在相干信号且信号角度相隔30°左右的条件下,依旧能够对信号的波达方向进行有效估计。

基于稀疏度自适应变步长的离格DOA估计方法

网格划分产生的量化误差是影响信源定位估计性能的一个重要缺陷。针对目前Lp类离格算法计算量大以及需要提前预知稀疏度的问题,提出了一种稀疏度自适应变步长的离格波达方向定位方法。首先根据一阶泰勒展开构建基于角度优化的离格参数模型,以残差能量的变化作为预估稀疏度K的条件。然后利用噪声子空间与信号子空间正交性作为原子误差入选判定依据,利用交替迭代优化方法实现离格模型下的准确求解。所提方法结合了贪婪算法支撑集选取策略与阵列协方差矩阵的有效信息。仿真实验表明,在满足稀疏性条件下,所提方法不仅大大缩短运算时间,而且可以实现空域角度范围内任意角度的精确估计。

稀疏阵列的鲁棒矩阵填充DOA估计算法

稀疏阵列布阵灵活,增大阵列孔径的同时还能减少阵元间耦合,但基于稀疏阵列的传统波达方向估计会导致角度模糊混叠,带来估计精度差和稳健性不足的问题。针对以上问题,提出一种适用于稀疏阵列波达方向估计的加权截断奇异值投影(weighted truncated singular value projection,WT-SVP)的鲁棒矩阵填充算法。在填充迭代过程中根据奇异值的大小分配权重,突出大奇异值包含的阵列信息,减少小奇异值中不必要的噪声信息,从而优化传统奇异值投影算法。该算法可以实现稀疏阵列的孔洞信息恢复,对不连续阵元充分利用,同时WT-SVP填充算法实现了稀疏阵列波达方向估计的高精度、高分辨以及在低信噪比、低快拍时的高鲁棒性。

DOA Estimation Based on Sparse Representation of the Fractional Lower Order Statistics in Impulsive Noise

This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.