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.

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.

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.

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.

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.

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 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.

A novel DOA estimation algorithm using directional antennas in cylindrical conformal arrays

In this paper, a novel direction of arrival(DOA) estimation algorithm using directional antennas in cylindrical conformal arrays(CCAs) is proposed. To eliminate the shadow effect, we divide the CCAs into several subarrays to obtain the complete output vector. Considering the anisotropic radiation pattern of a CCA, which cannot be separated from the manifold matrix, an improved interpolation method is investigated to transform the directional subarray into omnidirectional virtual nested arrays without non-orthogonal perturbation on the noise vector. Then, the cross-correlation matrix(CCM) of the subarrays is used to generate the consecutive co-arrays without redundant elements and eliminate the noise vector. Finally, the full-rank equivalent covariance matrix is constructed using the output of co-arrays,and the unitary estimation of the signal parameters via rotational invariance techniques(ESPRIT) is performed on the equivalent covariance matrix to estimate the DOAs with low computational complexity. Numerical simulations verify the superior performance of the proposed algorithm, especially under a low signal-to-noise ratio(SNR) environment.

Computationally efficient MUSIC based DOA estimation algorithm for FMCW radar

This paper proposes low-cost yet high-accuracy direction of arrival(DOA)estimation for the automotive frequency-modulated continuous-wave(FMcW)radar.The existing subspace-based DOA estimation algorithms suffer fromeither high computational costs or low accuracy.We aim to solve such contradictory relation between complexity and accuracy by using randomizedmatrix approximation.Specifically,we apply an easily-interpretablerandomized low-rank approximation to the covariance matrix(CM)and R∈C^(M×M)throughthresketch maties in the fom of R≈OBQ^(H).Here the approximately compute its subspaces.That is,we first approximate matrix Q∈C^(M×z)contains the orthonormal basis for the range of the sketchmatrik C∈C^(M×z)cwe whichis etrated fom R using randomized unifom counsampling and B∈C^(z×z)is a weight-matrix reducing the approximation error.Relying on such approximation,we are able to accelerate the subspacecomputation by the orders of the magnitude without compromising estimation accuracy.Furthermore,we drive a theoretical error bound for the suggested scheme to ensure the accuracy of the approximation.As validated by the simulation results,the DOA estimation accuracy of the proposed algorithm,eficient multiple signal classification(E-MUSIC)s high,closely tracks standardMUSIC,and outperforms the well-known algorithms with tremendouslyreduced time complexity.Thus,the devised method can realize high-resolutionreal-time target detection in the emerging multiple input and multiple output(MIMO)automotive radar systems.

Determination of Direction of Arrival of Seismic Wave by a Single Tri-axial Fiber Optic Geophone

A fiber Bragg grating (FBG) geophone and a surface seismic wave-based algorithm for detecting the direction of arrival (DOA) are described. The operational principle of FBG geophone is introduced and illustrated with systematic experimental data, demonstrating an improved FBG geophone with many advantages over the conventional geophones. An innovative, robust, and simple algorithm is developed for obtaining the bearing information on the seismic events, such as people walking, or vehicles moving. Such DOA estimate is based on the interactions and projections of surface-propagating seismic waves generated by the moving personnel or vehicles with a single tri-axial seismic sensor based on FBGs. Of particular interest is the case when the distance between the source of the seismic wave and the detector is less than or comparable to one wavelength (less than 100 m), corresponding to near-field detection, where an effective method of DOA finding lacks.

Direction and polarization estimation for coherent sources using vector sensors

A two-dimensional direction-of-arrival （DOA） and polarization estimation algorithm for coherent sources using a linear vector-sensor array is presented. Two matrices are first constructed by the receiving data. The ranks of the two matrices are only related to the DOAs of the sources and independent of their coherency. Then the source’s elevation is resolved via the matrix pencil （MP） method, and the singular value decomposition （SVD） is used to reduce the noise effect. Finally, the source’s steering vector is estimated, and the analytics solutions of the source’s azimuth and polarization parameter can be directly computed by using a vector cross-product estimator. Moreover, the proposed algorithm can achieve the unambiguous direction estimates, even if the space between adjacent sensors is larger than a half-wavelength. Theoretical and numerical simulations show the effectiveness of the proposed algorithm.

Beamforming and Angle-of-Arrival Estimation of Square Planar Antenna Array

This paper presents a dual-band planar antenna array for ISM band applications (2.4 GHz and 2.45 GHz). This antenna is proposed for indoor applications and enables adaptive beamforming and angle of arrival (AOA) estimation. An adaptive beamforming algorithm is applied for a planar antenna array, which is able to steer its main beam and nulls in azimuth and elevation planes over a wide frequency band. Planar antenna array operates as a spatial filter in 3D space, processing the received signals with weighting schemes. A planar antenna array is designed for AOA estimation in azimuth and elevation planes by using MUltiple SIgnal Classification (MUSIC) based on subspace algorithm. The Base Station (BS) equipped with this planar antenna is preferred to be at the center position on the room ceiling to cover all sectors of the room. It is designed to use four directional triangular elements arranged to form a square planar antenna array. Planar antenna with four elliptical slotted triangular elements (PAFESTE) is used to obtain optimal directivity in four directions in azimuth plane with specific orientation of 30? in elevation plane. It is characterized by half power beamwidth in elevation plane of about 60? and half power beamwidth in azimuth plane of about 90?.

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。