一种基于迭代近端投影的被动声纳探测离网格DOA估计方法

Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach often introduces errors into the sparse representation model,necessitating the development of improved DOA estimation algorithms.Moreover,conventional DOA estimation methods typically assume that the signal coincides with a predetermined grid.However,in reality,this assumption often does not hold true.The likelihood of a signal not aligning precisely with the predefined grid is high,resulting in potential grid mismatch issues for the algorithm.To address the challenges associated with grid mismatch and errors in sparse representation models,this article proposes a novel high-performance off-grid DOA estimation approach based on iterative proximal projection(IPP).In the proposed method,we employ an alternating optimization strategy to jointly estimate sparse signals and grid offset parameters.A proximal function optimization model is utilized to address non-convex and non-smooth sparse representation problems in DOA estimation.Subsequently,we leverage the smoothly clipped absolute deviation penalty(SCAD)function to compute the proximal operator for solving the model.Simulation and sea trial experiments have validated the superiority of the proposed method in terms of higher resolution and more accurate DOA estimation performance when compared to both traditional sparse reconstruction methods and advanced off-grid techniques.

Exploration on 2D DOA Estimation of Linear Array Motion:Uniform Linear Motion

Generally,due to the limitation of the dimension of the array aperture,linear arrays cannot achieve two-dimensional(2D)direction of arrival(DOA)estimation.But the emergence of array motion provides a chance for that.In this paper,a generalized motion scheme and a novel method of 2D DOA estimation are proposed by exploring the linear array motion.To be specific,the linear arrays are controlled to move along an arbitrary direction at a constant velocity and snap per fixed time delay.All the received signals are processed to synthesize the comprehensive observation vector for an extended 2D virtual aperture.Subsequently,since most of 2D DOA estimation methods are not universal to our proposed motion scheme and the reduced-dimensional(RD)method fails to handle the case of the coupled parameters,a decoupled reduced-complexity multiple signals classification(DRC MUSIC)algorithm is designed specifically.Simulation results demonstrate that:a)our proposed scheme can achieve underdetermined 2D DOA estimation just by the linear arrays;b)our designed DRC MUSIC algorithm has the good properties of high accuracy and low complexity;c)our proposed motion scheme with the DRC method has better universality in the motion direction.

Improved Capon Estimator for High-Resolution DOA Estimation and Its Statistical Analysis

Despite some efforts and attempts have been made to improve the direction-of-arrival(DOA)estimation performance of the standard Capon beamformer(SCB)in array processing,rigorous statistical performance analyses of these modified Capon estimators are still lacking.This paper studies an improved Capon estimator(ICE)for estimating the DOAs of multiple uncorrelated narrowband signals,where the higherorder inverse(sample)array covariance matrix is used in the Capon-like cost function.By establishing the relationship between this nonparametric estimator and the parametric and classic subspace-based MUSIC(multiple signal classification),it is clarified that as long as the power order of the inverse covariance matrix is increased to reduce the influence of signal subspace components in the ICE,the estimation performance of the ICE becomes equivalent to that of the MUSIC regardless of the signal-to-noise ratio(SNR).Furthermore the statistical performance of the ICE is analyzed,and the large-sample mean-squared-error(MSE)expression of the estimated DOA is derived.Finally the effectiveness and the theoretical analysis of the ICE are substantiated through numerical examples,where the Cramer-Rao lower bound(CRB)is used to evaluate the validity of the derived asymptotic MSE expression.

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.

Triad-displaced ULAs configuration for non-circular sources with larger continuous virtual aperture and enhanced degrees of freedom

Non-uniform linear array(NULA)configurations are well renowned due to their structural ability for providing increased degrees of freedom(DOF)and wider array aperture than uniform linear arrays(ULAs).These characteristics play a significant role in improving the direction-of-arrival(DOA)estimation accuracy.However,most of the existing NULA geometries are primarily applicable to circular sources(CSs),while they limitedly improve the DOF and continuous virtual aperture for noncircular sources(NCSs).Toward this purpose,we present a triaddisplaced ULAs(Tdis-ULAs)configuration for NCS.The TdisULAs structure generally consists of three ULAs,which are appropriately placed.The proposed antenna array approach fully exploits the non-circular characteristics of the sources.Given the same number of elements,the Tdis-ULAs design achieves more DOF and larger hole-free co-array aperture than its sparse array competitors.Advantageously,the number of uniform DOF,optimal distribution of elements among the ULAs,and precise element positions are uniquely determined by the closed-form expressions.Moreover,the proposed array also produces a filled resulting co-array.Numerical simulations are conducted to show the performance advantages of the proposed Tdis-ULAs configuration over its counterpart designs.

DOA Estimation Algorithm Based on Adaptive Filtering in Spatial Domain

In this paper, a novel DOA estimation methodology based upon the technology of adaptive nulling antenna is proposed. Initially, the nulling antenna obtains the weight vector by LMS algorithm and power inversion criterion.Afterwards, reciprocal of the antenna pattern is defined as the spatial spectrum and the extracted peak values are corresponded to the estimated DOA. Through observation of the spectrum and data analysis of variable steps and SNRs, the simulation results demonstrate that the proposed method can estimate DOA above board. Furthermore, the estimation error of the proposed technique is directly proportional to step size and is inversely proportional to SNR. Unlike the existing MUSIC algorithm, the proposed algorithm has less computational complexity as it eliminates the need of estimating the number of signals and the eigenvalue decomposition of covariance matrix. Also it outperforms MUSIC algorithm, the recently proposed MUSIC-Like algorithm and classical methods by achieving better resolution with narrow width of peaks.

Underdetermined DOA estimation via multiple time-delay covariance matrices and deep residual network

Higher-order statistics based approaches and signal sparseness based approaches have emerged in recent decades to resolve the underdetermined direction-of-arrival(DOA)estimation problem.These model-based methods face great challenges in practical applications due to high computational complexity and dependence on ideal assumptions.This paper presents an effective DOA estimation approach based on a deep residual network(DRN)for the underdetermined case.We first extract an input feature from a new matrix calculated by stacking several covariance matrices corresponding to different time delays.We then provide the input feature to the trained DRN to construct the super resolution spectrum.The DRN learns the mapping relationship between the input feature and the spatial spectrum by training.The proposed approach is superior to existing model-based estimation methods in terms of calculation efficiency,independence of source sparseness and adaptive capacity to non-ideal conditions(e.g.,low signal to noise ratio,short bit sequence).Simulations demonstrate the validity and strong performance of the proposed algorithm on both overdetermined and underdetermined cases.

2D DOA Estimation Algorithm with Increased Degrees of Freedom for Two Parallel Linear Arrays

In this paper,a two-dimensional(2 D)direction-of-arrival(DOA)estimation algorithm with increased degrees of freedom for two parallel linear arrays is presented.Being different from the conventional two-parallel linear array,the proposed two-parallel linear array consists of two uniform linear arrays with non-equal inter-element spacing.Propagator method(PM)is used to obtain a special matrix which can be utilized to increase the virtual elements of one of uniform linear arrays.Then,the PM algorithm is used again to obtain automatically paired elevation and azimuth angles.The simulation results and complexity analysis show that the proposed method can increase the number of distinguishable signals and improve the estimation precision without increasing the computational complexity.

DOA ESTIMATION USING A SPARSE LINEAR MODEL BASED ON EIGENVECTORS

To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.

Joint Estimation of 2-D DOA and Polarization by Using the Linear Array with Diverse Polarizations

A linear array of diversely polarized antennas with one pair of identical sensors is used to obtain closed-form unambiguous estimation of 2-D direction of arrival (DOA) and polarization. Spatial phase information together with weighted 3-D polarization-angular coherence structure (PACS) are first recovered with fourth-order cumulants manipulation via a new 2-D ESPRIT variant. Spatial filtering is performed to obtain the scaled PACS, from which the closed-form 2-D DOA and polarization estimates can be derived with only quadrant ambiguity involved. The undesired quadrant ambiguity can be further resolved by using the acquired estimate of spatial phase factor.

MULTI-INVARIANCE ESPRIT-LIKE ALGORITHMS FOR COHERENT DOA ESTIMATION

Estimation of Signal Parameters via Rotational Invariance Technique(ESPRIT) algorithm can estimate Direction-Of-Arrival(DOA) of coherent signal,but its performance can not reach full satisfaction.We reconstruct the received signal to form data model with multi-invariance property,and multi-invariance ESPRIT algorithm for coherent DOA estimation is proposed in this paper.The proposed algorithm can resolve the DOAs of coherent signals and performs better in DOA estimation than that of ESPRIT-like algorithm.Meanwhile,it identifies more DOAs than ESPRIT-like algorithm.The simulation results demonstrate its validity.

A Real-Valued 2D DOA Estimation Algorithm of Noncircular Signal via Euler Transformation and Rotational Invariance Property

The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is proposed,which combines the Euler transformation and rotational invariance(RI)property between subarrays.In this work,the effective array aperture is doubled by exploiting the noncircularity of signals.The complex arithmetic is converted to real arithmetic via Euler transformation.The main contribution of this work is not only extending the NC-Euler-ESPRIT algorithm from uniform linear array to double parallel uniform linear arrays,but also constructing a new 2 Drotational invariance property between subarrays,which is more complex than that in NCEuler-ESPRIT algorithm.The proposed 2 DNC-Euler-RI algorithm has much lower computational complexity than2 DNC-ESPRIT algorithm.The proposed algorithm has better angle estimation performance than 2 DESPRIT algorithm and 2 D NC-PM algorithm for double parallel uniform linear arrays,and is very close to that of 2 D NC-ESPRIT algorithm.The elevation angles and azimuth angles can be obtained with automatically pairing.The proposed algorithm can estimate up to 2(M-1)sources,which is two times that of 2 D ESPRIT algorithm.Cramer-Rao bound(CRB)of noncircular signal is derived for the proposed algorithm.Computational complexity comparison is also analyzed.Finally,simulation results are presented to illustrate the effectiveness and usefulness of the proposed algorithm.

Low complexity DOA estimation for massive UCA with single snapshot

In this paper, a low complexity direction of arrival(DOA) estimation method for massive uniform circular array(UCA) with single snapshot is proposed.Firstly, the coarse DOAs are estimated by finding the peaks from the circular convolution between a fixed coefficient vector and the received data vector.Thereafter, in order to refine coarse DOA estimates, we reconstruct the direction matrix based on the coarse DOA estimations and take the first order Taylor expansion with DOA estimation offsets into account.Finally, the refined estimations are obtained by compensating the offsets, which are obtained via least squares(LS) without any complex searches.In addition, the refinement can be iteratively implemented to enhance the estimation results.Compared to the offset search method, the proposed method achieves a better estimation performance while requiring lower complexity.Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

DOA estimation of incoherently distributed sources using importance sampling maximum likelihood

In this paper, an importance sampling maximum likelihood(ISML) estimator for direction-of-arrival(DOA) of incoherently distributed(ID) sources is proposed. Starting from the maximum likelihood estimation description of the uniform linear array(ULA), a decoupled concentrated likelihood function(CLF) is presented. A new objective function based on CLF which can obtain a closed-form solution of global maximum is constructed according to Pincus theorem. To obtain the optimal value of the objective function which is a complex high-dimensional integral,we propose an importance sampling approach based on Monte Carlo random calculation. Next, an importance function is derived, which can simplify the problem of generating random vector from a high-dimensional probability density function(PDF) to generate random variable from a one-dimensional PDF. Compared with the existing maximum likelihood(ML) algorithms for DOA estimation of ID sources, the proposed algorithm does not require initial estimates, and its performance is closer to CramerRao lower bound(CRLB). The proposed algorithm performs better than the existing methods when the interval between sources to be estimated is small and in low signal to noise ratio(SNR)scenarios.

DOA estimation based on multi-frequency joint sparse Bayesian learning for passive radar

This paper considers multi-frequency passive radar and develops a multi-frequency joint direction of arrival(DOA)estimation algorithm to improve estimation accuracy and resolution.The developed algorithm exploits the sparsity of targets in the spatial domain.Specifically,we first extract the required frequency channel data and acquire the snapshot data through a series of preprocessing such as clutter suppression,coherent integration,beamforming,and constant false alarm rate(CFAR)detection.Then,based on the framework of sparse Bayesian learning,the target’s DOA is estimated by jointly extracting the multi-frequency data via evidence maximization.Simulation results show that the developed algorithm has better estimation accuracy and resolution than other existing multi-frequency DOA estimation algorithms,especially under the scenarios of low signalto-noise ratio(SNR)and small snapshots.Furthermore,the effectiveness is verified by the field experimental data of a multi-frequency FM-based passive radar.

Generalized Array Architecture with Multiple Sub-Arrays and Hole-Repair Algorithm for DOA Estimation

Arranging multiple identical sub-arrays in a special way can enhance degrees of freedom(DOFs)and obtain a hole-free difference co-array(DCA).In this paper,by adjusting the interval of adjacent sub-arrays,a kind of generalized array architecture with larger aperture is proposed.Although some holes may exist in the DCA of the proposed array,they are distributed uniformly.Utilizing the partial continuity of the DCA,an extended covariance matrix can be constructed.Singular value decomposition(SVD)is used to obtain an extended signal sub-space,by which the direction-of-arrival(DOA)estimation algorithm for quasi-stationary signals is given.In order to eliminating angle ambiguity caused by the holes of DCA,the estimation of signal parameters via rotational invariance techniques(ESPRIT)is used to construct a matrix that includes all angle information.Utilizing this matrix,a secondary extended signal sub-space can be obtained.This signal sub-space is corresponding to a hole-free DCA.Then,dealing with the further extended signal sub-space by multiple signal classification(MUSIC)algorithm,the unambiguous DOAs of all incident signals can be estimated.Some simulation results are shown to prove the improved performance of proposed generalized array architecture in DOA estimation and the effectiveness of corresponding hole-repair algorithm in eliminating angle ambiguity.

DOA Estimation Method Using Sparse Representation with Orthogonal Projection

In order to reduce the effect of noises on DOA estimation,this paper proposes a direc-tion-of-arrival(DOA)estimation method using sparse representation with orthogonal projection(OPSR).The OPSR method obtains a new covariance matrix by projecting the covariance matrix of the array data to the signal subspace,leading to the elimination of the noise subspace.After-wards,based on the new covariance matrix after the orthogonal projection,a new sparse representa-tion model is established and employed for DOA estimation.Simulation results demonstrate that compared to other methods,the OPSR method has higher angle resolution and better DOA estima-tion performance in the cases of few snapshots and low SNRs.

Joint Frequency and DOA Estimation with Automatic Pairing Using the Rayleigh–Ritz Theorem

This paper presents a novel scheme for joint frequency and direction of arrival(DOA)estimation,that pairs frequencies and DOAs automatically without additional computations.First,when the property of the Kronecker product is used in the received array signal of the multiple-delay output model,the frequency-angle steering vector can be reconstructed as the product of the frequency steering vector and the angle steering vector.The frequency of the incoming signal is then obtained by searching for the minimal eigenvalue among the smallest eigenvalues that depend on the frequency parameters but are irrelevant to the DOAs.Subsequently,the DOA related to the selected frequency is acquired through some operations on the minimal eigenvector according to the Rayleigh–Ritz theorem,which realizes the natural pairing of frequencies and DOAs.Furthermore,the proposed method can not only distinguish multiple sources,but also effectively deal with other arrays.The effectiveness and superiority of the proposed algorithm are further analyzed by simulations.

DOA Estimation Based on Subspace Compensation for Unfolded Coprime Array

Direction of arrival(DOA)estimation for unfolded coprime array(UFCA)is discussed,and a method based on subspace compensation is proposed.Conventional DOA estimation meth-ods partition the UFCA into two subarrays for separate estimations,which are then combined for unique DOA determination.However,the DOA estimation performance loss is caused as only the partial array aperture is exploited.We use the estimations from one subarray as initial estimations,and then enhance the estimation results via a compensation based on the whole array,which is im-plemented via a simple least squares(LS)operation constructed from the initial estimation and first-order Taylor expansion.Compared to conventional methods,the DOA estimation performance is improved while the computational complexity is in the same level.Multiple simulations are con-ducted to verify the efficiency of the proposed approach.

Super-resolution DOA estimation for correlated off-grid signals via deep estimator

This paper develops a deep estimator framework of deep convolution networks(DCNs)for super-resolution direction of arrival(DOA)estimation.In addition to the scenario of correlated signals,the quantization errors of the DCN are the major challenge.In our deep estimator framework,one DCN is used for spectrum estimation with quantization errors,and the remaining two DCNs are used to estimate quantization errors.We propose training our estimator using the spatial sampled covariance matrix directly as our deep estimator’s input without any feature extraction operation.Then,we reconstruct the original spatial spectrum from the spectrum estimate and quantization errors estimate.Also,the feasibility of the proposed deep estimator is analyzed in detail in this paper.Once the deep estimator is appropriately trained,it can recover the correlated signals’spatial spectrum fast and accurately.Simulation results show that our estimator performs well in both resolution and estimation error compared with the state-of-the-art algorithms.