Received Array Data Research Articles

Multifrequency matched-field source localization based on Wasserstein metric for probability measures.

Matched-field processing (MFP) for underwater source localization serves as a generalized beamforming approach that assesses the correlation between the received array data and a dictionary of replica vectors. In this study, the processing scheme of MFP is reformulated by computing a statistical metric between two Gaussian probability measures with the cross-spectral density matrices (CSDMs). To achieve this, the Wasserstein metric, a widely used notion of metric in the space of probability measures, is employed for developing the processor to attach the intrinsic properties of CSDMs, expressing the underlying optimal value of the statistic. The Wasserstein processor uses the embedded metric structure to suppress ambiguities, resulting in the ability to distinguish between multiple sources. In this foundation, a multifrequency processor that combines the information at different frequencies is derived, providing improved localization statistics with deficient snapshots. The effectiveness and robustness of the Wasserstein processor are demonstrated using acoustic simulation and the event S5 of the SWellEx-96 experiment data, exhibiting correct localization statistics and a notable reduction in ambiguity. Additionally, this paper presents an approach to derive the averaged Bartlett processor by evaluating the Wasserstein metric between two Dirac measures, providing an innovative perspective for MFP.

Tow ship interference mitigation in shallow ocean using correlated mode decomposition technique

Passive towed arrays assume great importance in shallow ocean surveillance, owing to their capability to detect long range underwater acoustic targets. The detection and classification performance is severely impacted by the tow ship interference manifestation in the pressure sensor array towed behind the ship. In this work, a robust tow ship multipath interference mitigation algorithm intended for shallow ocean operation is developed, based on the dynamic mode decomposition (DMD) technique, which in turn exploits the coherent structure of the multimode acoustic wave propagation inherent in the shallow ocean scenario. The proposed algorithm effectively identifies the coherent normal mode interference subspace and eliminates its components from the received array data vector. Further, this approach compliments the shallow ocean normal mode acoustic field propagation and ensures simultaneous mitigation of all the multipath generated interferences, making it a superior method to reduce the azimuth spread of the interference and tow ship spectral leakage into the panoramic detection beams. This greatly enhances the detection and classification capability of sonar, especially for distant stealthy targets. The efficacy of the algorithm is validated using Monte Carlo simulations and further ratified by experimental data captured during the field trials in the Arabian Sea.

DOA Tracking Based on Unscented Transform Multi-Bernoulli Filter in Impulse Noise Environment.

Aiming at the problem of multiple-source direction of arrival (DOA) tracking in impulse noise, this paper models the impulse noise by using the symmetric α stable (SαS) distribution, and proposes a DOA tracking algorithm based on the Unscented Transform Multi-target Multi-Bernoulli (UT-MeMBer) filter framework. In order to overcome the problem of particle decay in particle filtering, UT is adopted to select a group of sigma points with different weights to make them close to the posterior probability density of the state. Since the α stable distribution does not have finite covariance, the Fractional Lower Order Moment (FLOM) matrix of the received array data is employed to replace the covariance matrix to formulate a MUSIC spatial spectra in the MeMBer filter. Further exponential weighting is used to enhance the weight of particles at high likelihood area and obtain a better resampling. Compared with the PASTD algorithm and the MeMBer DOA filter algorithm, the simulation results show that the proposed algorithm can more effectively solve the issue that the DOA and number of target are time-varying. In addition, we present the Sequential Monte Carlo (SMC) implementation of the UT-MeMBer algorithm.

An effective localization method for mixed far-field and near-field strictly non-circular sources

In this paper, an effective direction-of-arrival (DOA) and range estimations method for mixed far-field and near-field non-circular sources is proposed based on a large centrosymmetric uniform linear array (ULA). By exploiting the non-circularity of the sources, an extended signal is generated by concatenating the received array data and its conjugate counterparts. Then the DOAs of far-field signals are estimated based on the extended covariance matrix with the traditional MUSIC algorithm. After eliminating the far-field components from the extended signal subspace, the extended covariance matrix of the near-field signals is obtained. Thus a near-field estimator is constructed based on symmetric property of the extended array manifold where the generalized ESPRIT method is adopted to estimate the DOAs of near-field sources. Finally, the range estimator is derived using the DOA estimations of near-field sources. Simulation results are provided to validate that the proposed method has achieved a better performance than existing ones and is quite suitable for massive MIMO (multiple-input multiple-out) system.

Detection of Array Signal Number With Multiple Sensors Based on Transfer Component Analysis

The conventional algorithms for estimating number of array signals are only suitable for the background of Gaussian white noise, and need many snapshots, but their performance will reduce seriously in the circumstance of impulse noise and small samples. Therefore, a new method of detecting array signal number with multiple sensors based on transfer component analysis is proposed in this paper. First, the array signals in Gaussian white and impulse noise are respectively modeled. Then the received array data are transformed into a common hidden space by the mapping function, thus, data in the hidden space have the same distribution, and most initial characteristics are retained. Finally, a support vector machine or K-means clustering are used for classifying the mapped data into two categories, on this basis, the array signal number can be estimated.

Adaptive and compressive matched field processing.

Matched field processing is a generalized beamforming method that matches received array data to a dictionary of replica vectors in order to locate one or more sources. Its solution set is sparse since there are considerably fewer sources than replicas. Using compressive sensing (CS) implemented using basis pursuit, the matched field problem is reformulated as an underdetermined, convex optimization problem. CS estimates the unknown source amplitudes using the replica dictionary to best explain the data, subject to a row-sparsity constraint. This constraint selects the best matching replicas within the dictionary when using multiple observations and/or frequencies. For a single source, theory and simulations show that the performance of CS and the Bartlett processor are equivalent for any number of snapshots. Contrary to most adaptive processors, CS also can accommodate coherent sources. For a single and multiple incoherent sources, simulations indicate that CS offers modest localization performance improvement over the adaptive white noise constraint processor. SWellEx-96 experiment data results show comparable performance for both processors when localizing a weaker source in the presence of a stronger source. Moreover, CS often displays less ambiguity, demonstrating it is robust to data-replica mismatch.

Finite data performance analysis of a sidelobe canceller

The performance of the generalized sidelobe canceller (GSC) is affected by the desired signal (DS) even if all signals are uncorrelated with each other when the DS exists in the received array data with finite snapshot number. Under the condition that the DS is blocked totally in the auxiliary array, a novel expression of the weight vector of the GSC, where the auxiliary array is separated from the main array, is derived for the finite data. Based on the new weight vector, the corresponding expressions of the output signal-to-interference-plus-noise ratio (SINR) can be developed for the case that all signals, including the DS and interference signals, are independent with each other. Then, effects on the SINR for some parameters, including the signal-to-noise ratio, the array antenna number, the direction-of-arrival of the interference signal and the interference-to-noise ratio, are studied, respectively. Some guidelines can thus be obtained for the practical application.

DOA estimation of multiple sources in sparse space with an extended array technique

An algorithm to improve direction of arrival (DOA) estimation accuracy with an extended sensor array in the presence of multiple coherent signal sources is proposed. The algorithm uses virtual element theory to extend the sensor array, estimates virtual element information via linear prediction and expands the array aperture in practical sense; the sparsity of the target orientation in angle space is exploited to establish an over-complete dictionary and a reception model for the array signal in sparse space; the received array data is preprocessed using singular value decomposition (SVD) method and target DOA estimation is realized by calculating the best atoms. The algorithm improves DOA estimation accuracy by extended array and uses SVD to control computational complexity effectively, which ensures the accuracy and efficiency. Computer simulation shows that the proposed algorithm is able to accurately estimate the DOA for both single-target and closely spaced multi-target cases in low signal-to-noise ratio environments, and also has excellent DOA estimation performance in the presence of multiple coherent signal sources.

Efficient Two-Dimensional Direction-of-Arrival Estimation for a Mixture of Circular and Noncircular Sources

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for a mixture of circular and noncircular sources is considered. In particular, we focus on a 2-D array structure consisting of two parallel uniform linear arrays and build a general array model with mixed circular and noncircular sources. The received array data and its conjugate counterparts are combined together to form a new data vector, based on which a series of 2-D DOA estimators is derived. Compared with existing methods, the proposed one has three main advantages. First, it can give a more accurate estimation in situations, where the number of sources is within the traditional limit of high-resolution methods. Second, it can still work effectively when the number of mixed signals is larger than that of the array elements. Finally, the paired 2-D DOAs of the proposed method can be obtained automatically without the complicated 2-D spectrum peak search and, therefore, has a much lower computational complexity.

Multiple snapshot and multiple frequency compressive matched field processing

Matched field processing is a generalized beamforming method which matches received array data to a dictionary of replica vectors to locate and track a source. Its solution set generally is sparse since there are considerably fewer sources than replicas. The problem is also underdetermined since the number of sensors are less than the number of unique depth-range cells. Using compressive sensing (CS), the traditional spatial matched-filter problem is reformulated as a convex optimization problem subject to a row-sparsity constraint (RSC). The RSC selects the best match among the replica dictionary when using multiple snapshots. It is found that CS performance is equivalent to the Bartlett processor when comparing the sparse solution to the ambiguity surface’s peak for any number of snapshots in a single frequency—single source scenario. Results also indicate that CS performs similarly to the adaptive white noise constraint processor in a multiple source scenario. The RSC can further be exploited to select a common depth-range cell from snapshots corresponding to multiple frequencies to improve the source tracking in the presence of data-replica mismatch. Results are demonstrated using both simulated and SWellEx-96 experiment data.

Single and multiple snapshot compressive matched field processing

Matched field processing is a generalized beamforming method which matches received array data to a dictionary of replicas to locate and track a source. The solution set generally is sparse since there are considerably fewer sources than replicas. This underdetermined problem can be solved with sparse processing (SP) which potentially is attractive for several reasons. The traditional spatial matched-filter problem is reformulated as a convex optimization problem subject to a sparsity constraint. For example, an elastic net seems to be an appropriate penalty in order to find the best match among a correlated group of replicas. Another advantage is that SP does not require inversion of the sample covariance matrix and therefore can outperform conventional high-resolution processors in snapshot deficient scenarios (i.e., fast moving sources). A third potential advantage is that SP can achieve super-resolution at high SNR and discriminate between closely spaced sources. Here, we demonstrate the performance of single and multi-snapshot SP to track a towed source using the SWellEx-96 data set. Results are benchmarked using the Bartlett and the white noise constraint processors. We further discuss the processing of multiple frequencies in order to improve the source tracking.

Performance improvement of direction finding algorithms in non-homogeneous environment through data fusion

This paper proposes a new effective approach to improve the performance of DOA (Direction Of Arrival) algorithms when bursts affect the array data. The proposed approach is based on the combining of data fusion techniques and the results of theoretical performance analysis of conventional DOA algorithms. For this purpose, the received array data is first split in M time-segments. Then, the DOAs are estimated from each data segment using a conventional DOA algorithm. The obtained estimates are fused using the federated fusion algorithm according to their statistical accuracy obtained from the well-documented performance analysis of the considered algorithm. As proof of concept of the proposed approach, numerical experiments have been conducted by considering the MUSIC algorithm. The obtained results show that the new algorithm outperforms the conventional one in terms of accuracy in a non-homogeneous environment. Therefore, it exhibits enhanced robustness capability. Moreover, it reduces the memory cost and computational complexity which makes it suitable for real time applications. To our knowledge, it is the first time that theoretical performance analysis results are exploited for the derivation of new subspace-DOA methods.

Two-Dimensional Direction Estimation for a Mixture of Noncoherent and Coherent Signals

This paper deals with the two-dimensional (2-D) direction-of-arrival (DOA) estimation of a mixture of noncoherent (including uncorrelated and partially correlated) and coherent (i.e., fully correlated) narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays (ULAs). An oblique projection based approach for 2-D direction estimation (OPADE) is proposed by using some cross-correlations between the received array data. In the proposed OPADE, the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated, while the computationally intensive eigendecomposition is avoided, and the estimated elevation and azimuth angles are paired automatically. Further, an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the DOAs of coherent signals. The Cramér-Rao lower bound (CRB) for the mixture of noncoherent and coherent signals is also derived explicitly, where the prior knowledge of the signal correlation is incorporated into the 2-D DOA estimation of noncoherent signals. Finally the effectiveness of the OPADE and the theoretical analysis are substantiated through numerical examples.

A New Algorithm of Range and DOA Estimation of Near Field Sources Based on FLOS-ESPRIT

A new algorithm based on fractional lower order statistics (FLOS) is presented to joint estimate the range and direction of arrival (DOA) parameters of near-field sources. The proposed algorithm adopts centra-symmetric uniform linear array, and constructs three fractional lower order statistics matrixes by the received array data, and utilizes TLS method to estimate the two dimension parameters, the algorithm has high estimation accuracy, only need a parameters pairing easily. The performance of proposed method is verified by computer simulations.

A Modified MUSIC Algorithm for DOA Estimation

In this paper, a method of being modified 2-D DOA estimation is presented. By reconstructing covariance matrix of the received array data, the correlativity of the incident signals is recreased, and mis-division between signal subspace and noise subspace is controlled, therefore the number of estimated signals would be equal to the number of actual incident signals. This method has good performance not only for DOA estimation of the correlation signals, but for DOA estimation of the non-correlation signals. In addition the computational complexity will not increase obviously. The simulation tests verify the validity of the presented algorithm.

FINITE DATA PERFORMANCE ANALYSIS OF LCMV ANTENNA ARRAY BEAMFORMERS WITH AND WITHOUT SIGNAL BLOCKING

A linearly constrained minimum variance (LCMV) antenna array beamformer using flnite data samples sufiers from slow convergence when the received array data contain the desired signal. It has been reported that signal blocking techniques speed up the convergence rate and increase the robustness of LCMV antenna array beamformers. However, the reason of this improvement has not been explored in the literature. Moreover, the existing formulas for the output signal-to-interference-plus-noise ratio (SINR) are too rough to realize the in∞uence of signal blocking techniques on the performance. In this paper, we show that the correlation due to flnite samples causes the redundant component (termed as the cross weight) embedded in the weight vector of a LCMV beamformer even if the signal sources and noise are independent. The cross power results from the cross weight degrades the performance when the sample size is small. In contrast, the cross weight and cross power can be fully eliminated when a signal blocking technique is used. The theoretical results presented in this paper provide a comprehensive description on the efiectiveness and the price of using signal blocking for antenna array beamforming. Simulation results are also given for conflrming the validity of the theoretical results.

ROBUST ADAPTIVE BEAMFORMING USING A FULLY DATA-DEPENDENT LOADING TECHNIQUE

This paper deals with adaptive array beamforming in the presence of errors due to steering vector mismatch and flnite sample efiect. Diagonal loading (DL) is one of the widely used techniques for dealing with these errors. However, the main drawback of DL techniques is that there is not an easy and reliable manner to determine the required loading factor. Recently, serval DL approaches proposed the so-called automatic scheme on computing the required loading factor. In this paper, we propose a fully data-dependent loading to overcome the di-culties. The novelty is that the proposed method does not require any additional sophisticated scheme to choose the required loading. The loading factor can be completely obtained from the received array data. Analytical formulas for evaluating the performance of the proposed method under random steering vector error are further derived. Simulation results are provided to conflrm the validity of the proposed method and make comparison with the existing DL methods.

ANTENNA ARRAY BEAMFORMING IN THE PRESENCE OF SPATIAL INFORMATION UNCERTAINTIES

This paper deals with adaptive antenna array beamform- ing under spatial information uncertainties including steering angle mismatch, random perturbations in array sensor positions, and mu- tual coupling between antenna array sensors. To make antenna array beamformers robust against the spatial information uncertainties, we present an iterative method to obtain an appropriate estimate of the actual direction vector for each of the desired signals. The proposed method uses only the a posteriori information of the received array data. It invokes an appropriate objective function for estimation and solves the minimization of the objective function by using a gradient based algorithm. The convergence property of the proposed method is investigated. Simulation results are provided for showing the efiec- tiveness of the proposed method.

DIRECTION OF ARRIVAL ESTIMATION BASED ON FOURTH-ORDER CUMULANT USING PROPAGATOR METHOD

In this paper direction-of-arrival estimation (DOA) of multiple narrow-band sources, based on higher-order statistics using propagator, is presented. This technique uses fourth-order cumulants of the received array data instead of second-order statistics (auto- covariance) and then the so-called propagator approach is used to estimate the DOA of the sources. The propagator is a linear operator which only depends on the array steering vectors and which can be easily extracted from the received array data. But it does not require any eigendecomposition of the cumulant matrix of the received data like MUSIC algorithm. Computer simulations are carried out to compare the performance of the proposed method to those of methods based on auto-covariance using MUSIC and propagator algorithms.

2-D Direction Finding for Coherent Cyclostationary Signals under Random Array Position Errors

This paper considers the problem of finding two-dimensional (2-D) direction of arrivals (DOAs) for coherent cyclostationary signals using a 2-D array with random position errors. To alleviate the performance degradation due to the coherence between the signals of interest (SOIs) and the random perturbation in 2-D array positions, a matrix reconstruction scheme in conjunction with an iterative algorithm is presented to reconstruct the correlation matrices related to the received array data so that the resulting correlation matrices possess the eigenstructures required for finding 2-D DOAs. Then, using the reconstructed matrices, we create a subspace orthogonal to the subspace spanned by the direction vectors of the SOIs. Therefore, the 2-D DOAs of the SOIs can be estimated based on a subspace-fitting concept and the created subspace. Finally, several simulation examples are presented for illustration and comparison.