Robust Underwater Direction-of-Arrival Estimation Method Using Acoustic Sensor Array under Unknown Swing Deviation Elements

Coherent signal-subspace processing of acoustic vector sensor array for DOA estimation of wideband sources

In this paper, the issue of direction of arrival (DOA) estimation is discussed, and a partial angular sparse representation (SR)-based method using a sparse separate nested acoustic vector sensor (SSN-AVS) array is developed. Traditional AVS array is improved by separating the pressure sensor array and velocity sensor array into two different sparse array geometries with nested relationship. This improved array geometry can achieve large degrees of freedom (DOF) after the extended vectorization of the cross-covariance matrix, and only partial SR of the angle is required by exploiting the cyclic phase ambiguity caused by the large inter-element spacing of the virtual array. Joint sparse recovery is developed to amend the grid offset and unitary transformation is utilized to transform the complex atoms into real-valued ones. After sparse recovery, the sparse vector can simultaneously provide high-resolution but ambiguous angle estimation and unambiguous reference angle estimation embedded in the AVS array, and they are combined to obtain unique and high-resolution DOA estimation. Compared to other state-of-the-art DOA estimation methods using the AVS array, the proposed algorithm can provide better DOA estimation performance while requiring lower complexity. Multiple simulation results verify the effectiveness of the approach.

The acoustic vector sensor (AVS) array is a powerful tool for direction of arrival (DOA) estimation of underwater targets. However, traditional DOA estimation algorithms generally suffer from low signal-to-noise ratio (SNR) as well as snapshot deficiency. A novel signal self-nulling based DOA estimation method is proposed. Firstly, achieve the crude estimation of the desired DOA using the traditional algorithms. Secondly, set the observation angular interval around the crudely estimated DOA. Thirdly, make the observation direction vary in the observation angular interval, and for each imaginary DOA, calculate the amplitude response of the minimum variance distortionless response (MVDR) beamformer. Finally, the pseudo spatial spectrum is achieved. Computer simulations verify that the proposed method is efficient in DOA estimation, especially in low SNR and insufficient snapshot data scenarios.

In this paper, the errors of acoustic vector sensor array are classified, the impact factor of each error for the array signal model is derived, and the influence of each type of error on the direction-of-arrival (DOA) estimation performance of the array is compared by Monte Carlo experiments. Converting the directional error and location error to amplitude and phase errors, the optimization model and error self-calibration algorithm for acoustic vector sensor array are proposed. The simulation experiments and field experiment data processing of MEMS vector sensor array show that the proposed self-calibration algorithm has good parameter estimation performance and certain engineering practicability.

The motivation of this work is to investigate the source number detectability by an oversampled or undersampled linear acoustic vector sensor (AVS) array. Sufficient conditions that ensure the extension of existing source number estimators and beamforming techniques from the acoustic pressure sensor (APS) array to the AVS array are established based on the linear independence of steering vectors of the AVS array, an issue closely related to the number of sources whose parameters [e.g., the direction of arrival (DOA)] can be uniquely determinable. The upper bound on the detectable number of sources with distinct DOAs under oversampled and undersampled array configurations is derived, where the difference of definitions of the distinct DOAs between the APS array and the AVS array is clarified. The number constraint on detectable sources with distinct spatial aliasing DOAs using the undersampled AVS array is also investigated. Under these conditions, advantages of eigenvalue-based source number estimators using AVS arrays are demonstrated, and the minimum description length (MDL) estimator is extended to the AVS array as an illustration to verify the established theories.

Most underwater target tracking algorithms are based on noisy bearing-only measurements. The bearing measurements are actually bearing estimates obtained from acoustic field measurements made by an array of sensors placed on a manoeuvrable platform. In this paper, we investigate the problem of tracking a manoeuvring target in the ocean directly from the acoustic field measurements. The use of acoustic field measurements eliminates the need for the use of a manoeuvrable platform, and also eliminates the intermediate step of bearing estimation. We consider the vector acoustic field measurements by an array of acoustic vector sensors (AVS), which are more informative than the scalar acoustic field measurements by an array of acoustic pressure sensors (APS). We model the target dynamics by a piecewise-constant turn rate model. The resultant nonlinear estimation problem is solved using the Gaussian approximation filtering approach. Within this framework, we consider the quasi-Monte Carlo Kalman filtering (QMC-KF) algorithm that employs an advanced numerical integration procedure to solve the multi-dimensional integrals appearing in the filtering process. We also derive the posterior Cramer-Rao lower bound (PCRLB) on the root mean square error (RMSE) of the sequential Bayesian estimator, and show that the PCRLB for acoustic field measurements is lower than that for bearing-only measurements. Simulation results indicate that acoustic field measurements yield a significantly better performance than bearing-only measurements, the QMCKF performs better than other deterministic filters, and an AVS array provides a much better performance than an APS array.

An acoustic vector sensor array consists of multiple sound pressure microphones and particle velocity sensors. A pressure microphone usually has an omni-directional response, yet a particle velocity sensor is directional and usually has a response pattern as a figure of eight. Currently, acoustic vector sensor arrays are under investigation for far field source localization and visualization. One of the major practical issues in these applications, however, is to determine the accurate position, orientation and complex (phase and amplitude) sensitivity of each sensor within the array. In this study, a new calibration method is verified with experiments. The method determines all the crucial parameters based on a limited number of measurements with a reference sensor and multiple sound sources located at known locations. The experiments are performed in an anechoic room. The results are promising.

Through in-pressure sensor array signal processing, the signal arrival angle can be estimated by the estimation of signal parameters via rotational invariance techniques (ESPRIT) if we regard the whole array as two sub-arrays with the same structure. The estimation angles arrived at by ESPRIT have a left-right ambiguity because of the inverse trigonometric function operation. An acoustic vector sensor array (AVSA), which measures particle velocity and pressure at the same time and point of the acoustic field, offers significant potential. The traditional ESPRIT algorithm can also be used for an AVSA with left-right ambiguity. A new algorithm with omnibearing and an high accuracy based on ESPRIT using an AVSA was proposed in this paper. An analytic particle velocity, which composes by acoustic vector sensor x-axis and y-axis velocities, embeds the signal angle in its phase. The signal broadside can be known by the ESPRIT based on analytic particle velocity and pressure sub-arrays. The estimation angle containing broadside information can be used as the driving angle for combined particle velocity. According to the signal broadside, an average cross-variance matrix of pressure and combined velocity was constructed. The signal angle can be estimated by ESPRIT based on this new combined cross-variance matrix. Theoretical analysis and computer simulations show that the proposed algorithm has no left-right ambiguity and also has higher accuracy than the analytic particle velocity algorithm in the case of low signal-to-noise ratio (SNR). The algorithm is based on pressure and particle velocity combined processing, which can suppress interference better than existing algorithms in isotropic noise. The algorithm is also based on the analytic particle velocity ESPRIT, which has no left-right ambiguity. So the new algorithm has better performance than the existing algorithms.

In this paper, based on the root-MUSIC algorithm for acoustic pressure sensor array, a new self-adapting root-MUSIC algorithm for acoustic vector sensor array is proposed by self-adaptive selecting the lead orientation vector, and its real-valued formulation by Forward-Backward(FB) smoothing and real-valued inverse covariance matrix is also proposed, which can reduce the computational complexity and distinguish the coherent signals. The simulation experiment results show the better performance of two new algorithm with low Signal-to-Noise (SNR) in direction of arrival (DOA) estimation than traditional MUSIC algorithm, and the experiment results using MEMS vector hydrophone array in lake trails show the engineering practicability of two new algorithms.

This paper considers the problem of tracking an acoustic sources in three dimensional (3-D) space by using a vertical acoustic vector sensor (AVS) array in a shallow ocean environment. The innovations of this work are double fold: 1) a particle filtering (PF) approach is developed to track the position of an acoustic source; and 2) based on the source motion and wave propagation models, the posterior Cramér-Rao bound (PCRB) is derived to provide a lower performance bound of 3-D position tracking in shallow ocean. The PF approach uses a number of samples to approximate the posterior distribution of interested parameters, by which a complex 3-D search can be avoided for 3-D position estimation. Also, due to incorporating both the source dynamic and measurement information, the tracking approach is able to provide a lower performance bound than the traditional localization approach. The tracking performance is further demonstrated by numerical experiments.

Recently, many direction-of-arrival (DOA) estimation techniques based on sparse representation have been proposed. However, these techniques often suffer from performance degradation issues in the presence of impulsive noise. This paper aims to overcome this challenge in conventional sparse-based techniques on an acoustic vector sensor array (AVSA). Firstly, to remove high outliers from the array output data, the output information of the AVSA is weighted by using the infinite norm. To further suppress outliers, a p-order cost function is formulated by extending the Frobenius norm to lower order, and then the expression of the signal power is quantified. Lastly, the DOA is approximated on the signal power by a spectral peak search mechanism. DOA estimation results based on Monte Carlo simulations validate the accuracy and robustness of the proposed techniques herein compared to the current, available methods in the context of intense impulsive noise, low generalized signal–to–noise ratio (GSNR), and a smaller number of snapshots.

Direction of Arrival Estimation via Acoustic Vector Sensor Array Under Missing Data

This paper provides a novel acoustic vector sensor array architecture for superdirectivity at low frequencies. It has a uniform 3 by 3 rectangular geometry of intersensor spacing less than 0.04 wavelength over its operation frequency band, with an up to 10.4 dB of directivity index in cylindrically isotropic noise. This is realized through a mode domain approach, which accesses the acoustic modes by fitting certain multipole models to the wavefield observations. Field experiments show that this is a practical solution of implementing a miniaturized vector sensor array with superdirectivity.

While the improvement of direction-of-arrival (DOA) estimation using coded covers with a single acoustic vector sensor (AVS) has been demonstrated, its extension to array-based systems remains relatively unexplored. To bridge this gap, we propose to extend the use of a coded cover from a single AVS setup to array-based acoustic measurement systems. The coded cover basically compresses the signals impinging on it from a large virtual array to a smaller physical array of sensors. To recover the uncompressed covariance matrix of the virtual array represented by the coded cover, we adopt compressed covariance sensing (CCS). Experimental results show that a 14 × 10 coded cover combined with an array of 12 probes that measure both pressure and particle velocity enables accurate localization of up to 100 sound sources in three dimensions, even under challenging conditions with a signal-to-noise ratio (SNR) as low as 10 dB. Furthermore, to address the impact of geometric mismatch—which distorts the compression matrix— we incorporate a grid-search-based calibration method to correct these perturbations. The proposed approach demonstrates both scalability and robustness, making it a promising solution for large-scale sound source localization.

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.