Although traditional subspace direction of arrival (DOA) algorithms enable super-resolution, the algorithm performance declines sharply when the number of sources is incorrectly estimated. This paper proposes a new DOA estimation method as an optimization problem similar to the conventional minimum variance distortionless response (MVDR) that fully considers the eigenvalues ranking problem. After a mathematical derivation, a concise DOA estimation expression is given based on the mapping between eigenvalues. As the algorithm considers the relative ranking of eigenvalues, the number of sources is not required for DOA estimations. Therefore, the performance of the algorithm does not degrade due to incorrect estimations in the number of sources. To enhance the algorithm performance, this paper analyzes the reasons for the formation of pseudo peaks based on the eigenvalues and gives the corresponding boundary conditions. Based on the analysis of white noise, in order to overcome the influence of color noise, this paper gives a way to deal with color noise. Finally, the theory of the proposed algorithm is verified through simulation experiments, and its performance is demonstrated through comparative experiments with MUSIC under white and color noise.

Differential beamforming techniques have gained significant attention due to their frequency-independent beampatterns, applicability for small apertures, and super-directivity. It is commonly known that the main lobe of a beam pattern based on a linear array is typically aligned with the end-fire direction. However, in some application scenarios, aligning the main lobe in the end-fire direction may not meet the actual requirements. This article focuses on studying the steering problem of differential beamformers based on linear acoustics vector sensor arrays (LAVSs). We propose a steerable differential beamformer for LAVSs, which addresses the problem of non-steerable beam patterns of linear arrays. Our approach involves approximating the beam pattern using a series expansion of the weighted steering vector to achieve frequency-independent differential directivity. The major contributions of this article include, but are not limited to, the following: First, we derive the first-order to third-order differential directivity based on the acoustics vector sensor (AVS) signal model, and obtain the weights of the corresponding channels using the least squares method. Second, we provide a theoretical analysis of the steering differential beamformer, demonstrating that the maximum directivity factor (DF) is a function of the steering angle. Finally, we conduct simulation experiments to validate the proposed method.

Since it is difficult to obtain the number of sources accurately in practical situations, direction-of-arrival (DOA) estimation methods without the number of sources are very much needed for non-cooperative targets and maritime attack-defense pairings. In this paper, a DOA estimation method using acoustic vector sensors (AVS) without a known number of sources is proposed. First, a reference matrix is introduced, and the eigenvalues corresponding to the noise of this matrix converge to 0. Next, a scanning matrix containing the scanning sources is created, and the analysis of noise power invariance is used to determine the power selection method of the scanning sources. The ordering law of the eigenvalues of the source matrix scanned at different angles is applied, and the purpose of estimating DOA without the number of sources is accomplished. The proposed algorithm is capable of performing DOA estimation in situations where the number of sources is uncertain and it does not rely on the array structure, which means it can be used for arbitrary arrays. Finally, the correctness and effectiveness of the proposed algorithm are verified by simulation and experiment.

The actual underwater acoustic field environment is subject to various interferences, resulting in high background noise, thereby complicating underwater target detection. Some traditional subspace direction-of-arrival (DOA) estimation algorithms often require prior knowledge of the number of sources, leading to performance degradation if the number of sources is estimated inaccurately. With advancements in sensor technology, scholars have developed acoustic vector sensors (AVS). However, some traditional algorithms applied directly to AVS result in degraded performance of the algorithm. To address these challenges, we propose a DOA estimation algorithm that is independent of the number of sources and is applicable to AVS. This is achieved by constructing the generalized minimum variance distortionless response (G-MVDR) model based on AVS and exploring the eigenvalue ordering principle under the G-MVDR framework. It provides high-resolution DOA results independent of the number of sources and can be flexibly applied to AVS arrays. The proposed algorithm is analyzed with respect to eigenvalue ranking, and the optimal threshold is determined. Finally, the accuracy and effectiveness of the proposed algorithm are validated through simulations and experiments.

As the eigenvalue ranking problem is analyzed, a direction-of-arrival (DOA) estimation method without knowing the number of sources is proposed. The proposed method is utilized through ranking the eigenvalue of specific covariance matrix to get the smallest eigenvalue and construct a new spatial spectrum. By deducing the novel algorithm, the mapping between the eigenvalues and power of signals is presented. Using the mapping, the minimum detection threshold for this algorithm is derived. Besides, the reason for the formation of pseudo-peaks is interpreted, and an approach to parameter selection is provided. The validity of the related theory of the algorithm is further investigated by simulations.

Conventional differential directivity algorithms are highly dependent on array configuration, especially when designing steerable differential beamformers. To this end, we proposed a method for designing fully steerable directional differential beamformer based on acoustic vector sensor (AVS) with arbitrary planar array. This method addresses the challenges posed by the limited size of small platforms, strict constraints on array configuration, and weak detection capability, thereby enabling fully steerable beamforming detection using small-sized arbitrary planar geometry AVS array (APG-AVSA). The Nth-order differential beamformer is implemented by obtaining individual channel weight vectors, which cause the steering vector to converge to the target beampattern through Jacobi-Anger expansion (JAE). The major advantages of this approach are as follows: 1) a fully steerable differential beamformer design method based on APG-AVSA, which overcomes the limitations of array geometry on the performance of steerable differential beamformer, is proposed and a closed-form solution for Nth-order beamformer is provided, and 2) a theoretical derivation of the first-order white noise gain (WNG) of the proposed algorithm is given, demonstrating the proposed algorithm overcomes the problem of white noise amplification inherent in conventional differential directional algorithms. Finally, the performance of the proposed algorithm was verified through simulation comparisons and external experimental data.