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In this paper, the closed form expression of spatial coherence of the noise between the combined vector sensor components in the isotropic noise field is derived, and a superdirective beamformer based on the Gram-Schmidt orthogonal transform is proposed. One such combined directional sensor is composed of a single-degree-of-freedom particle velocity sensor and an omnidirectional acoustic pressure sensor, and its spatial response is directional. The solution to the spatial coherence is solved to constitute the noise covariance matrix of the line array in the endfire direction. Compared to the traditional pressure sensor arrays, the vector sensor arrays can pick up signals at the desired direction and increase the array gain by 4dB - 6dB in a wide frequency band with low side lobes and no left-right ambiguity, which are useful to suppress the unwanted noise and interferences from other sides. The proposed superdirective method is superior to the conventional beamforming and the trade-off can be made between directivity index and robustness. The performance of high-order superdirectivity of the line vector sensor array is analyzed, which is useful to the underwater hydrophone array design.

In this study, the conventional beamforming (CBF) and the minimum variance distortionless response (MVDR) beamforming with a line hydrophone array mounted on an infinite rigid cylindrical baffle are proposed. Based on decomposing the sound field into a summation of harmonics, a model is introduced to compute the noise cross-spectral matrix in the spherically isotropic noise field. Some design examples are given with different array configurations and different kinds of incident signals. In comparison with the acoustically transparent array, the effects of the baffle scatter on the array gain and white noise gain are examined. Simulation results show that the baffled array has an advantage over the transparent array in a wide range of elevation angles.

This paper presents a method of direction-of-arrival estimation using the high-order superdirective beamforming for a circular hydrophone array. The weighting vectors with different orders used for DOA estimation can be obtained using the previously proposed eigenbeam decomposition and synthesis theory, which can provide frequency-invariant beampatterns in a wide frequency band. The DOA estimation result of this method is the sum of estimations with different orders and the robustness decreases with an increase of the number of order. The reduced-rank technique is applied to achieve robust DOA estimations by truncating some error-intolerable high order estimation results and reserving the low order ones. Simulation results show that the DOA method proposed in this paper can improve the angular resolution (when the sensor space to wavelength ratio is smaller than 1/2) compared to the conventional beamforming (CBF) method. An experiment was conducted in the South China Sea with a 12-hydrophone circular array, and the results show effectiveness and validity of the proposed method.

The received wind driven noise field can be described as a sum of fields radiated from many random sources on the sea surface. Wind driven noise source levels can be modeled by empirical relationship with local wind speed. A method for modeling wind-driven ambient noise based on ray approach in deep ocean is presented. Simulations are performed to demonstrate the validity of the method. The wind-driven ambient noises are attributed to not only the near noise sources but also distant noise sources. The depth dependence and vertical directionality of ambient noise caused by wind agitation are analyzed by using the proposed modeling method, and vertical directionality frequency dependence is also described. In addition, the relationship between the logarithm of wind speed and noise levels is also analyzed at near surface and bottom depth. The power of wind speed with respect to received noise levels is equal to that of wind speed with respect to noise source levels approximately.

In this paper, Argo data combined with altimetry data were used to investigate the effect of eddy on Sound Speed Profile (SSP) in Northwestern Pacific Ocean. A combination of the closed contours method and the Okubo-Weiss method is used to detect the eddy. Statistics of SSP anomalies induced by eddy have been calculated by removing the climatology from Argo profiles in eddy. Then effects of eddy on close range Direction of Arrival (DOA) estimation have been studied with a conventional beamforming method. Results suggest that the DOA estimation performance may deteriorate due to presence of the eddy. The deterioration occurs when the receiver is placed near the direct path range. This is because the direct path range is sensitive to the SSP anomalies and the presence of the eddy may lead to the receiver falling in/out of the direct path range.

This paper first presents a superdirective frequency-invariant beamforming method for circular sensor arrays. The weighting vector of this method is in close-form, which is derived using the criterion of minimizing the mean square error between the desired and synthesized beampatterns. A detailed experimental study of this superdirective frequency-invariant beamforming method is then followed, which is used to further demonstrate its performance. In the experiment, the superdirective frequency-invariant broadband beamformers with a specific response are designed so that they can be applied to effectively suppress the ambient noise. The experimental data are processed in the time domain in which finite impulse response filters are designed according the obtained superdirective frequency-invariant broadband beamformers. The results show that this superdirective frequency-invariant beamforming method provides good signal-to-noise ratio enhancement.

Ocean ambient noise mainly includes uncorrelated noise and correlated noise. The uncorrelated noise only affects the diagonal elements in the noise covariance matrix, and it can be suppressed by subtracting a value on the diagonal elements. Utilizing this feature, a high array-gain beamforming based on diagonal reducing is presented. Meanwhile, the robustness becomes poor. So, the array weight norm constraint is used to ensure the robustness of this method, and the threshold is selected by some criterions. Then, the diagonal reducing value is calculated by the newton iteration method. After subtracting the diagonal reducing value, the covariance matrix is used in the minimum variance distortionless response (MVDR) beamformer. Both the numerical simulations and experimental results show that the proposed method can improve the array gain and the resolution capacity of multi-targets and it also can provide a tradeoff between array gain and robustness by changing the diagonal reducing value.

This paper studies the effects of hydrophone gain errors and self-noise on the direction-of-arrival (DOA) performance of three methods: the conventional beamforming (CBF) method, the minimum variance distortionless response (MVDR) method and the multiple signal classification (MUSIC) method. Simulations for a 16-hydrophone uniform circular array whose diameter is 2 m are provided in three different scenarios, in which the incident signal is supposed to be a narrow-band signal. The results show that both the gain errors and the self-noise make the main-lobes of the beam patterns wide and the side-lobes high, and the self-noise caused by data channels has less influence on the DOA performance than the gain errors caused by the external pressure. Experiments with a 16-hydrophone uniform circular array at a depth of 3500 m in the South China Sea show that the three methods cannot obtain the direction of a real target at a low signal to noise ratio (SNR) when two hydrophones have large self-noise. By contrast, when the amplitude of each channel signal is normalized individually, the direction of the real target can be estimated using the above-mentioned three methods. If gain errors of some hydrophones are large, amplitude normalization can eliminate the errors very well. Consequently, amplitude normalization can reduce the negative effects of hydrophone gain errors and self-noise and improve the DOA performance.

Underwater sensors will diverge from the initial position because of the ocean current when the underwater sensors are deployed in the deep ocean. Assuming that the xy-plane coincides with the sea surface, a local Cartesian x-y coordinates system is set up in such a way that, when the sensors and sources are projected onto the local xy-plane, its origin coincides with the initial point of the sensors and the x-axis is parallel with east direction and positive y-axis is parallel with north direction. The depth of sensors can be obtained from press transducers, and the accurate position of the sources can be obtained from the GPS receiver attached to the ship and depths of the sources are preset. When the minimum time arrivals are snapped to a certain name, multipath time delay arrivals relative to the minimum time arrivals can be extracted from the measured signal and results of standard ray approach. The horizontal distance between the sensors and the sources can be estimated by matched time delays measured with ones calculated by BELLHOP model. Then the position of underwater sensors can be estimated by three points distance intersection method. Simulations and experiments are performed to demonstrate the feasibility of the method in the deep ocean. With the proposed method, the position of the underwater sensors can be localized in the deep ocean successfully.

This paper studies and discusses robust minimum variance distortionless response (MVDR) beamformer with subarray multistage processing for circular hydrophone arrays, which is an extension of the multistage MVDR beamformer with line microphone arrays for noise reduction. The basic theory is to divide the hydrophones into a certain number of groups with each group only having two hydrophones for MVDR beamforming. After the beamforming, it is equivalent that the number of hydrophones is half of that at the adjoining former stage. Then the grouping and beamfoming processing will be repeated till that there is only one hydrophone. This subarray multistage MVDR beamformer has the following properties in the isotropic noise field: first, it is much more robust than the conventional MVDR beamformer; second, its array gain is lower than that of the conventional MVDR beamformer; moreover, the larger the sensor number in each subarray is, the higher the array gain will be, but with lower white noise gain. By choosing a proper hydrophone number of each subarray, a tradeoff can be made between the array gain and robustness.

An ensemble Kalman filter (EnKF) approach is proposed to perform sequential tracking of water column sound speed profile (SSP) using a moving acoustic source. First, the SSPs are discretized in depth and range, and are expressed by the empirical orthogonal functions (EOFs). Second, the acoustic source state information and the first three orders of EOF coefficients are expressed as the state variable, and the acoustic field information received by the vertical line array are the measured values. Successively, the state variables and measured values are used to establish the state-measure model. Last, the EnKF is utilized to track the state variables. The simulation results show that the root mean square error of SSP and the absolute error of source are all small, and thus the acoustic source tracking-positioning has high accuracy.

Waveguide sound propagation in continental slope with a varying-gradient water-sediment interface and special environment is very complex. Given three different gradients for shelf break areas and a defined gradient for the continental slope, numerical simulations with a full-wave range-dependent acoustic model show that the energy distributes distinctly in different depth in the sound field, in which the slope enhancement and mudslide effect are robust with different bottom properties. The greater gradient slope transfers more energy from shallow to the deep areas, but the transmission loss will be similar between different gradient slopes with range reaching to 20 km because of the significant bottom loss. Comparing to the effects on sound intensity by varying sediment thickness and sediment sound speed gradient, the latter influences more in the bottom loss. One purpose of this paper is the feasibility of these effects in ocean continent transition zone for a short range (10 km – 30 km). Another purpose is the acoustic propagation characters affected by different gradient slope in this region. These results provide a better interpretation on acoustic signals at whole depth for deployed hydrophone in continental slope.