Passive source localization based on multipath arrival angles with a vertical line array using sparse Bayesian learning.

Bottom loss inference from ambient noise inversion has been shown to yield accurate and robust predictions of undersea sound propagation and sonar detection performance using vertical line arrays and a conventional beamformer [Arvelo, J. Acoust. Soc. Am., 123, 679, 2008]. However, any array with a vertical aperture should be good candidates for ambient noise inversion. The main problem with vertical line arrays is that they are not well suited to rapidly survey a large area. Platform translation with a vertical array is expected to cause extreme array shape distortions that could seriously limit the accuracy of the results. To mitigate array shape distortion, a smaller array with vertical aperture could be mounted on the survey platform, which would allow it to survey the area at greater speeds. The platform's diameter certainly limits the vertical aperture of the array. A limited vertical aperture limits the frequency range, resolution, and accuracy of the estimated bottom loss. Since the array is rigidly fixed to the platform's body, an aggressive adaptive beamformer may be adopted to increase the resolution and accuracy of the inverted bottom loss to very low frequencies. The performance is demonstrated via comparisons against conventional beamformers with numerical simulations and measurements.

Various line array configurations are evaluated for the source localization performance based on the analysis of mode decomposition matrix in this paper. The guideline of array shape design focuses on improving the localization performance of matched filed processing, meanwhile reducing the difficulty of deploying equipment in practical experiments. In the shallow water environment, when the environment is well known, the source localization result can be obtained by matched field processing algorithms effectively, but the source localization performance is affected by the array parameters, such as array length, the number of sensors, and the configurations of various horizontal and vertical line arrays. The modal decomposition method provides a useful insight into the questions of how many modes are needed and how to design the array to resolve the modes. Therefore, the method of utilizing a normal mode acoustic propagation model to decompose mode is proposed by vertical line array, horizontal line array and combined array respectively. Then we can evaluate the source localization performance of various line array configurations by studying the characteristic of normal mode decomposition matrix, thus establishing a qualitative or even quantitative relationship between each other. The more the normal mode decomposition matrix tends to be diagonalized, the better performance of line array localization will be obtained. Simulation results show that the localization performance of matched field processing with the combined arrays will be severely degraded when the mode amplitudes cannot be accurately deduced by one of the sub-arrays. Considering the requirements for the practical experiments and various environments, the source localization performance of short vertical line array and combined array are mainly discussed in this paper. The combined array can increase the azimuth and depth information of the source and realize three-dimensional target detection while the vertical array provides range-depth information and the horizontal array provides bearing information. Simulation result indicates that the design guidelines based on the normal mode decomposition are appropriate for arrays employed for matched filed processing. Meanwhile, the combined arrays perform better than the short vertical array, which is benefited by the horizontal array's suppressing the side lobes, which leads the ratio of peak to sidelobe to increase, and thus improving the location accuracy. The values of localization accuracy of combined arrays are all above 90% according to the simulation experiment. Take the practical application into account, the combined array is undoubtedly a compromise choice for the localization performance and the test complexity.

Wind-generated noise is ubiquitous in ocean environments and highly influences the passive sonar performance. Since it originates from sources near the ocean surface, one of its physical features is that it largely represents only the intermediate- and high-order modes. The array-level signal-to-noise ratio (SNR), which includes the array-sampled sound intensity, background noise power, and array gain, is an essential quantity determining the sonar array performance. What is investigated in this work is how the array-level SNR of the vertical line array (VLA) varies with the source depth in downward-refracting shallow water, contributed by the modal structure of the surface noise. On the assumption that the modes are well sampled, it is theoretically demonstrated that the SNR varying with the source depth can be approximated as a linear combination of the lower-order mode-amplitude intensities varying with the water depth. Particularly, when the surface noise especially dominates and the water channel is highly downward refractive, this variation can be represented nearly only by the 1<sup>st</sup>-order mode-amplitude intensity varying with depth. The structure is meaningful in practice. It suggests the SNR will be inherently larger when the source is submerged than it is near the ocean surface, and will be maximized at a source depth slightly below the 1<sup>st</sup>-order mode peak across different source ranges. The above assertions are demonstrated in a typical downward-refracting shallow-water channel; the effects from the dominant degree of the surface noise, sound speed gradient in water column, and array aperture are investigated numerically. The obtained results are shown below. 1) Under certain circumstances, the variation of SNR with source depth is nearly irrelevant to the source range. 2) When the surface noise is more significant, the largest SNR in a certain source range will be more significantly larger than the SNR for the source near the surface, the corresponding source depth will be closer to that presenting the 1<sup>st</sup>-order mode’s peak, and the variation of SNR with source depth is increasingly irrelevant to the source range. 3) A stronger downward-refracting sound speed also enhances this SNR superiority and irrelevance to the source range, but causes the source depth presenting the largest SNR to be more deviated from the 1<sup>st</sup>-order mode’s peak. 4) Although the structure is unraveled on the assumption that the VLA spans the full water column, it can be seen when the VLA does not but covers the low-order modes' main part; when the array aperture is insufficiently large it will become approximately periodic in the source range, with the source depth presenting the largest SNR fluctuating lightly and nearly periodically around the 1<sup>st</sup>-order mode peak.

This In order to reduce the difficulty of the practical application of the time reversal method (TRM), this paper proposed a new method of virtual TRM with a short vertical line array. The measurement field received by the short array is used to reconstruct an acoustic field of a virtual long vertical array. The method is mainly divided into three steps: Initially, using the modal decomposition to decompose the sound field received by the short vertical array into a modal function matrix and a modal coefficient vector. Furthermore, we obtain the estimated values of the modal coefficients of each order. In this paper, an iterative algorithm was used to obtain the modal coefficients of each order, and then the measured field of the long vertical line array is extended through the obtained modal coefficients. Finally, we use the extended vertical line array measurement field for time reversal processing. The results from the final computer simulation indicated that, due to the measurement field of the long vertical line after continuation contains more environmental information, the virtual time reverse processing method with the extended measurement field has superior focus positioning performance.

The INTIFANTE'00 sea trial was a multidisciplinary experiment including testing of an autonomous surface vehicle, underwater communications, source localization and acoustic ocean tomography. The results shown concentrate on the source localization and ocean tomography data sets. The data gathered during a 24 hour run along a range independent track shows strong oceanographic features, possibly due to internal tide signature, both on the temperature data, as measured on the thermistor chain collocated with a vertical line array (VLA), and on the acoustic data. A range dependent track between 120 and 60 m water depth, shows a highly variable channel impulse response along time and range when the source was moving outwards from the VLA. In another acoustic track, the source was navigatated across a underwater canyon where the energy was rapidly distributed over a deep acoustic channel with sound trapped well below the thermocline. Good agreement between the modeled and measured channel responses represents the first step towards matched-fleld processing-like methods such as source localization and tracking and ocean tomography.

A method is developed in this paper to calculate the spatial gain of a vertical line array when the plane-wave assumption is not applicable and when the oceanic ambient noise is correlated. The proposed optimal array gain (OAG), which can evaluate the array’s performance and effectively guide its deployment, can be given by an equation in which the noise gain (NG) is subtracted from the signal gain (SG); hence, a high SG and a negative NG can enhance the performance of the array. OAGs and SGs with different array locations are simulated and analyzed based on the sound propagation properties of the direct-arrival zone (DAZ) and the reliable acoustic path (RAP) using ray theory. SG and NG are related to the correlation coefficients of the signals and noise, respectively, and the vertical correlation is determined by the structures of the multipath arrivals. The SG in the DAZ is always high because there is little difference between the multipath waves, while the SG in the RAP changes with the source-receiver range because of the variety of structure in the multiple arrivals. The SG under different conditions is simulated in this work. The “dual peak” structure can often be observed in the vertical directionality pattern of the noise because of the presence of bottom reflection and deep sound channel. When the directions of the signal and noise are close, the conventional beamformer will enhance the correlation of not only the signals but also the noise; thus, the directivity of the signals and noise are analyzed. Under the condition of having a typical sound speed profile, the OAG in some areas of the DAZ and RAP can achieve high values and even exceed the ideal gain of horizontal line array 10 logN dB, while, in some other areas, it will be lowered because of the influence of the NG. The proposed method of gain analysis can provide analysis methods for vertical arrays in the deep ocean under many conditions with references. The theory and simulation are tested by experimental data.

The horizontal wavenumbers and modal depth functions are estimated by block sparse Bayesian learning (BSBL) for broadband signals received by a vertical line array in shallow-water waveguides. The dictionary matrix consists of multi-frequency modal depth functions derived from shooting methods given a large set of hypothetical horizontal wavenumbers. The dispersion relation for multi-frequency horizontal wavenumbers is also taken into account to generate the dictionary. In this dictionary, only a few of the entries are used to describe the pressure field. These entries represent the modal depth functions and associated wavenumbers. With the constraint of block sparsity, the BSBL approach is shown to retrieve the horizontal wavenumbers and corresponding modal depth functions with high precision, while a priori knowledge of sea bottom, moving source, and source locations is not needed. The performance is demonstrated by simulations and experimental data.

A recent publication by McCargar and Zurk [(2013). J. Acoust. Soc. Am. 133(4), EL320-EL325] introduced a modified Fourier transform-based method for passive source depth estimation using vertical line arrays deployed below the critical depth in the deep ocean. This method utilizes the depth-dependent modulation caused by the interference between the direct and surface-reflected acoustic arrivals, the observation of which is enhanced by propagation through the reliable acoustic path. However, neither the performance of this method nor its limits of applicability have yet been thoroughly investigated. This paper addresses both of these issues; the first by identifying and analyzing the factors that influence the resolution and ambiguity in the transform-based depth estimate; the second by introducing another, much simpler depth estimation method, which is used to determine the target trajectories required for observation of the interference pattern and the array requirements for accurate depth estimation.

The array invariant, a robust approach to source-range estimation in shallow water, is based on the dispersion characteristics of broadband signals in ideal waveguides. It involves time-domain plane-wave beamforming using a vertical line array (VLA) to separate multiple coherent arrivals in beam angle and travel time. Typically, a probe signal (i.e., a cooperating source) is required to estimate the Green's function, but the array invariant has been recently extended to a ship of opportunity radiating random signals using a ray-based blind deconvolution [Byun, Kim, Cho, Song, and Byun, J. Acoust. Soc. Am. 142, EL286-EL291 (2017)]. Still, one major drawback is its sensitivity to the array tilt, shifting the beam angles and adversely affecting the array invariant parameter that determines the source range. In this paper, a simple optimization algorithm for simultaneous estimation of the array tilt and the source range is presented. The method is applied to a ship of opportunity (200-900 Hz) circling around a 56-m long VLA at a speed of 3 knots (1.5 m/s) at ranges of 1.8-3.6 km in approximately 100-m deep shallow water. It is found that the standard deviation of the relative range error significantly reduces to about 4%, from 14% with no compensation of the array tilt. The estimated tilt angle displayed as a function of the ship's azimuth angle reveals that the VLA is tilted about 3° towards the northwest, suggesting that the array invariant can serve as a remote sensing technique for calibration of the array tilt using a source of opportunity.

The spatial and energy resources available on small underwater platforms are limited, imposing strict restrictions on the structure, weight, and channel count of the sonar array they carry. To enhance the direction of arrival (DOA) estimation capabilities of small platform sonars under these constraints, this paper examines a combined vertical array (CVA), composed of a single vector hydrophone and pressure hydrophones. The vertical line array is insensitive to azimuthal variations, but the CVA is capable of horizontal direction estimation with better gain compared to a single vector hydrophone. A novel DOA estimation algorithm, based on the joint processing of sound pressure and particle velocity signals from a CVA, has been proposed: By jointly processing the sound pressure signals from the vertical array and the particle velocity signals from a single vector hydrophone, the method achieves gain transformation of the CVA in three-dimensional space, effectively enhancing the horizontal bearing estimation capability. Expressions for the horizontal gain of the CVA were derived, and the impact of array and signal parameters on the horizontal direction estimation accuracy of the CVA was simulated using the Monte Carlo method. Numerical simulations and experimental results indicate that the horizontal direction estimation accuracy of the CVA surpasses that of traditional vector hydrophones, with high-frequency gain stability unaffected by grating lobes in the elevation direction. This allows for high-precision, unambiguous estimation of target directions.

Warm-core eddy effects on sound propagation in the South China sea

During the New Jersey Shelf RAGS03 experiment, acoustic signals emitted by ships of opportunity (merchant ships) are simultaneously recorded on three vertical line arrays (VLAs) and a horizontal line array (HLA). Recorded broadband (50–750 Hz) acoustic data sets are used to demonstrate the source localization capability as well as geoacoustic inversion capability. Waveguide invariant theory applied to beamforming by two vertical arrays that provided a range ratio of the source to the receivers. Beamforming by a horizontal array provided time‐evolving spectrum for a particular look direction (LOFARgram). The trajectories of the striations observed both in vertical array beamformer output and LOFARgrams are used to estimate the source speed, range, and azimuthal direction as well as bottom geoacoustic parameters. Trajectories of striations are identified by the Hough transform that converts a difficult global detection problem in the image domain into a simpler local peak detection problem. Analysis of both...

Large, transient increases in underwater noise intensity (noise bursts) were repeatedly observed during the ASIAEX experiment on a 48-hydrophone array consisting of vertical and horizontal line arrays. The arrays were located in the South China Sea in the area known for exceptionally strong nonlinear internal waves (NIWs). The ASIAEX experiment was intended to study sound propagation in the presence of NIWs and featured extensive, concurrent acoustic and oceanographic observations. The NIWs propagating past the acoustic array site were characterized using water temperature measurements with a nearby thermistor chain. Remarkable correlation is found between noise intensity increases on the vertical array hydrophones and the NIW presence. Intensity of the noise bursts strongly depends on the hydrophone depth. The low acoustic frequencies below 30–40 Hz are primarily responsible for the noise enhancement during the NIW passage. Analysis of the spectral properties and the depth dependence of the noise intensity suggests the flow noise due to NIW-induced currents as the physical mechanism of the noise bursts in the South China Sea. [Work was supported, part, by ISF award 946/20.]

Source depth estimation is always a problem in underwater acoustic area, because depth estimation is a nonlinear problem. Traditional depth estimation methods use a vertical line array, which has disadvantage of poor mobility due to the size of sensor array. In order to estimate source depth with a horizontal line array, we propose a matched-mode depth estimation method based on autoregressive (AR) wavenumber estimation for a moving source in shallow water waveguides. First, we estimate the mode wavenumbers using the improved AR modal wavenumber spectrum. Second, according to the mode wavenumber estimation, we estimate the mode amplitudes by the wavenumber spectrum, which is obtained by generalized Hankel transform. Finally, we estimate source depth estimation by the peak of source depth function wherein the data mode best matches the replica mode that is calculated using a propagation model. Compared with synthetic aperture beamforming, the proposed method exhibits a better performance in source depth estimation under low signal-to-noise ratio or the small range span. The robustness of the proposed method is illustrated by simulating the performance in mismatched environment.

Distributed vertical line array (DVLA) measurements of a controlled towed source were made as part of the Office of Naval Research Philippine Sea 2009 experiment (PhilSea09). The vertical line array consisted of two 1000 m sections, one spanning the sound channel axis (∼1000 m) and the other spanning the surface conjugate depth (∼5000 m). The source transmitted a combination of narrowband tones and LFM signals ranging between 20 and 450 Hz was towed at ranges from 3 to over 100 km from the DVLA. In this paper, matched field localization methods, developed in the 1990s are applied to the pair of DVLA receivers. A comparison of the detection and localization skill of each array is made as a function of source range and source receiver. Deep-water propagation for shallow sources is dominated by convergence zone propagation and, therefore, the axial and deep receivers will be illuminated by the source at different times. Narrowband and broadband geo-acoustic inversion results will be presented. Seafloor roughness is shown to be a significant feature of the bottom bounce paths and a beam-based matched field processing technique is applied to mitigate for the spreading of bottom interacting ray-paths.