Match-Mode Autoregressive Method for Moving Source Depth Estimation in Shallow Water Waveguides

A method of range and depth estimation was studied using a single hydrophone based on the dispersive characteristic and time-frequency analysis for low frequency underwater acoustic pulse signals in shallow water environment. First, the signal received on a single hydrophone can be decomposed into a series of modes within the frame work of normal mode theory, and then the dispersive characteristic of the propagating modes can be analyzed using the time-frequency analysis. In order to improve the time-frequency resolution, the use of the time-frequency distribution with adaptive radial-Gaussian kernel extracts the arrival time difference of propagating modes in dispersion curve, which can be used to estimate source range. Mode energy can be extracted using binary time-frequency mask filtering based on multi-mode joint matching processing; and the source depth can be estimated by comparing the differences of the mode energy of the real data and simulated replica data, yielding a contrast function. Simulation results from a shallow-water Pekeris waveguide show that the time-frequency distribution with adaptive radial-Gaussian kernel represents well the dispersion characteristics of the underwater acoustic pulse signals, provides higher time-frequency resolution and overcomes the problem of the inherent limit for the time resolution and frequency resolution in the traditional short-time Fourier transform, so that the modes can be separated and identified more easily in the time-frequency plane. From the result of the range estimation, the different mode combinations have different results of the range estimation. The range estimation result can be obtained accurately by using the mode with high energy in the time-frequency plane. The relative error in range estimation is less than 2% by using the mode with high energy. In terms of the depth estimation, the more the number of joint matching mode, the more sharp peak and low fake peaks the contrast function has, so that the depth estimation is further improved by incorporating more modes. This research has great significance for studying the extraction and separation of low frequency underwater acoustic pulse signals.

Passive sonar limits the ability to sample vertical scale spatiotemporally, and the received signal is indistinct by noise, resulting in the performance degradation or even failure of the source depth estimation method in deep ocean bottom bounce area. When vertical line array is arranged near the sea surface to locate the source by matched-field processing in bottom bounce area, there is great ambiguity in depth dimension. In this work, the problem of source depth estimation in bottom bounce area is addressed. The peak stripe of angle-range interference pattern is modeled and analyzed based on the ray theory, and a source depth estimation method is proposed, which comprises two parts: estimating sound source depth by utilizing peak stripe fluctuation characteristic combined with spatial spectrum analysis, and reconstructing interference pattern using principal component analysis. The flowchart of the method is listed as follows. Firstly, the spatial spectrum corresponding to each range is spliced to obtain the original angle-range interference pattern. Secondly, the original interference pattern is denoised by principal component analysis to obtain the reconstructed interference structure. Finally, the fluctuation period of peak fringes is extracted from the reconstructed interference pattern to calculate the source depth. Under the low signal-to-noise ratio (SNR) condition, the peak stripe destroyed by noise will reappear in the reconstructed interference pattern and the estimation result of sound source depth will be more accurate, making the source depth estimation method suitable for bottom bounce area. The method combines the space-time cumulative gain of the array and the low-rank characteristic of the interference pattern. The simulation results obtained by Bellhop indicate that the fluctuation period of peak stripe depends on the depth and frequency of the source, which is consistent with the modeling result, and the source depth can be estimated precisely by spatial Fourier transform. The simulation results also show that the rank of the interference pattern is very low and the peak stripe can be composed of a few principal components. Monte Carlo experimental results indicate that the estimated results of the source depth by using reconstructed interference pattern are more accurate than those without using principal component analysis at low SNR condition. The proposed method can achieve more than 80% accuracy at –3 dB SNR.

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.

In this Letter, a simplified expression of the vertical dimension narrowband interference pattern in deep water direct arrival zone is theoretically derived. The correlation between the vertical dimension interference pattern and source depth is analyzed, and the depth span corresponding to a complete interference cycle (interference period) is derived theoretically. A source depth estimation method is proposed based on matching the vertical interference pattern calculated from the data with theoretical predictions. The effectiveness of the theoretical approach in predicting the vertical interference pattern and effectiveness of the proposed depth estimation method are verified by 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.

A method of source depth estimation based on the multi-path time delay difference is proposed. When the minimum time arrivals in all receiver depths are snapped to a certain time on time delay-depth plane, time delay arrivals of surface-bottom reflection and bottom-surface reflection intersect at the source depth. Two hydrophones deployed vertically with a certain interval are required at least. If the receiver depths are known, the pair of time delays can be used to estimate the source depth. With the proposed method the source depth can be estimated successfully in a moderate range in the deep ocean without complicated matched-field calculations in the simulations and experiments.

We estimate yields and source depths for the six North Korean underground nuclear explosions (UNEs) in 2006, 2009, 2013, 2016 (January and September), and 2017, based on regional seismic observations in South Korea. Spectral ratios of event pairs are calculated using seismograms from the six UNEs observed along the same propagation paths and at the same receivers. These relative seismic source scaling spectra for Pn provide a basis for a grid search source solution that estimates source yields and depths for each event pair based on assumed explosion source models by Mueller and Murphy (1971; MM71), Denny and Johnson (1991; DJ91), and Walter and Ford (2018; WF18). The grid search is used to identify the best fit to the empirical spectral ratios subject to the source models by minimizing the root mean square misfit in the frequency range of 0.2–15 Hz. To address the trade-off between depth and yield, a modified grid search was implemented that includes elastic propagation effects for different source depths using reflectivity Green’s functions, thus modeling slight differences in propagation path based on source depth. This addition reduces trade-offs between depth and yield, and results in better model fits to frequencies as high as 15 Hz compared with cases in which depth effects were not included. The modified grid search results indicate that both MM71 and WF18 models provide comparable source depth and yield estimates with good agreement between theoretical and observed spectral ratios matching both the long-period levels and the corner frequencies, whereas the DJ91 model estimates produce lower yields due to a difference in corner frequency scaling. The best grid search solutions produce yields from ∼0.9 kt for the first UNE and up to ∼290 kt for the explosion in 2017, with depths varying from ∼280 to ∼750 m.

Range estimation based on the array invariant concept exploits the inherent properties of shallow-water waveguide propagation. Multipath arrivals observed on a vertical line array, indexed on vertical arrival angle and time difference of arrival, form what is known as a beam migration pattern in the shape of an ellipse that is a function of source range and the acoustic invariant beta. Fitting the beam migration pattern to an ellipse yields the source range. A property of this beam migration pattern is that it is independent of source depth. Source depth determines how the multipath arrivals are distributed along that ellipse. We will extend previous work on estimating range and present how to estimate depth. This decouples the two estimates and reduces a 2D search process to two 1D processes. We will explore the CRLB structure of the range and depth estimates and demonstrate the results of processing experiment data from the RADAR 2007 experiment in shallow water off the coast of Portugal.

A high-resolution method of source depth estimation in waveguide is proposed. The method is based on the mode filtering to get a data set consisting of eigenfunctions, and then the orthogonal decomposition technique is used to process this data set. High-resolution depth estimation is obtained even for the shortest data length-only two mode eigenfunctions.

Source localized modelling to estimate the depth of anisotropy beneath eastern Himalaya using spatial coherency of shear-wave splitting parameters

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.

In deep water, multipath time delays or frequency-domain interference periods of the acoustic intensity combined with multipath arrival angles are typically used for source localization. However, depth estimate is hard to achieve for a narrowband source at a remote part of the direct arrival zone as the required bandwidth increases with the source range. In this paper, a passive source localization method with a vertical line array, suitable for both broadband and narrowband sources, is proposed. Based on the variation trends of multipath angles with source range and depth, source localization is achieved by only matching the measured angles of the direct path and surface-reflected path with model-based values of a predefined grid of potential source locations. Considering the angle resolution limited by the array aperture and the presence of coherent multipath, sparse Bayesian learning is used and compared with the conventional beamforming and the minimum-variance distortionless-response beamforming to resolve and estimate the multipath angles. Simulations and experimental data of explosive sources collected by a vertical line array in the South China Sea are carried out to illustrate the method and demonstrate the performance.

Depth estimation of deep water moving source based on ray separation

In this study, we present a method for all-around depth estimation from multiple omnidirectional images for indoor environments. In particular, we focus on plane-sweeping stereo as the method for depth estimation from the images. We propose a new icosahedron-based representation and ConvNets for omnidirectional images, which we name "CrownConv" because the representation resembles a crown made of origami. CrownConv can be applied to both fisheye images and equirectangular images to extract features. Furthermore, we propose icosahedron-based spherical sweeping for generating the cost volume on an icosahedron from the extracted features. The cost volume is regularized using the three-dimensional CrownConv, and the final depth is obtained by depth regression from the cost volume. Our proposed method is robust to camera alignments by using the extrinsic camera parameters; therefore, it can achieve precise depth estimation even when the camera alignment differs from that in the training dataset. We evaluate the proposed model on synthetic datasets and demonstrate its effectiveness. As our proposed method is computationally efficient, the depth is estimated from four fisheye images in less than a second using a laptop with a GPU. Therefore, it is suitable for real-world robotics applications. Our source code is available at https://github.com/matsuren/crownconv360depth.

The polarization of the acoustic field in the ocean waveguide environment is a unique property that can be measured by using a particle velocity sensor in the water column. It can provide new ideas for locating and detecting the underwater target, so it is interesting to study the polarization. The polarization of a monochromatic signal has been described by the Stokes parameters, a set of four real-valued quantities in previous work. In this work, the Stokes parameters are extended to the broadband form, and the expression is simplified by using the nonstationary phase approximation, which reduces the complexity of the theoretical derivation and reveals the physical mechanism behind the significant variations in polarization with source depth and symmetrical depth. Theoretical analysis shows that the polarization characteristics in the ideal waveguide vary significantly in the sea surface, the sea bottom, the depth of the sound source and symmetrical depth. In this work the numerical simulation is used to verify the theoretical analysis and study the relationship between range and integral bandwidth when nonstationary phase approximation method is effective. The numerical results demonstrate that the simplified expression using the nonstationary phase approximation is effective and can better characterize the depth distribution characteristics of the polarization. Additionally, by normalizing the broadband Stokes parameters, the effect of range on the depth distribution characteristics of polarization can be removed. It means that the normalized broadband Stokes parameters are in theory free of the range and depend on the environment, the receiver depth and the source depth, which have the potential to be used for source depth estimation. Subsequently, focusing on normalized broadband Stokes parameters, we analyzes the effects of parameters such as source frequency, source depth, sound speed profile and water depth on the depth distribution characteristics of polarization. The analysis results show that environmental factors have great influence on the depth distribution characteristics of polarization. In the end, the validity of the nonstationary phase approximation and the range-independent property of the normalized broadband Stokes parameters are verified by the results of the RHUM-RUM experimental data processing. The findings provide a theoretical basis for passive target depth estimation based on polarization.