Depth estimation as a sequential process following array invariant range estimation

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.

The array invariant is derived from the waveguide invariant, and can be used to predict the shape of multipath arrival patterns on a 2D plane with axes of time and angle of arrival. The shape observed on a vertical line array is an ellipse that is a function of the waveguide invariant and the range. Once the range is obtained, ray tracing can be used to invert the multipath pattern for a depth estimate. We will compare results of using the physics-based range and depth estimator with results obtained by training a neural network on synthetic data produced by a ray tracer. We will produce two sets of exemplars to train our estimator. In one, we will provide the range as an input, and train the network to produce a depth. In the second, we will train the network to produce both range and depth. The method derived from the array invariant is expected to be brittle with respect to range-dependent bathymetry. We will compare how well the machine learning approach deals with such variability, compared to the array invariant approach.

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.

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.

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 paper develops an approach that estimates the range and depth of a broadband source by adopting the vector hydrophone vertical array (VHVA) in the deep ocean. The sound field in the direct wave zone is mainly composed of direct (D) and once-sea-surface-reflected (S1B0) waves. The arrival angles and time delays of the two waves are consistent. The combined beamforming technology is applied to the VHVA to accurately obtain the elevation angles and further enhance the received signal-to-noise ratio (SNR). The source ranges are then estimated according to the simple geometric relationship. The source depth estimation model is established based on the Lloyd-mirror principle, which relates the interference properties of D and S1B0 to the oscillation period of the combined signals of VHVA. The feasibility and availability of this method are validated by both simulations and sea trials in the South China Sea. The experimental results indicate the range estimation error of the moving vessel is less than 10% and the surface or submerged targets can be effectively determined. Our proposed algorithm has the strong benefits of simple principle, low computational complexity and small error. These properties indicate this algorithm can be used in target detection in the deep sea.

This study develops a hybrid positioning scheme that combines both differential time of arrival (DTOA) and angle of arrival (AOA) observations of the 1090-MHz automatic dependent surveillance-broadcast (ADS-B) signal and implements it on a wide area multilateration (WAM) test bed. The major issue when combining DTOA and AOA observations is synchronization. A synchronization design for DTOA and AOA observations is thus evaluated. The positioning algorithm that combines AOA and DTOA observations is a filter-based approach. Based on the measurement errors from actual ADS-B signals received from real flights, simulation is used to evaluate the positioning performance of the proposed 1090-MHz ADS-B WAM with the integration of AOA/DTOA approach under two scenarios, namely DTOA alone and AOA combined with DTOA.

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.

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.

The aim of this paper is to estimate possibilities of matched-field geoacoustic inversion (MFI) in shallow water, and to recommend optimal arrangements of signal source and hydrophone array in variety of particular environments. We assumed ocean to be range independent with bottom consisting of homogeneous liquid layers. Sound fields were calculated as superposition of normal modes and continuous spectrum for tonal point source and vertical line array. MFI based on Bartlett processor was used. Possibilities of MFI were characterized by MFI penetration depth, sensitivity to various bottom parameters and non-uniqueness of inverted data. These characteristics were analysed as functions of frequency and the source depth and range for different values of sound attenuation in sediments and for various sound-speed profiles. To estimate possibilities of MFI in real ocean conditions, influence of array tilt and inadequacy of geoacoustic model were analysed. The influence of continuous spectrum was also discussed. Among the major results, optimal source ranges corresponding to the maximum penetration depth of MFI were calculated, and high influence of attenuation in sediments on possibilities of MFI was revealed.

Most methods used to track marine mammals with passive acoustics require that time differences of arrivals (TDOAs) are established and are associated between hydrophone pairs. Consequently, multiple animal trackers commonly apply single-animal TDOA localization methods after performing a call separation and/or TDOA association step. When a wide-baseline array is used with multiple animals that make similar calls with short inter-call-intervals, the separation/association step can be challenging and potentially rejects valid TDOAs. This paper extends a model-based TDOA method to deal with multiple-animal datasets in a way that does not require a TDOA association step; animals are separated based on position. Advantageously, false TDOAs (e.g., a direct path associated with a multipath arrival) do not need to be removed. An analogous development is also presented for a model-based time of arrival tracking method. Results from simulations and application to a multiple sperm whale dataset are used to illustrate the multiple-animal methods. Although computationally more demanding than most track-after-association methods because separation is performed in a higher-dimensional space, the methods are computationally tractable and represent a useful new tool in the suite of options available for tracking multiple animals with passive acoustics.

Experimental data from the SACLANTCEN 1993 Mediterranean Experiment are reviewed to assess the reduction of the search space for the localization and tracking of an acoustic source in a three-dimensional environment. Key to this goal is the availability of an initial estimate of source range and depth (called the 2D initial guess); an ambiguous estimate of source bearing can be obtained from the 2D initial guess through Environmental Signal Processing, and the ambiguity can be removed by searching for the source only in the range/bearing regions where bearing estimates are higher. This search provides a new estimate of source range and a single bearing, which together with the estimate for source depth constitute the center of the reduced search space for source localization and tracking. The suggested approach is tested on experimental data from the SACLANTCEN experiment considering different frequencies, as well as a stationary and a moving source.

The position and velocity estimation of underwater moving targets is an important part of the application of underwater sensor networks. The commonly used fusion of time difference of arrival (TDOA) and angle of arrival (AOA) can only roughly estimate the target position, but also has some limitations for nonlinear problems. So in order to overcome the nonlinear problem and improve the accuracy of underwater target location.Based on TDOA and AOA, this paper adopts a three-step location method which combines frequency difference of arrival (FDOA).At the same time, the whale algorithm is used to optimize the measurement error based on the weighted least square method (Tswls). Finally, the experimental results show that compared with TDOA location method and tdoa/aoa hybrid location algorithm, this method is superior to the above methods in the accuracy and bias of position and velocity estimation.

Aiming at the problem of positioning underwater targets in a wide range of sea areas, the modern optimization technology simulated annealing algorithm is introduced into the non-linear programming of the multistatic sonar azimuth estimation. According to the development trend of long-distance wireless positioning technology <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</sup> , the data fusion positioning model based on Time Difference Of Arrival(TDOA) and Angle of Arrival(AOA) is analyzed, and a TDOA/AOA data fusion positioning method based on the simulated annealing(SA) algorithm is proposed. Simulation experiments are conducted to analyze the positioning accuracy of this method in a wide range of sea areas under different working conditions, which verifies the effectiveness and feasibility of the method.

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.