Replica Vector Research Articles

Source Localization in a Deep Ocean Using the Time Difference of Multipath Arrivals

Bottom bounce is a typical sound propagation mode in deep oceans. A receiver moored below the sea surface receives sound waves transmitted from a submerged source through multipath paths. Four of them which traveled by bottom bounce mode play the leading role in source localization. A passive broadband source localization method is proposed herein based on the four arrival paths and using a single receiver. Through autocorrelation of the signal that is mainly composed of four multipath arrivals, six positive relative time diff erences that are dependent on the source range and depth are acquired via combination. The time diff erences are sorted in an ascending order to form a measured vector. A ray-tracing model is used to predict the replica vector. Then, the source is localized by fitting the replica vector to the measured one. An experiment is conducted in the South China Sea. The proposed method is utilized to successfully localize a source at a depth of 47 m below the surface and at a distance of 13.6 km.

Multi-frequency sparse Bayesian learning for matched field processing in non-stationary noise

Using simulations and data, we localize a quiet source in the presence of an interferer. The SWellEx-96 Event S59 consists of a submerged source towed along an isobath over a 65 min duration with an interferer traversing the source track. This range independent, multi-frequency scenario includes mismatch, non-stationary noise, and operational uncertainty. Mismatch is defined as a misalignment between the actual source field observed at the array and the modeled replica vector. The noise process changes likely with time. This is modelled as a heteroscedastic Gaussian process, meaning that the noise variance is non-stationary across snapshots. Sparse Bayesian learning (SBL) has been applied previously to the matched field processing application [Gemba et al, J. Acoust. Soc. Am., 141:3411-3420, 2017]. Results demonstrate that SBL exhibits desirable robustness properties and improved localization performance when compared to the white noise constraint and Bartlett processors.

Multi-frequency sparse Bayesian learning for matched field processing

Compressive sensing has been applied to underwater acoustic problems. Using multi-frequency sparse Bayesian learning (SBL), we present simulation and data results (SWellEx-96 Event S5) including mismatch. Mismatch is defined as a misalignment between the actual source field observed at the array and the modeled replica vector. Results for a multiple-source scenario indicate that SBL outperforms WNC and MUSIC when localizing a quiet source in the presence of a stronger source. Furthermore, simulations (including snapshots not corresponding exactly to replicas) and data results demonstrate that SBL offers robustness to mismatch including array-tilt. The array-tilt mismatch in the data varies over time and is especially pronounced at the closest point of approach, being 2 degrees. Because of its computational efficiency and performance, SBL is practical for real time applications requiring an adaptive and robust processor.

Robust multi-frequency sparse Bayesian learning: Theory and simulations

Compressive sensing based techniques have recently been applied successfully to underwater acoustics problems such as beamforming and matched field processing. Sparse Bayesian Learning (SBL) is one of the fast compressive sensing methods and is formulated using Bayesian statistics. In the SBL framework, source amplitudes are modeled as complex Gaussian random variables with unknown variance. Evidence maximization is performed to estimate the unknown source amplitude variance and source position. A major advantage of SBL over more commonly used methods such as basis pursuit is that it is computationally faster. In this work, we develop a robust sparse Bayesian learning algorithm that can account for model mismatch leading to errors in the replica vector dictionary. Specifically, the likelihood function is modified so that it takes into account the covariance matrix of error in replica vectors. We also extend the SBL algorithm to process observations from multiple frequencies. The derived update rule combines observations from all the frequencies in a holistic manner. We demonstrate the robust SBL algorithm with simulations. A comparison is done with other compressed sensing methods including basis pursuit and orthogonal matching pursuit.

Robust multi-frequency sparse Bayesian learning: Data results

Compressive sensing based techniques have been applied successfully to underwater acoustics problems. We present data results using a robust multi-frequency sparse Bayesian learning (SBL) algorithm that can account for model mismatch leading to errors in the replica vector dictionary. We use the SWellEx-96 Event S5 data set to demonstrate SBL capabilities for the beamforming and matched field processing (MFP) application. Beamforming results using the entire 64 element array (design frequency of 400 Hz) and source frequencies ranging from 50 to 400 Hz indicate that multi-frequency SBL outperforms Bartlett and WNC processors in identifying multipath arrivals over the approximately 10 km source track. MFP results in a multiple-source scenario indicate that SBL offers a degree of robustness in the presence of data-replica mismatch when tracking a quiet source. The data-replica mismatch is especially pronounced at the closest point of approach due to array tilt of approximately 2 degrees. Data results further indicate that the two SBL tuning parameters (diagonal loading of the replica vector covariance matrix and number of sources for the algorithm’s noise estimate) do not require excessive calibration.

Robust source localization based on mode subspace reconstruction in uncertain shallow ocean environment

Existing localization methods have mismatch problem when applied to the real uncertain ocean, and this will lead to performance degradation. In normal mode models, some modal eigenfunctions remain to be more correlated than others in the presence of environmental uncertainties. Based on this, we have proposed a mode subspace reconstruction robust localization method, which uses stable modes to reconstruct the replica vector to grantee the localization performance. The data from simulation and experiment are used to verify the effectiveness of the proposed method. Performances of the matched field processor (MFP) and the robust ML (maximum localization) estimator are also given here for comparison. Results show that: (1) the generally used MFP method has a low localization performance even at high SNR values; (2) the proposed method outperforms the robust ML estimator and the generally used MFP.

A virtual time reversal method for passive source localization in a range-dependent waveguide

Matched-field replica vector should be calculated using parabolic equation in a range-dependent waveguide, this means that the matched-field localization is too computationally intensive, hence its engineering application is seriously hindered. A virtual time-reversal method for passive source localization for a range-dependent waveguide is presented. The number of parabolic equation computational grids in virtual time-reversal method is much smaller than that in matched-field processing for a range-dependent waveguide. Thus, the computational cost can be greatly reduced. Different from the matched-field processing, the virtual time-reversal method is a back-propagation process, which explores and utilizes the properties of reciprocity and superposition. It can be realized by weighting the replica surface with the complex conjugate of the data received on the corresponding element, followed by a summation of the processed received data. This performance of virtual time-reversal method for source localization is validated through numerical simulations and data from the Mediterranean Sea.

Nonlinear optimization for beamforming a geometrically deficient vertical line array: Application to sediment tomography

The 1996 Shelfbreak PRIMER experiment included broadband acoustic transmissions in the vicinity of a shelfbreak front collected using a geometrically deficient vertical line array (VLA). The broadband signals were used to tomographically image sediment sound speed and attenuation. The VLA spanned the lower half of the water column. Hence, the orthonormal properties of the underlying normal modes cannot be guaranteed for any replica vector based on the local modal structure. This produces modal sidelobes in the output of the geometrically deficient VLA. Various methods of extracting the normal modes from VLA data have been developed including a generalized least squares method shown to improve the performance of a geometrically deficient VLA processing phase encoded tomography signals [Chiu et al., IEEE J. Ocean. Eng. 22, 522–533 (2005)]. The present study seeks to enhance the modal resolution for the reception of high-amplitude, impulsive signals transmitted over a wide variety of source receiver paths in shallow water where ensemble averaging is not an option. The method uses nonlinear optimization techniques to compute a set of array element coefficients that enhance suppression of modal sidelobes, while maintaining adequate spatial matching with the desired mode. [Work supported by Office of Naval Research.]

Non-perturbative phenomena in the three-dimensional random field Ising model

A systematic approach to the calculations of the non-perturbative contributionsto the free energy in the ferromagnetic phase of the random field Ising modelis developed. It is demonstrated that such contributions appear due toinstanton-like excitations localized in space, which exist only in dimensionsD≤3.It is shown that away from the critical region such instanton solutions are described by the set ofthe mean-field saddle-point equations for the replica vector order parameter, and these equationscan be formally reduced to the only saddle-point equation of the pure system in dimensions(D−2). In themarginal case, D = 3, the corresponding non-analytic contribution is computed explicitly. The nature of thephase transition in the three-dimensional random field Ising model is discussed.

Matched-field replica vector stability in the winter ocean on the New Jersey (USA) shelf—RAGS03

A measure of the environmental influence on matched-field processing is the temporal autocorrelation of the coherent acoustic field passing through a vertical aperture. The matched-field autocorrelation times provide estimates of the time interval over which matched-field replica vectors will remain valid. In December 2003 the Naval Research Laboratory moored three vertical arrays at ranges of 10, 20 and 30 km distant from fixed 300- and 500-Hz CW acoustic sources. The purpose of the experiment was to measure the relationship of array gain to shelf break fluid processes (RAGS03). Data was recorded continuously for more than 20 days. Range and time dependent temporal autocorrelation times derived from this data will be presented and compared to similar measurements made at the South China Sea shelf break during the ONR AsiaEx01 acoustic propagation experiment. Preliminary RAGS03 results show that matched-field autocorrelation times are shortened during strong wind events and that sound speed fluctuations caused by semi-diurnal tidal processes forced quarter-diurnal fluctuations in the matched-field processor output. [Work supported by ONR.]

Quantification of deterministic matched-field source localization error in the face of random model inputs

Deterministic source localization using matched-field processing (MFP) has yielded good results in propagation scenarios where the nonrandom model parameter input assumption is valid. In many shallow water environments, inputs to acoustic propagation models may be better represented using random distributions rather than fixed quantities. One can estimate the negative effect of random source inputs on deterministic MFP by (1) obtaining a realistic statistical representation of a signal model parameter, then (2) using the mean of the parameter as input to the MFP signal model (the so-called ‘‘replica vector’’), (3) synthesizing a source signal using multiple realizations of the random parameter, and (4) estimating the source localization error by correlating the synthesized signal vector with the replica vector over a three dimensional space. This approach allows one to quantify deterministic localization error introduced by random model parameters, including sound velocity profile, hydrophone locations, and sediment thickness and speed. [Work supported by DARPA Advanced Technology Office.]

Robust maximum energy adaptive matched field processing

Adaptive array processing algorithms have achieved widespread use because they are very effective at rejecting unwanted signals (i.e. controlling sidelobe levels) and in general have very good resolution (i.e. have narrow mainlobes). However, many adaptive high-resolution array processing algorithms suffer a significant degradation in performance in the presence of environmental mismatch. This sensitivity to environmental mismatch is of particular concern in problems such as acoustic array processing in the ocean where the array processor's knowledge of the propagation characteristics of the ocean is usually imperfect. A maximum energy matched field processor is formulated which tunes the replica vector used by a minimum variance distortionless response (MVDR) matched field processor to adjust for fluctuations in the environment. The resulting processor has the same structure as the two-stage MVDR processor interpretation of the adaptive minmax matched field processor proposed previously. However, the criteria which the two processors use to tune replica vector differ. The result is that the MEMV processor achieves a level of performance superior to that of the adaptive minmax processor and close to that of traditional adaptive processors while limiting the sensitivity of the processor to environmental mismatch. An algorithm for implementing the professor is developed, and the performance of the processor is analyzed. >