Environmental Perturbation Constraints Research Articles

A waveguide invariant adaptive matched filter for active sonar target depth classification

This paper addresses depth discrimination of a water column target from bottom clutter discretes in wideband active sonar. To facilitate classification, the waveguide invariant property is used to derive multiple snapshots by uniformly sub-sampling the short-time Fourier transform (STFT) coefficients of a single ping of wideband active sonar data. The sub-sampled target snapshots are used to define a waveguide invariant spectral density matrix (WI-SDM), which allows the application of adaptive matched-filtering based approaches for target depth classification. Depth classification is achieved using a waveguide invariant minimum variance filter (WI-MVF) which matches the observed WI-SDM to depth-dependent signal replica vectors generated from a normal mode model. Robustness to environmental mismatch is achieved by adding environmental perturbation constraints (EPC) derived from signal covariance matrices averaged over the uncertain channel parameters. Simulation and real data results from the SCARAB98 and CLUTTER09 experiments in the Mediterranean Sea are presented to illustrate the approach. Receiver operating characteristics (ROC) for robust waveguide invariant depth classification approaches are presented which illustrate performance under uncertain environmental conditions.

Environmentally tolerant waveguide‐invariant target depth classification for active sonar.

Shallow‐water environments produce active sonar returns with many target‐like returns from bottom clutter. Scatterer depth classification methods which can discriminate bottom clutter from water column targets are thus critical for controlling false alarms. In recent work, the waveguide invariant (WI) property of shallow‐water channels has been used to obtain multiple snapshots of frequency‐domain target return data from a single active sonar ping. These snapshots are, in turn, used to estimate a waveguide invariant spectral density matrix (WI‐SDM), which can serve as a basis for depth classification. One method employing the WI‐SDM performs minimum variance filtering (MVF) matched to depth‐dependent signal replicas derived from a normal mode model. While MVF is capable of depth classification when the environment is known, it is sensitive to mismatch when the channel parameters are uncertain. In this paper, robustness of the WI MVF to mismatch is achieved by using environmental perturbation constraints derived from a WI‐SDM for the signal averaged over the uncertain channel parameters. Simulated and real data results are presented from the CLUTTER‐09 experiment in the Mediterranean Sea. [Work sponsored by ONR.]

Robust matched-field processor in the presence of geoacoustic inversion uncertainty

This presentation examines the performance of a matched-field processor incorporating geoacoustic inversion uncertainty. Uncertainty of geoacoustic parameters is described via a joint posterior probability distribution (PPD) of the estimated environmental parameters, which is found by formulating and solving the geoacoustic inversion problem in a Bayesian framework. The geoacoustic inversion uncertainty is mapped into uncertainty in the acoustic pressure field. The resulting acoustic field uncertainty is incorporated in the matched-field processor using the minimum variance beamformer with environmental perturbation constraints (MV-EPC). The constraints are estimated using the ensemble of acoustic pressure fields derived from the PPD of the estimated environmental parameters. Using a data set from the ASIAEX 2001 East China Sea experiment, tracking performance of the MV-EPC beamformer is compared with the Bartlett beamformer using the best-fit model.

Comparison of robust matched-field processing algorithms in a real, shallow water environment

In recent years, a number of matched-field processing (MFP) algorithms have been proposed to mitigate the ever-present problem of mismatch. This paper compares the source localization performance of six processors—Bartlett, Midpoint, Minimum Variance (MV) Distortionless Response, White Noise Constrained, MV with Neighboring Location Constraints, and MV with Environmental Perturbation Constraints—in a real, shallow water environment. MFP was performed on an 84.4-m aperture, 16-element subset of a MPL vertical line array deployed from the R/P FLIP west of Point Loma in approximately 200-m water. A continuous wave source, emitting ten tonals from 53–197 Hz, was towed over both range-independent and range-dependent tracks at source ranges of 1–7 km and at source depths of 60–130 m. First, MFP results utilizing a detailed geoacoustic model of the region, water column sound speed profiles measured during the experiment, and a priori knowledge of array tilt, demonstrate general processor characteristics. Second, MFP results which assume: (1) reasonable though further mismatched geoacoustic parameters; (2) water column sound speed profiles based upon historical data; and (3) no a priori knowledge of array tilt, illustrate processor performance under various mismatch conditions likely to be encountered in realistic applications.

Reduction in computational requirements with matched field processing

The sensitivity of matched field techniques to source location is a significant benefit from a localization accuracy perspective. Unfortunately, the implementation of matched field techniques in real-time systems is hampered by the computationally demanding hypothesis testing of source location in range and depth. Furthermore, operational requirements of such systems generally do not demand a high degree of accuracy. The Minimum Variance with Environmental Perturbation Constraints (MV-EPC) processor developed by Krolik [J. Acoust. Soc. Am. 92, 1408–1419 (1992)] has been used to reduce the sensitivity to environmental uncertainty. This same approach can be used to reduce the sensitivity to source location, thereby reducing the number of source location hypotheses. This produces a computational tractable approach to real-time, robust matched field processing. Illustrative simulations and real data results using SWellEX-96 data are presented.

Matched-field source tracking with SWELLEX-1 data

The optimal approach to tracking a moving source in an uncertain environment is one which incorporates a priori knowledge about both the continuity of the propagation environment and the nature of the source movement. The optimum uncertain field tracking algorithm (OUFTA) [S. L. Tantum and L. W. Nolte, ‘‘Tracking and localizing a moving source in an uncertain shallow water environment,’’ J. Acoust. Soc. Am. (submitted)] extends the optimum uncertain field processor (OUFP) [A. M. Richardson and L. W. Nolte, J. Acoust. Soc. Am. 89, 2280–2284 (1991)] to include modeling of the source motion as a Markov process. This differs from the suboptimal approach which performs a series of independent source localizations and then combines the results to estimate the path taken by the source. The performance of the OUFTA and the suboptimal approach is evaluated using the SWELLEX-1 data collected off the San Diego coast. Results using the SWELLEX-1 data are also presented which show how this optimal philosophy can be used to guide the modification of some popular beamformers, such as the minimum variance adaptive beamformer with environmental perturbation constraints (MV-EPC) [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1419 (1992)], to incorporate source motion. [Work supported by ONR.]

Robust wideband matched-field processing with a short vertical array

This paper addresses the problem of matched-field passive localization of broadband underwater acoustic sources with a short vertical array. In previous work, incoherent averaging of narrow-band Bartlett ambiguity surfaces has been proposed to improve the robustness of matched-field processing (MFP) to environmental uncertainties. While computationally efficient, the effectiveness of this approach is dependent on the type of environmental mismatch present. In this paper, to provide robust source localization performance for short arrays, an alternative wideband MFP method is proposed which utilizes the fourth-order statistics of the data. The method is “coherent” in that it exploits cross-frequency dependencies in the random acoustic channel response. The proposed coherent wideband minimum variance method with environmental perturbation constraints (MV-EPC) consists of minimizing the squared output power of a beamformer subject to constraints defined across the signal band. The constraints are designed to provide robustness over an ensemble of random environmental realizations. Monte Carlo simulation results using a canonical shallow-water scenario indicate that the coherent wideband MV-EPC method yields improved probability of correct localization performance versus incoherent averaging of narrow-band Bartlett ambiguity functions with a short array above a threshold signal-to-noise ratio.

The performance of matched-field beamformers with Mediterranean vertical array data

Minimum variance (MV) adaptive beamforming has been widely proposed for matched-field processing because it provides a means of suppressing ambiguous beampattern sidelobes. A difficulty with MV methods, however, is their sensitivity to signal wavefront mismatch. In this work, the performance of three robust MV methods and the Bartlett beamformer is evaluated using vertical array data from the Mediterranean Sea collected by the NATO SACLANT Centre. The three MV methods considered are: (1) the reduced MV beamformer (RMV), (2) the MV beamformer with neighborhood location constraints (MV-NLC), (3) the MV beamformer with environmental perturbation constraints (MV-EPC). While the Bartlett, RMV, and MV-NLC methods assume the ocean environment is known precisely, the MV-EPC method models the environment as being random with known statistics. Experimental and companion simulation results indicate that for modest environmental uncertainty, the MV-EPC beamformer achieves a higher probability of correct localization and better sidelobe performance than the other three methods.

Minimum variance matched‐field source localization with SACLANT Mediterranean sea trial data

The minimum variance (MV) adaptive beamformer has been widely proposed for matched‐field processing because it provides a means of suppressing ambiguous beampattern ‘‘sidelobes.’’ In this paper, the performance of three robust MV methods is evaluated using vertical array data from the Mediterranean Sea collected by the NATO SACLANT Centre north of Elba [D. F. Gingras and P. Gerstoft, 3234 (1994)]. The three MV methods considered are (1) the reduced MV method (RMV) [C. L. Byrne et al., 2493–2502 (1990)], (2) the MV method with neighborhood location constraints (MV‐NLC) [H. Schmidt et al., 1851–62 (1990)], and (3) the MV method with environmental perturbation constraints (MV‐EPC) [J. Krolik, 1408–19 (1992)]. Real data results indicate that each approach has different merits. Projecting the data onto the reduced space defined by the modal eigenfunctions as in the RMV is necessary to avoid instabilities caused by highly correlated noise. Using neighboring location constraints as in the MV‐NLC reduces the need to finely sample the ambiguity surface. And using constraints derived from the second‐order statistics of the signal wavefront averaged over an ensemble of perturbed environmental parameters as in the MV‐EPC increases robustness to environmental mismatch. [Work supported by ONR.]

COMPUTATIONALLY EFFICIENT MONTE CARLO ESTIMATION ALGORITHMS FOR MATCHED FIELD PROCESSING IN UNCERTAIN OCEAN ENVIRONMENTS

In this paper, Monte Carlo estimation techniques are presented for computationally efficient implementation of two methods for matched field source localization in uncertain ocean channels. In the Optimal Uncertain Field Processor (OUFP), Monte Carlo integration is used to integrate out the environmental parameters and thus estimate the a posteriori distribution of the source location parameters. In the Minimum Variance Beamformer with Environmental Perturbation Constraints (MV-EPC), Monte Carlo estimation of the signal correlation matrix averaged over the ensemble of environmental realizations is used to estimate the beamformer constraints. Using the OUFP, detection performance bounds are evaluated which indicate that source position uncertainty affects performance much more than environmental uncertainty. An upper bound on source localization performance is also obtained indicating that for short observation times a threshold signal-to-noise ratio (SNR) exists, dependent upon environmental uncertainty, below which source localization performance rapidly degrades. Among robust minimum variance beamforming methods, the MV-EPC method demonstrated superior probability of correct localization (PCL), both in single source scenarios and in the presence of interference. The OUFP at high SNR and the MV-EPC at large observation times both achieved near perfect source localization performance, although for large environmental uncertainty the OUFP provides an upper bound on P CL .

Environmental data assimilation in matched-field processing with a random normal mode model

Numerical acoustic propagation models used in matched-field processing typically assume that ocean environmental parameters, such as the range-dependent sound-speed profile, are either known exactly or are characterized by stationary prior statistics. However, neither of these modeling approaches is well suited for accurately assimilating measurements of the correct ocean realization into the calculation of point-source acoustic wave front statistics. In this paper, environmental data is assimilated into a random adiabatic normal mode propagation model by calculating the conditional correlation matrix of an acoustic wave front given a set of contemporaneous sound-speed profile measurements made at different points in space. First-order perturbation theory is used to map the conditional statistics of Gaussian-distributed excess sound-speed variations into an estimate of the conditional point-source wave front correlation matrix. Minimum variance beamforming with environmental perturbation constraints [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1419 (1992)] conditioned on current environmental measurements is demonstrated as a means of exploiting this random wave front model to achieve improved matched-field source localization performance. [Work supported by ONR.]

Matched-field processing in a shallow-water channel with a random bottom

An important source of uncertainty in shallow-water propagation models used for minimum variance (MV) matched-field processing is bottom roughness or irregular bathymetry. A perturbative solution to the Helmholtz equation which gives the point source field in a shallow-water waveguide with rough boundaries has been derived in [W. Kuperman and H. Schmidt, J. Acoust. Soc. Am. 86, 1511–1522 (1989)]. This formulation yields an expression for the point-source wave front correlation matrix which is determined by the coherent field and a scattered field generated by random secondary sources at the bottom interface. Alternatively, adiabatic normal modes and first-order perturbation of the horizontal modal wave numbers also provides a solution for the wave front correlation matrix in terms of the second-order statistics of the random bottom depth. In this paper, matched-field source localization performance under both these models is evaluated for several MV beamforming approaches. Minimum variance beamforming with environmental perturbation constraints [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1418 (1992)] is demonstrated to be an approach which can exploit these random propagation models to achieve robust matched-field source localization. [Work supported by ONR.]