A stable data adaptive method for matched-field array processing in acoustic waveguides

Abstract

The presence of a “modal noise” component leads to estimator instability when Capon's maximum likelihood (ML) method is applied to the processing of data from a vertical array in an acoustic waveguide. The physics of the waveguide forces signal vectors and noise vectors alike to be projected onto the span of the “mode” vectors, when the number of sensors (N) exceeds the number of propagating modes (M). The instability occurs whenever the (single snapshot) N × 1 data vectors have the form x = Us + Uγ + white noise, where the matrix U is N × M (sampling the normal modes at the hydrophone locations and independent of the actual acoustic disturbances present), and s and γ correspond to signal and ambient noise sources, respectively. This condition arises in normal-mode and local normal-mode propagation. The dominant eigenvectors of R−1 (where R is the cross-spectral matrix) are sensitive to slight inaccuracies in the calculation of R−1 in ways that affect the performance of the ML estimator. Following transformation of the N × N matrix R to the M × M modal space cross-spectral matrix T, Capon's method is applied to T to obtain the “reduced maximum likelihood” (RML) estimator. This procedure, which is a development of the sector focused stability technique of Steele and Byrne [Proceed. ISSPA 87, 24–28 August 1987, Brisbane, Australia, pp. 408–412], largely eliminates instabilities due to inaccurate inversion of R. Simulations are presented for a shallow-water environment to provide comparison between the ML and the RML estimators. These indicate that the degree of instability depends upon the level of noise (both correlated noise and white noise) and that a significant improvement in performance can be expected by use of the RML estimator in both cases.

Matched Field Processing in Ocean Acoustics

“…Uoth approaches are often used; in particular, Ozard introduces a "reduced minimum variance beamformer (RMVB) [75] and Byrne discusses it in terms of modal decompositions. [15] 4.5. "Power law" MFP's One can generalize upon the SVD approaches for MVDF in an MFP.…”

“…3. The field has covariance K which has uncorrelated signal and noise components with covariances K. and Kn with K= Ks+Kn (15) While we assume in much of our discussion that these covariance are known, generally, these covariances must be estimated from the data or predicted using some propagation model.…”

Matched field source detection and localization in high noise environments: A novel reduced-rank signal processing approach

“…Byrne et. ale applied Capon's maximum likelihood method (MLM) to estimate the range and depth of an acoustic source [24]. The MLM offers the capability to adapt to the actual noise rather than requiring an a priori estimate for prewhitening.…”

“…Lastly, we recommend further investigation in the GLRT maxima analysis area. We derive the three dimensional reduced wave equation for the cylindrically symmetric case given by equation (8) of reference [24]. This derivation is the mathematical basis for the PIE Solver algorithm used in this investigation.…”

Parallel Algorithms for Adaptive Matched-Field Processing in Distributed Array Systems

“…5 The adaptive MFP algorithms, which combine the MVDR technique with the MFP algorithm, were extensively used to improve the performance and robustness of beamforming by employing environmental perturbation constraints and dimension reduction on simulated and field data. [6][7][8][9][10] The MVDR-MFP algorithm is used as our baseline for adaptive MFP algorithms.…”