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.