Reducing instability through dimensionality reduction, with application to matched-field processing

Abstract

High-resolution estimators of source parameters, such as Capon’s maximum-likelihood (ML) method, become unstable in the presence of nonwhite ambient noise and can degrade rapidly when the data includes perturbations due to model mismatch, finite averaging, system phase errors and the like. To combat the instability, some have suggested the use of multiple mainlobe constraints or derivative constraints (Vural, Steele). Stability through beamspace processing was proposed by Gray and was suggested as a way of avoiding nonwhite noise by Bienvenu and Kopp; dimensionality reduction (DR) is an extension of this idea. In matched-field processing (MFP), DR can be introduced through mode-space processing (Yang) or through ‘‘reduced ML’’ (Byrne). When the number of propagating modes approximates the number of phones more dramatic improvement over ML can be achieved through ‘‘sector-focusing’’ (SF) (Byrne and Steele). The basic idea of SF is to project the data vectors onto a subspace of lower dimension. Application of SF to MFP is considered by Frichter etal. [J. Acoust. Soc. Am. 88, 2843–2851 (1990)].