Adaptive estimation of acoustic normal modes

Abstract

Normal mode theory provides an efficient description of signals which propagate axially in the SOFAR channel and are detectable at long ranges. Mode amplitudes and their second order statistics are useful in studies of long-range acoustic propagation and for applications such as Matched Mode Processing (MMP) and Matched Field Tomography (MFT). The purpose of this research is to investigate techniques for estimating the average power in the modes of a signal given pressure measurements from a vertical line array. This thesis develops the problem of mode estimation within a general array processing framework which includes both deterministic and stochastic characterizations of the modal structure. A review of conventional modal beamforming indicates that these methods provide poor resolution in low signal-to-noise ratio environments. This is not surprising since standard estimation techniques rely on minimizing a squared error criterion without regard to the ambient noise. The primary contribution of this thesis is an adaptive estimator for coherent modes that is based on a method suggested by Ferrara and Parks for array processing using diversely-polarized antennas. Two formulations of the adaptive method are investigated using a combination of analytical techniques and numerical simulations. The performance evaluation considers the following issues: (i) power level of the noise, (ii) orthogonality of the sampled modeshapes, (iii) number of data snapshots, and (iv) coherence of the signal. The new approach is fundamentally different from other modal estimators such as those used in MMP because it is data-adaptive and maximizes the received power instead of minimizing the squared error. As a result, the new methods perform significantly better than least squares in high noise environments. Specifically, the Ferrara/Parks formulations are able to maintain nulls in the modal spectrum since they do not suffer the bias error that significantly affects the least squares processor. A second contribution of the thesis is an extension of the coherent estimator to facilitate estimation of phase-randomized modes. Although the results of this work are preliminary, the extended formulation appears to offer several advantages over least squares in certain cases.