IEEE Workshop on Underwater Acoustic Signal Processing, Fall 2001
Title: Optimal Array Design and Sensitivity for Mode Filtering
Authors: Tsung-Jieh Shiao, John R. Buck

The pressure field in a shallow water acoustic channel is often well characterized by a  finite, discrete set of propagating normal modes. Mode filtering is defined as the estimation of the amplitudes of these normal modes from the observed pressure samples obtained at a vertical hydrophone array. Many researchers have proposed the use of mode amplitudes, or coefficients, for underwater source localization or remote sensing of oceanographic features. The success of any of these techniques relies on accurate estimates of the mode amplitudes.

The Cramer-Rao Lower Bound (CRLB) gives the smallest possible variance of any unbiased estimator. Buck, Preisig, and Wage [JASA 103(4) (1998)] derived this bound for the variance of unbiased mode filters and observed that the array geometry  is the only factor controlling performance under scientists' control. The difficulty lies in designing an appropriate array for variable ocean environments. This research includes two parts.

Robust array design for a range of environments is a difficult problem. Therefore, our initial efforts examine the problem of designing the optimal array for a known environment. Specially the optimal array is optimized to minimize the total error power of the mode estimates. Two search methods are applied to find the optimal array: exhaustive search method and steepest descent method. In several simple prototype problems, it is possible to design nonuniform arrays whose total error power is significantly lower than an uniformly spaced array. Moreover, the steepest descent method is more computationally efficient than the exhaustive search method of optimizing arrays.

Second, the sensitivity of the optimal array's performance to environmental mismatch is studied since ocean is well-known to be capricious. Two common causes of mismatch for mode filtering in the shallow water environment are tidal water depth changes and sensor location errors. The perturbation of the optimal array's performance can be analytically bounded and thus the deterioration of mode filter performance due to mismatch can be predicted.

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