Abstract
The Cramer–Rao lower bound (CRLB) gives the smallest possible variance of any unbiased estimator. Buck, Preisig, and Wage [J. Acoust. Soc. Am. 103 (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. First, the minimax optimization criteria and the gradient descent method are applied to find optimal arrays over a range of possible deployment environments. In several simple prototype problems, it is possible to design nonuniform arrays whose worst case CRLB is significantly lower than a uniformly spaced array. This contradicts conventional wisdom that uniformly spaced arrays provide the most flexibility for multiple or extended deployments. Moreover, the gradient descent method is more computationally efficient than exhaustive search methods of optimizing arrays. Second, the sensitivity of the optimal array’s performance to environmental mismatch is studied and the perturbation of this performance is analytically bounded. This bound works well in the preliminary results and predicts the deterioration of mode filter performance due to mismatch. [Work supported by ONR Young Investigator Program.]