Optimal spatial filtering for design of a conformal velocity sonar array

In stark contrast to the ubiquitous optimization problem posed in the array processing literature, tactical hull sonar arrays have traditionally been designed using extrapolations of low spatial resolution empirical self noise data, dominated by hull noise at moderate speeds, in conjunction with assumptions regarding achievable conventional beamformer sidelobe levels by so-called Taylor shading for a time domain, delay-and-sum beamformer. That ad hoc process defaults to an extremely conservative (expensive and heavy) design for an array baffle as a means to assure environmental noise limited sonar performance. As an alternative, this dissertation formulates, implements, and demonstrates an objective function that results from the expression of the log likelihood ratio of the optimal Bayesian detector as a comparison to a threshold. Its purpose is to maximize the deflection coefficient of a square-law energy detector over an arbitrarily specified frequency band by appropriate selection of array shading weights for the generalized conformal velocity sonar array under the assumption that it will employ the traditional time domain delay-and-sum beamformer. The restrictive assumptions that must be met in order to appropriately use the deflection coefficient as a performance metric are carefully delineated.; A series of conformal velocity sonar array spatial filter optimization problems was defined using a data set characterized by spatially complex structural noise from a large aperture conformal velocity sonar array experiment. The detection performance of an 80-element cylindrical array was optimized over a reasonably broad range of frequencies (from k₀a = 12.95 to k ₀a = 15.56) for the cases of broadside and off-broadside signal incidence. In each case, performance of the array using optimal real-valued time domain delay-and-sum beamformer weights was much better than that achieved for either uniform shading or for Taylor shading. The result is an analytical engine with which to consider not only the tradeoff between optimality and robustness in the definition of array baffle design requirements, but numerous other tradeoffs within the array design error budget allocation process as well.