Current high-resolution wavenumber processors are either applicable only to linear equi-spaced arrays or require a manifold search over the ideal array response. As a result of this they exhibit a loss of resolution, bias and increased variance in bearing estimates when the receiving array is subjected to spatial sampling errors. This thesis has addressed the nature of these problems and proposed signal processing algorithms which are robust to the spatial sampling errors. A review of current super-resolution methods is included, explaining why each exhibits a performance degradation. An eigen decomposition of the array cross-spectral matrix is shown to retain information about the spatial sampling process which can be then made available after suitable processing. The required procedure involves rotating all the principal eigenvectors in the signal subspace until they have elements of equal magnitude. Gradient search techniques are derived which can be applied to solve the resulting non-linear equations. A novel matrix notation is introduced which allows the non-linear equations to be written more concisely, this in turn leads to their solution by constrained Lagrangian optimization and several new algorithms are proposed. The minimization equations are then reformulated as a maximization which enables all the eigenvectors to be rotated simultaneously, as opposed to' pairwisc or individually in the minimization case. These formulae are generalized to allow rotating vectors without pre-calculation of the signal subspace but using the cross-spectral and data matrices directly. Extensive simulations have been performed comparing the new methods with similar previous work, MUSIC and the Cramer-Rao lower bound. Air acoustic experiments on a 16 element array have also been performed to verify the practical implementation and evaluate the algorithms performance with a deformed line array using real data.