Adaptive spectrum estimation in one and two dimensions

A general adaptive method with linear constraints is developed for application to the multidimensional spectrum estimation problem. The proposed method is formulated in a frequency-variational-approach framework, where a function of a discretized spectrum is to be optimized, subject to a set of linear constraints. This set of constraints can be defined by a nonregular domain. The objective function to be optimized can be any function of the spectra, only assuming that a suboptimum solution will be achieved if it has more than one extreme point. The estimation obtained in each iteration fits the set of constraints even if this set is adapted during the procedure. The algorithms presented can be used in one- or two-dimensional environments