When the singularity expansion method is applied to measured data, the accuracy of the results is often severely limited by the noise and clutter present in the measurement. An effective method of reducing these contaminations is repeating and averaging the measurements. The effectiveness of this approach is related to the number of measurements which are combined. The present paper develops a method which expands the set of measurements which may be combined from the set of identical measurements to the set of all measurements made on the target. The measurements are combined using an optimal weighting scheme to provide a superior estimate for a specified pole. An algorithm is described which increases the accuracy of the estimated pole locations and accurately computes the residues associated with these new pole locations. The algorithm is used to extract a single pole and residue, and additional poles and residues may be obtained through iterative application of the algorithm.