Estimating the Two-Dimensional Coherence Function

In this paper, we extend the one-dimensional Capon-based magnitude square coherence (MSC) spectral estimator, to form two-dimensional Capon- and APES-based MSC spectral estimators. The resulting estimators are found to yield significantly improved estimates as compared to the typical Welch-based estimator. Furthermore, we introduce a computationally efficient time-updating of the presented MSC estimators, exploiting their inherent time-varying displacement structure. The presented updating is found to dramatically lower the computational requirement of reevaluating the MSC spectral estimates.