Estimating and Time-Updating the 2-D Coherence Function

In this correspondence, we extend the recently introduced one-dimensional Capon-based Magnitude Square Coherence (MSC) spectral estimator, to form two-dimensional Capon- and Amplitude and Phase EStimation (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