In this correspondence, we extend the recently introduced onedimensional 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

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... varying displacement structure. The presented updating is found to dramatically lower the computational requirement of reevaluating the MSC spectral estimates. Index Terms-Coherence spectrum, computational complexity, iterative methods, spectrum analysis, time varying systems.