Efficient time recursive coherence spectrum estimation

The coherence spectrum is of notable interest as a bivariate spectral measure in a variety of application, and the topic has lately attracted notable interest with the recent formulation of several high-resolution data adaptive estimators. In this work, we present computationally efficient time recursive implementations of the recent iterative adaptive approach (IAA) estimator, examining both the case of complete data sets and when some observations are missing. The algorithms continues the recent development of exploiting the estimators' inherently low displacement rank of the necessary products of Toeplitz-like matrices, extending these to time-updating formulations for the IAA-based coherence estimation algorithm. Numerical simulations together with theoretical complexity measures illustrate the performance of the proposed algorithm.