Rational parametric coherence estimation via convolved correlations

In this paper, the magnitude squared (MS) coherence is computed by estimating the parameters of a rational model. The parameters are constrained so that the estimated MS coherence is real-valued on the unit circle. The method entails first estimating the auto- and cross-correlation lags from raw data sequences. These lag estimates are then used to define two auxiliary sequences, the convolution of the cross-correlation function with itself and the convolution of the two autocorrelation functions. The MS coherence parameters will nearly satisfy a homogeneous set of equations involving these auxiliary sequences. This system of linear equations is solved via an eigenspace decomposition. The algorithm is compared with two traditional periodogram based estimation methods.