Direct coherence estimation via a constrained least-squares linear-predictive fast algorithm

Estimation of multi-channel auto-spectra, cross-spectra, and coherences via linear-predictive techniques suffers from cross-feed between the limited number of data points available of each channel process. Here, the coherence between two channels is estimated directly, without diversion from auto-spectra estimation, so as to minimize only the valid computable linear-predictive errors that can be formed from given finite data records. Furthermore, the least-squares minimization procedure is constrained so as to yield physically-consistent magnitude-squared coherence estimates, and can be accomplished by a fast algorithm in a recursive fashion. The resulting nonlinear programming problem that is encountered is solvable via a recursion employing the Hessian of an unconstrained error measure. Examples of application of the technique to short data records yields good coherence estimates.