A method for computing the information matrix of stationary Gaussian processes

This paper proposes a new method for the efficient computation of the Fisher information matrix of zero-mean complex stationary Gaussian processes. Its complexity (measured by the number of floating point operations) is smaller than the fastest previously available procedure. The key idea exploited is that the Fisher information matrix depends only on the sum of the diagonals of the inverse covariance matrix derivative (with respect to the model parameters), rather than on the whole matrix. To obtain the referred sum, a new efficient technique, built upon the Trench algorithm for computing the inverse of a Toeplitz matrix, is presented.