Identification Algorithms for Linear Systems with Correlated Input and Output Noise

We consider the estimation of the parameters of the frequency characteristics of a multidimensional linear systems from observations of input and output signals, corrupted by stationary correlated noise. Estimation algorithms are proposed which, in a wide class of non-Gaussian noise, produce asymptotically normal $\sqrt{N}$-consistent estimators, where $N$ is the number of observations. The optimal form of these algorithms is determined, ensuring the lowest asymptotic covariance of the estimators. For the particular case when noise corrupts only the outputs of a multidimensional linear system and the noise spectral matrix is singular, we propose an algorithm which produces $N^{1/2+\nu}$-consistent estimators, where $0<n\leq 1/2$.