This paper presents the derivation and evaluation of an asymptotically unbiased statistical estimator for the parameters in the vector difference equation canonical description of a linear multi variable system disturbed by correlated plant and measurement noise processes having rational spectral densities. The sequential estimation algorithm utilizes instrumental variables generated by a recursive filter incorporating the current parameter estimate in a novel manner. A spectral factorization technique for the identification of the noise process is discussed. Numerical results comparing the estimation algorithm with other methods are reported for scalar-output and multivariable-output cases.