System identification from noisy measurements by using instrumental variables and subspace fitting

This paper considers the estimation of the parameters of a linear discrete-time system from noisy input and output measurements. The conditions imposed on the system are quite general. The proposed method makes use of an instrumental variable (IV) vector whose cross-covariance with the system´s regression vector is pre- and post-multiplied by some prechosen weights. The singular vectors of this matrix possess complete information on the system parameters. A weighted sub-space fitting (WSF) method is then applied to these singular vectors to consistently estimate the parameters of the system. The proposed method is non-iterative, easy to implement and has a small computational burden. The asymptotic distribution of its estimation errors is derived and the result is used to motivate the choice of the weighting matrix in the WSF step and also to predict the estimation accuracy. A numerical example is included to illustrate the performance