Unbiased identification of stochastic linear systems from noisy input and output measurements

This paper is concerned with identification of stochastic linear systems from noisy input and output measurements. A modified scheme that employs extra delayed noisy measurements is derived to estimate the variances of white input and output noises. These estimated noise variances are then applied for removal of the bias from a least-squares parameter estimate via an iterative procedure to achieve estimation consistency. The new identification algorithm incorporated with this modified estimation scheme for the noise variances demonstrates greatly improved performances. Compared with the previously developed method, the new identification algorithm can converge at a much faster rate and produce much more accurate parameter estimates at only a slightly increased numerical cost. The theoretical predictions are confirmed through Monte-Carlo stochastic simulation studies