Error whitening criterion for linear filter estimation

Mean square error (MSE) has been the most widely used tool to solve the linear filter estimation or system identification problem. However, MSE gives biased results when the input signals are noisy. This paper presents a novel error whitening criterion (EWC) to tackle the problem of linear system identification in the presence of additive white disturbances. We would motivate the theory behind the new criterion and derive an online stochastic gradient algorithm based on EWC. Convergence proof of the stochastic gradient algorithm is derived making mild assumptions. Simulation results show the effectiveness of this criterion. We compare its performance with MSE as well as the powerful total least squares method.