Stochastic error whitening algorithm for linear filter estimation with noisy data

Mean squared 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 stochastic gradient algorithm based on the recently proposed error whitening criterion (EWC) to tackle the problem of linear filter estimation in the presence of additive white disturbances. We will briefly motivate the theory behind the new criterion and derive an online stochastic gradient algorithm. Convergence proof of the stochastic gradient algorithm is derived making mild assumptions. Further, we will propose some extensions to the stochastic gradient algorithm to ensure faster, step-size independent convergence. We will perform extensive simulations and compare the results with MSE as well as total-least squares in a parameter estimation problem. The stochastic EWC algorithm has many potential applications. We will use this in designing robust inverse controllers with noisy data.