Fast error whitening algorithms for system identification and control with noisy data

Linear system identification with noisy input/output is a critical problem in signal processing and control. Conventional techniques based on the mean squared-error (MSE) criterion can at best provide a biased parameter estimate of the unknown system being modeled. Recently, we proposed a new criterion called the error whitening criterion (EWC) to solve the problem of linear parameter estimation in the presence of additive white noise. Accordingly, the central idea is to partially whiten the error signal beyond a predetermined correlation lag. In the first-half of the paper, we will derive a fast Quasi-Newton type recursive algorithm to compute the optimal EWC solution in an online manner. The algorithm has O(N2) complexity where, N represents the length of the parameter vector to be estimated. One of the primary limitations of EWC is the assumption that the input noise must be white. In the second-half of this paper, we will introduce a modified cost function that overcomes this assumption and allows the noise in the input to be colored. The analysis of this modified cost function is then presented followed by a sample-by-sample stochastic gradient algorithm to optimally compute the analytical solution. Finally, we will show the experimental results with EWC as well as the modified criterion in system identification and controller design problems.