Fast error whitening algorithms for system identification and control

Linear system identification with noisy inputs 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 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. In this paper, we present a fixed-point type algorithm with O(N²) complexity for EWC, called the recursive error whitening (REW) algorithm. We would also show that the EWC solution could be solved using the computational principles of total least squares (TLS). A novel EWC-TLS algorithm with O(N²) complexity is derived. We will then apply the EWC methods for adaptive inverse control and show the superiority over existing methods.