Unbiased RLS identification of errors-in-variables models in the presence of correlated noise

We propose an unbiased recursive-least-squares(RLS)-type algorithm for errors-in-variables system identification when the input noise is colored and correlated with the output noise. To derive the proposed algorithm, which we call unbiased RLS (URLS), we formulate an exponentially-weighted least-squares problem that yields an unbiased estimate. Then, we solve the associated normal equations utilizing the dichotomous coordinate-descent iterations. Simulation results show that the estimation performance of the proposed URLS algorithm is similar to that of a previously proposed bias-compensated RLS (BCRLS) algorithm. However, the URLS algorithm has appreciably lower computational complexity as well as improved numerical stability compared with the BCRLS algorithm.