Unbiased Recursive Least-Squares Estimation Utilizing Dichotomous Coordinate-Descent Iterations

We propose an unbiased recursive least-squares algorithm for errors-in-variables system identification. The proposed algorithm, called URLS, removes the noise-induced bias when both input and output are contaminated with noise and the input noise is colored and correlated with the output noise. To develop the algorithm, we define an exponentially-weighted least-squares optimization problem that yields an unbiased estimate. Then, we solve the system of linear equations of the associated normal equations utilizing the dichotomous coordinate-descent iterations. The URLS algorithm features significantly reduced computational complexity as well as improved numerical stability compared with a previously proposed bias-compensated recursive least-squares algorithm while having similar estimation performance. We show that the URLS algorithm is asymptotically unbiased and convergent in the mean-square sense. We also calculate its steady-state mean-square deviation. Simulation results corroborate the efficacy of the URLS algorithm and the accuracy of the theoretical findings.