Recursive Generalized Total Least Squares with Noise Covariance Estimation

We propose a recursive generalized total least-squares (RGTLS) estimator that is used in parallel with a noise covariance estimator (NCE) to solve the errors-in-variables problem for multi-input-single-output linear systems with unknown noise covariance matrix. Simulation experiments show that the suggested RGTLS with NCE procedure outperforms the common recursive least squares (RLS) and recursive total instrumental variables (RTIV) estimators when all measured inputs and the measured output are noisy. Moreover, when all measured inputs are noise-free, RGTLS with NCE performs similarly to RLS, which in this special case is the optimal estimator, and again RTIV was inferior compared with the RGTLS and NCE procedure.