A Robust and Regularized Algorithm for Recursive Total Least Squares Estimation

In this letter, a novel recursive total least squares (RTLS) algorithm that is grounded in a constrained Lagrange optimization of the errors-in-variables model is presented. The proposed RTLS method and its regularized counterpart are shown to be computationally efficient and produce robust estimates in the face of heavily unfavorable noise conditions, sub-optimal parametric initializations, and ill-conditioned input-output data. A Monte Carlo simulation study empirically demonstrates the improved stability and convergence properties of the proposed algorithms compared to the well-known recursive least squares algorithm, and a benchmark RTLS algorithm which is based on the minimization of the constrained generalized Rayleigh quotient. Furthermore, the applicability of the proposed method is validated with an experimental case study for online vehicle gear ratio estimation, highlighting its relevance in industrial settings.