A Regularized RLS Algorithm for the Identification of Third-Order Tensors

The recently proposed recursive least-squares (RLS) algorithm for trilinear forms, namely RLS-TF, was designed for the identification of third-order tensors of rank one. In this context, a high-dimension system identification problem can be efficiently addressed (gaining in terms of both performance and complexity) based on tensor decompositions and modelling. In this paper, following the framework of the RLS-TF, we propose a regularized version of this algorithm, where the regularization terms are incorporated within the cost functions. Furthermore, the optimal regularization parameters are derived, aiming at attenuating the effects of the system noise. Simulation results support the performance features of the proposed algorithm, especially in terms of its robustness in noisy environments.