Variable regularized least-squares algorithm: One-step-ahead cost function with equivalent optimality

This paper proposes a new variable regularized least-squares (VR-LS) algorithm by recursively constructing a weighting scalar of the regularized least-squares (LS) cost function. Since the recursive LS (RLS) algorithm provides the best performances by all of VR-LS algorithms, the design objective of the weighting scalar is chosen such that equivalent optimality is ensured between one-step-ahead cost functions of the RLS and of the VR-LS algorithm. The proposed VR-LS algorithm functions similarly as the RLS with uncorrelated inputs; however, this is not the case with colored (correlated) inputs. Therefore, a conventional filtering technique is applied to both on the inputs and on the desired signals so as to obtain whitened inputs. This enables the proposed algorithm handle the case of correlated inputs.