Accelerating recursive least squares adaptation/learning algorithms using a dynamic adaptation gain

The concept of “dynamic adaptation gain/learning rate” has been introduced in Landau et al. (2023) in order to accelerate the adaptation/learning transients in the context of adaptation/learning algorithms using constant scalar adaptation gain/learning rate. The present paper shows that inserting a ”dynamic adaptation gain/learning rate” into adaptation/learning algorithms with time varying matrix adaptation gain/learning rate belonging to the family of recursive least squares algorithms leads also to a significant acceleration of the adaptation/ learning transients. The proposed algorithms are analyzed in a deterministic and stochastic environment. This allows to emphasize the potential of these algorithms compared with the classical recursive least squares type algorithms. Comparative simulations and experimental results (an active noise control system) further illustrate the performance of these algorithms.