A Variable Step-Size Regularization-Based Quasi-Newton Adaptive Filter for System Identification

The family of least mean square (LMS) based adaptive filtering algorithms suffers from convergence performance limitation due to the sensitivity of such algorithms to the eigenvalue spread of the input correlation matrix. The quasi-Newton family of adaptive filtering algorithms addresses this limitation, but its performance is restricted by the estimation accuracy of the correlation matrix inverse, especially for highly correlated input signals. Furthermore, the convergence rate and the steady-state performance of both LMS and quasi-Newton families are thoroughly depending on their step-sizes. In this paper, a variable step-size regularized quasi-Newton adaptive algorithm is proposed in the context of system identification. In this algorithm, inspired by the matrix inversion lemma, a modified regularized matrix inverse with a time-varying regularization is computed such that during the convergence, the contribution of matrix inverse in the weight update is reduced, resulting in a more noise-robust algorithm. The paper further provides a convergence analysis of the proposed quasi-Newton algorithm, wherein a variable step-size is proposed to achieve a high initial convergence rate and a low steady-state error in the context of system identification applications.