An optimized NLMS algorithm for system identification

•An optimized normalized least-mean-square (NLMS) algorithm is developed for system identification, in the context of a state variable model.•The proposed algorithm is based on a joint-optimization on both the normalized step-size and regularization parameters, in order to minimize the system misalignment.•The performance of the proposed joint-optimized NLMS (JO-NLMS) algorithm is evaluated in the framework of acoustic echo cancellation.•The JO-NLMS algorithm achieves both fast convergence and tracking, but also low misadjustment.

The normalized least-mean-square (NLMS) adaptive filter is widely used in system identification. In this paper, we develop an optimized NLMS algorithm, in the context of a state variable model. The proposed algorithm follows a joint-optimization problem on both the normalized step-size and regularization parameters, in order to minimize the system misalignment. Consequently, it achieves a proper compromise between the performance criteria, i.e., fast convergence/tracking and low misadjustment. Simulations performed in the context of acoustic echo cancellation indicate the good features of the proposed algorithm.