When the input signals for acoustic echo cancellation (AEC) are related signals, the convergence speed of the traditional normalized least mean square (NLMS) algorithms is significantly reduced. In this paper, a joint optimization robust AEC algorithm is proposed to solve this problem. Based on the analysis of the convergence of the normalized subband adaptive filtering (NSAF) algorithm, the algorithm is optimized by minimizing the mean square error (MSE) of the NSAF algorithm, combining sub-band time-varying step factor and time-varying regularization parameter to update the filter weight vectors. And when the impulse noise occurs, the sub-band cut-off parameter is updated in a recursive manner, which makes the algorithm achieve fast convergence speed and low steady-state error, and has strong robustness to impulse noise. In a series of experiments on AEC, simulation results show that the performance of the algorithm is better than the existing algorithms.
