A novel gradient adaptive step size LMS algorithm with dual adaptive filters

Least mean square (LMS) adaptive filter has been used to extract life signals from serious ambient noises and interferences in biomedical applications. However, a LMS adaptive filter with a fixed step size always suffers from slow convergence rate or large signal distortion due to the diversity of the application environments. An ideal adaptive filtering system should be able to adapt different environments and obtain the useful signals with low distortion. Adaptive filter with gradient adaptive step size is therefore more desirable in order to meet the demands of adaptation and convergence rate, which adjusts the step-size parameter automatically by using gradient descent technique. In this paper, a novel gradient adaptive step size LMS adaptive filter is presented. The proposed algorithm utilizes two adaptive filters to estimate gradients accurately, thus achieves good adaptation and performance. Though it uses two LMS adaptive filters, it has a low computational complexity. An active noise cancellation (ANC) system with two applications for extracting heartbeat and lung sound signals from noises is used to simulate the performance of the proposed algorithm.