The well-known adaptive algorithm called least-mean square (LMS) is a simple and efficient approach to active noise cancellation application problems. However, in the presence of non-Gaussian noises or non-linear environments, the standard LMS commonly cannot reach satisfactory performance. Therefore, a wide range of robust adaptive processing techniques have been investigated in the last few decades. This thesis proposes a robust adaptive filtering approach for noise cancellation. In particular, the model uses the classical filtered-X framework with the developed method in this research, it is based on hyperbolic tangent exponential generalized Kernel M-estimator function (HEKM), which achieves optimal performance in terms of Average Noise Reduction (ANR). The results demonstrate the cost-effectiveness of the proposed algorithm in suppressing spurious noises in different input systems.