Constrained Adaptive Filtering Algorithms Based on Arctangent Framework Against Impulsive Noise

In practice, impulsive noise may significantly degrade the filtering performance of constrained adaptive filtering (CAF) algorithms derived from the second-order signal statistics. In this paper, two robust constrained arctangent least mean square (CATLMS) algorithms are proposed to overcome this problem, inspired by the boundedness of the arctangent function against outliers. First, a CATLMS algorithm is derived using the gradient descent method. To accelerate the convergence rate in the case of correlated input signals and improve steady-state performance, a recursive CATLMS (RCATLMS) algorithm is further proposed based on the matrix inversion lemma. The computational complexity of our proposed algorithm is comparable to that of other existing robust algorithms. Simulation results demonstrate the effectiveness of our proposed algorithms against impulsive noise environments and the superior filtering performance compared to other CAF algorithms. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.