A Modified Multidimensional Quaternion-valued Process Founded on FXLMS Algorithm for Active Noise Control

Filtered-x least mean square (FXLMS) algorithm is the classic and most frequently adopted method in active noise control (ANC) systems. The least mean square (LMS) was expanded to the complex field as the kernel of adaptive filter system design. Along with the quaternion field behalf of an extension of the complex domain against this background, the paper puts forward a FXLMS algorithm built on quaternion (FXQLMS) with a simple structure suitable for the active noise control system. The experimental results confirm that the proposed FXQLMS algorithm can realize better convergence property over the other two algorithms in the narrowband noise environments.