Set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order

Nowadays, the use of adaptive filters plays an important role in multiple signal processing applications, such as active noise control, acoustic echo cancellers, system identifiers, channel equalizer, among others. Until date, many of the existing adaptive algorithms such as affine projection algorithms offer a high convergence speed. However, its computational cost is also high. Currently, several authors make extraordinary efforts to reduce its computational cost to be used in practical applications. In this paper, we propose a new set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order (SMAP-PC-VO). Specifically, we propose two techniques to create this algorithm; 1) the new algorithm uses an error bound, which is obtained by calcuting the percentage change of the error signal, to avoid the computation of the variance of additive noise, since in existing approaches this parameter determines the error bound. In practical applications, the computation of the variance of additive noise is infeasible since this signal is not available; 2) we propose a new method to dynamically modify the projection order in the new algorithm. As a consequence, its computational cost is reduced. To demonstrate its performance, the proposed algorithm was successfully tested in different environments for system identification and active noise control for headphone applications. The simulation results demonstrate that the proposed algorithm presents good convergence properties. In addition, the proposed algorithm exhibits a low overall computational complexity.