Combined-Step-Size Affine Projection Andrew's Sine Estimate for Robust Adaptive Filtering

Recently, an affine-projection-like M-estimate (APLM) algorithm has gained popularity for its ability to effectively handle impulsive background disturbances. Nevertheless, the APLM algorithm's performance is negatively affected by steady-state misalignment. To address this issue while maintaining equivalent computational complexity, a robust cost function based on the Andrew's sine estimator (ASE) is introduced and a corresponding affine-projection Andrew's sine estimator (APASE) algorithm is proposed in this paper. To further enhance the tracking capability and accelerate the convergence rate, we develop the combined-step-size APASE (CSS-APASE) algorithm using a combination of two different step sizes. A series of simulation studies are conducted in system identification and echo cancellation scenarios, which confirms that the proposed algorithms can attain reduced misalignment compared to other currently available algorithms in cases of impulsive noise. Meanwhile, we also establish a bound on the learning rate to ensure the stability of the proposed algorithms.