Adaptive proximal forward-backward splitting applied to Huber loss function for sparse system identification under impulsive noise

摘要

In this paper, we propose a robust sparsity-aware adaptive filtering algorithm under impulsive noise en­vironment, by using the Huber loss function in the frame of adaptive proximal forward-backward splitting (APFBS). The APFBS attempts to suppress a time-varying cost function which is the sum of a smooth function and a non-smooth function. As the smooth function, we employ the weighted sum of the Huber loss functions of the output residuals. As the nonsmooth function, we employ the weighted ℓ_1 norm. The use of the Huber loss function ro-bustifies the estimation under impulsive noise and the use of the weighted ℓ_1 norm effectively exploits the sparsity of the system to be estimated. The resulting algorithm has low-computational complexity with order O(N), where N is the tap length. Numerical examples in sparse system identification demonstrate that the proposed algorithm outperforms conventional algorithms by achieving robustness against impulsive noise.