Spline adaptive filtering algorithm based on Heaviside step function

To reduce the interference of impulsive noise when the spline adaptive filter (SAF) algorithm is used to identify nonlinear systems, this paper proposes a family of SAF algorithms using the Heaviside step function (HSF). The suitability of those cost functions proposed are investigated; those cost functions are design based on some HSF’s approximate functions. Then based on that, four SAF algorithms have been developed: SAF-HSF-sigmoid, SAF-HSF-erfc, SAF-HSF-atan, and SAF-HSF-tanh. Also, the bound of the learning rate has been derived for those proposed algorithms. The proposed SAF-HSF algorithms have been evaluated for nonlinear system identification and simulation studies to demonstrate their robustness.