Abstract
In this paper, a sign normalised least mean square algorithm (SNLMS) based on Hammerstein spline adaptive filter (HSAF) is proposed, which is derived by minimising the absolute value of the a posteriori error. The control points, collected in an adaptive lookup table which is interpolated by a local low-order polynomial spline curve and the tap weights of the linear filter are updated by using the direction information of the a posteriori error. The minimization of the absolute value of the a posteriori error reduces the impact of impulsive noises. The new algorithm is called HSAF-SNLMS and can be used to identify the Hammerstein-type nonlinear systems. Furthermore, the convergence performance analysis is carried out by considering the identification of the Hammerstein-type system and the computational complexity of the proposed algorithm is also analyzed. Simulation results in system identification demonstrate the proposed HSAF-SNLMS obtains more robust performance when compared with the existing spline adaptive filter algorithms in impulsive noise environments.
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