A family of logarithmic hyperbolic cosine spline nonlinear adaptive filters

Spline nonlinear adaptive filters are well known for their ability to efficiently model nonlinear systems while having low computational complexity. However, the performance of traditional spline adaptive filter degrades in the presence of impulsive disturbances. For improving the performance of spline adaptive filters in impulsive noise scenarios, a logarithmic hyperbolic cosine spline adaptive filter is proposed in this paper. To improve the convergence rate while maintaining low steady-state error, a variable parameter approach for the logarithmic hyperbolic cosine spline adaptive filter is also proposed. In addition, a robust nonlinear active noise control approach is also designed based on the proposed logarithmic hyperbolic cosine spline adaptive filter. The computational complexity of the proposed algorithms is studied and two approximate versions of the logarithmic hyperbolic cosine spline adaptive filter are proposed to decrease computational cost without degrading performance. Bound on learning rates are also derived to ensure the stability of the proposed adaptive systems. The simulation studies conducted, demonstrate the enhanced performance achieved by the proposed algorithms.