Sigmoid distance metric-based spline adaptive filters for nonlinear adaptive noise cancellation

Abstract

This article devises a spline adaptive filter (SAF) algorithm with robustness for nonlinear adaptive noise cancellation (NANC), called the SAF-SDM, which is built on a distance-based metric with a sigmoid kernel. The presented SAF-SDM delivers insignificant coefficient updates when the system is subjected to remarkable outliers, which leads to low steady-state errors. Additionally, we thoroughly analyze the mean behaviour and mean-square performance of the SAF-SDM at the theoretical level and validate the analysis results using nonlinear system identification (NSI) simulations. To fulfill the higher computational efficiency when a longer linear filter order is selected in the SAF, an improved SAF-SDM is developed through a frequency domain (FD) filtering program, called the FDSAF-SDM. Then, we provide an analysis of the calculation complexity of the two presented algorithms and compare them with those of several similar algorithms. Finally, simulation and experiment results demonstrate the excellence of the presented algorithms in NSI and NANC.