Adaptive threshold nonlinear correlation algorithm for robust filtering in impulsive noise environments

In this paper, we first present mathematical models for two types of impulse noise in adaptive filtering systems; one in additive observation noise and another at filter input. To combat such impulse noise, a new algorithm named Adaptive Threshold Nonlinear Correlation Algorithm (ATNCA) is proposed. Through analysis and experiment, we demonstrate effectiveness of the ATNCA in making adaptive filters highly robust in the presence of both types of impulse noise while realizing convergence as fast as the LMS algorithm. Fairly good agreement between simulated and theoretical convergence behavior in transient phase and steady state proves the validity of the analysis.