Robust Huber adaptive filter

Classical filtering methods are not optimal when the statistics of the signals violate the underlying assumptions behind the theoretical development. Most of the classical filtering theory like least-squares filtering assumes Gaussianity as its underlying distribution. We present a new adaptive filter that is optimal in the presence of Gaussian noise and robust to outliers. This novel robust adaptive filter minimizes the Huber objective function. An estimator based on the Huber objective function behaves as an L₁ norm estimator for large residual errors and as an L₂ norm estimator for small residual errors. Simulation results show the improved performance of the Huber adaptive filter (configured as a line enhancer) over various nonlinear filters in the presence of impulsive noise and Gaussian noise