Robust Huber adaptive filter

A robust band-dependent variable step size NSAF algorithm against impulsive noises

“…The impulsive noise ϑðnÞ is usually modeled as a BernoulliGaussian (BG) process, i.e., ϑðnÞ ¼ cðnÞAðnÞ [8][9][10][11][12][13][14], where cðnÞ is a Bernoulli process with the probability density function defined by p cðnÞ ¼ 1 È É ¼ Pr and p cðnÞ ¼ 0 È É ¼ 1 ÀPr (with Pr denoting the probability of the occurrence of the impulsive noises), and AðnÞ is a white Gaussian process with zero mean and variance σ 2 12,13]. Also, to assess the tracking capability of the algorithms, the unknown vector is changed from w o to Àw o at the 4:5 Â 10 5 th input samples.…”

A Robust Variable Step-Size NLMS Algorithm Through A Combination of Robust Cost Functions

“…It is associated with how thealgorithm constrains the energy of the filter update at eachiteration. Various adaptive algorithms use other robust costfunctions for robustness against impulsive measurement noise [12]- [14]. When the magnitude of the output error is largerthan a threshold, the Huber mixed-norm M-estimate costfunction uses the 1 L norm minimization [12], on the otherhand, the Hampel three-part redescending M-estimate costfunction sets the error signal as a constant value [13], [14].…”

A variable step-size SIG algorithm for realizing the optimal adaptive FIR filter

“…are two key factors in the adaptation algorithm (1), because they govern the convergence speed as well as the steady-state misadjustment of the algorithm. Up to now, a lot of stepsizes (usually variable step-sizes [3][4][5][6][7][8][9][10][11]) and error functions (usually error nonlinearities [12][13][14][15][16]) have been proposed to improve the convergence performance. The previous studies, however, focus only on one of the two factors, and to the best of our knowledge, no reports in the literature have attempted to optimize both the stepsize and error nonlinearity at the same time.…”