Developments Of Adaptive Filtering Algorithms In The Presence Of Impulsive Noise

The noise as a negative factor always disturbs us in our daily life.A survey conducted by the World Health Organization?WHO?indicates that the noise is the second pollution faced by mankind.However,most adaptive filter algorithms are designed in the case of Gaussian noise.In practice,another noise called impulsive noise is a more common noise source.Due to the impulsive nature,the performance of approaches designed for the Gaussian noise deteriorates significantly and even sometimes they fail.In this thesis,the impulsive noise suppression problem is studied under the framework of adaptive filters.The main contributions are summarized as follows.In this thesis,first,the impulsive noise is modeled by the alpha-stable distribution and its sparse property in the time domain is also revealed.By utilizing its sparse property,the cost functions of least mean squares?LMS?,recursive least squares?RLS?,Kalman filter?KF?are redesigned by incorporating the noise as a new variable.In doing so,the useful signal and noise can be simultaneously obtained.To derive the solutions,by utilizing the classical steepest decent algorithm,the recursive updates of the signal and noise are respectively provided.Moreover,for the proposed LMS method,its convergence analysis and condition are also derived.The effectiveness of the proposed approaches is confirmed by simulations and comparisons with state-of-the-art algorithms also indicate the superior performance provided by the proposed approaches.During the studies of the impulsive noise suppression,it is found although the noise happens rather quickly,it still lasts a period of time.That is to say the noise presents the so-called group sparse property.To promote this property,three penalty functions of log?.?,atan?.?,rational?.?and the L_1,2-norm are introduced to penalize the noise term.By considering the group sparse promoters,the updates of signal and noise are also derived.Compared with the non-group sparse algorithms by simulations,the approach with the group sparse promoter demonstrates faster convergence rate and lower steady error.