Adaptive Filtering Algorithms In α-Stable Impulsive Noise Environment

On the basis ofα-stable noise's property and typical adaptive filtering algorithms in Gaussian noise condition, this paper mainly studies several adaptive filtering algorithms inα-stable noise conditions, and makes much improvement to one of them. More details below:Firstly, this paper presents the definition and important characteristic ofα-stable distribution,and discusses the definitions and properties of fractional lower-order moment, minimum dispersion, and some important theorems and conclusions.Then the adaptive filtering principle in Gaussian noise condition is introduced, and two typical adaptive filtering algorithms are presented,including the least mean square algorithm and the recursive least square algorithm. Two new methods are studied derived from above algorithms, namely, the least mean l pnorm and the recursive least l pnorm adaptive filtering algorithms. Their performance is analyzed via computer simulation.Some new quasi-Newton adaptive filtering algorithms are presented, including the quasi-Newton least mean l p norm algorithm and the quasi-Newton recursive least l p norm adaptive filtering algorithm. Besides, the total least l p norm algorithm and the recursive total least l p norm algorithm are introduced, and their advantages are showed via computer simulation. These two typical algorithms form a firm basis for the improved algorithm below.At last, the quasi-Newton method is applied into the recursive total least l p norm algorithm. A positive matrix which satisfies the quasi-Newton equation is used to approach the contrary autocorrelation matrix of the extended input vector, and it is iterated with DFP formula. So forms the improved algorithm. And then we apply it into IIR adaptive filter. It can be seen that the new algorithm's stability has certain improvement comparing with other several algorithms.