Nonlinear least Lp-norm filters for nonlinear autoregressive (alfa)-stable processes

The ?-stable distribution family has received great interest recently, due to its ability to successfully model impulsive data. ?-stable distributions have found applications in areas such as radar signal processing, audio restoration, financial time series modeling, and image processing. Various works on linear parametric models with ?-stable innovations have been reported in the literature. However, some recent work has demonstrated that linear models are not in general adequate to capture all characteristics of heavy-tailed data. Moreover, it is known that the optimal minimum dispersion estimator for ?-stable data is not necessarily linear. Therefore, in this paper, we suggest a shift in the interest to nonlinear parametric models for problems involving ?-stable distributions. In particular, we study a simple yet analytic nonlinear random process model namely polynomial autoregressive ?-stable processes. Polynomial autoregression and Volterra filtering have been successful models for some biomedical and seismic signals reflecting their underlying nonlinear generation mechanisms. In this paper, we employ ?-stable processes instead of classical Gaussian distribution as an innovation sequence and arrive at a model capable of describing asymmetric as well as impulsive characteristics. We provide a number of novel adaptive and block type algorithms for the estimation of model parameters of this class of nonlinear processes efficiently. Simulation results on synthetic data demonstrate clearly the superiority of the novel algorithms to classical techniques. The paper concludes with a discussion of the application areas of the techniques developed in the paper, including impulsive noise suppression, nonlinear system identification, target tracking, and nonlinear channel equalization.