Nonlinear least lp-norm filters for nonlinear autoregressive alpha-stable processes

Kuruoglu E. E.

Nonlinear autoregressive process  Alpha-stable distrribution  Non-Gaussian process  Nonlinear least lp-norm estimation  Polynomial prediction  Volterra filter  Adaptive filters  Probability and Statistics (stochastic processes)  Stable processes 

The alpha-stable distribution family has received great interest recently, due to its ability to succesfully model impulsive data. alpha-stable distributions have found applications in areas such as radar signal processing, audio restoration, financial time series modelling and image processing. Various work on linear parametric models with alpha-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 alpha-stable data is not necessarily linear. Therefore, in this paper, we suggest a shift in the interest to nonlinear parametric models for problems involving alpha-stable distributions. In particular, we study a simple yet analytic nonlinear random process model namely polynomial autoregressive alpha-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 alpha-stable processes instead of classical Gaussian distribution as innovation sequence and arrive at a model capable of describing unsymmetric 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.

Source: ISTI Technical reports, pp.2–33, 2001