Diffusion Least Mean P-Power Algorithms for Distributed Estimation in Alpha-Stable Noise Environments

Introduction: Emergent wireless sensor networks based applications have motivated the development of distributed adaptive estimation schemes. Distributed least mean squares (LMS) [1] and recursive least squares (RLS) type algorithms have received more attentions [2]. Readers can refer to [3] and the references therein for details about up to date diffusion strategies for adaptation and learning over networks. The distributed LMS and RLS type strategies are all second order statistics (SOS) based, the target is to minimize the mean square error (MSE) of the estimator. For the MSE based techniques, the noise is often assumed to be white Gaussian with finite second-order statistics. However, in some circumstances, the noise may not have finite SOS, such as impulsive noise, which can be modeled by a heavy-tailed alpha stable distribution [4]. Alpha stable signal processing techniques have received more attentions. Parameter estimation and blind channel identification in alpha stable signal environments are introduced in [5]. System identification problem in alpha stable noise environments is discussed in [6]. Particle filtering for acoustic source tracking in impulsive noise with alpha-stable process is proposed in [7]. The existing LMP algorithms are all global or centralized, distributed LMP have not been studied yet. In this paper, we exploit the diffusion LMP strategies for distributed estimation in impulsive noise environments. The additive impulsive noise is with symmetric alpha-stable distribution.