Tracking dynamic systems in alpha-stable environments

Abstract

In order to accommodate for modern adaptive filtering applications, the classic adaptive filtering paradigm is considered from a more general perspective. The new formulation allows for time dependent variations in the state of the system and more importantly it relaxes the Gaussian assumption to the generalized setting of α-stable distributions. In this work, based on the principles of gradient descent and fractional-order calculus, a cost-effective technique for tracking the state of such a system is derived. For rigour, performance of the derived filtering technique is analyzed and convergence conditions are established.