Filtering Structures for <i>α</i>-Stable Systems
Sayed Pouria Talebi, Simon Godsill, Danilo P. Mandic
Abstract
Recent years have brought to attention filtering and state estimation paradigms in systems that exhibit rapidly changing states. Dynamics of such systems falls beyond what can be accurately modelled using the ubiquitous Gaussian statistics, and thus, classical state estimation and filtering techniques have started to lose their effectiveness. In order to formulate a more general filtering approach, in this letter, the paradigm of adaptive filtering is revised from the perspective of the characteristic function. The so formulated approach is based on fractional-order calculus and is designed to deal with the more general setting of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stable statistics in an efficient manner. Formulating the filtering structure form perspective of the characteristic function accommodates for general adaptive filtering structures parametrised by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> factor, while fractional-order calculus allows for mathematically tractable solutions. Thus, accommodating demands of modern filtering applications. Finally, effectiveness of the derived framework is demonstrated over a number of numerical simulations.