Fractional-Order Correntropy Filters for Tracking Dynamic Systems in α-Stable Environments

Abstract

In an increasing number of modern filtering applications, the encountered signals consist of frequent sharp spikes, that cannot be accurately modeled using Gaussian random processes. Modeling the behavior of such signals requires the more general framework of α-stable random processes. In order to present an inclusive filtering solution, this brief derives a new class of fractional-order correntropy adaptive filters that are robust to the jittery α-stable signals. In contrast to conventional correntropy filters, the proposed objective function is compatible with the characteristic function of α-stable processes and captures fractional moments; therefore, the resulting algorithms do not depend on non-existing second-order moments. The work also includes performance and convergence analysis of the derived algorithms. Finally, simulations are conducted to illustrate the effectiveness of the proposed filtering techniques, which indicate that the proposed filters can outperform their counterparts and show less sensitivity to changes in the α parameter.