Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative

Abstract

Two gradient descent based fractional methods are proposed for systems with outliers in this paper. The outliers in the collected data usually causes biased estimates, resulting in a poor identification model. Tradition fractional gradient descent (FGD) algorithm has an assumption that the fractional derivative is a scalar, which leads to slow convergence rates, especially for systems with an ill-conditioned matrix. The proposed algorithms in this paper have several advantages over the traditional identification methods: (1) can get unbiased estimates; (2) have faster convergence rates; (3) enrich the FGD estimation framework. Simulation examples demonstrate the effectiveness of the proposed algorithms.