Triple Estimation of Fractional Variable Order, Parameters, and State Variables Based on the Unscented Fractional Order Kalman Filter

Abstract

In this paper, a method for states, parameters, and fractional order estimation is presented. The proposed method is an extension of the traditional dual estimation method and uses three blocks of filters with appropriate data interconnections. As the main part of the estimation algorithm, the Fractional Unscented Kalman Filter was used. The proposed Triple Estimation algorithm might be treated as a convenient tool for estimation and analysis of a wide range of dynamical systems with fractional constants or variable order nature, especially when knowledge about the identified system is very restricted and both order and system parameters are unknown. In order to show the performance of the proposed algorithm, sets of numerical results are presented.

Keywords

• fractional calculus
• fractional Kalman filter
• estimation of fractional order systems