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.
Highlights
Fractional calculus is a generalization of traditional differential calculus for cases where orders of differentiation and integration are real or even complex numbers
In [18], an advanced numerical optimization algorithm was used to obtain the value of the fractional order, and in [11], the dual estimation method was used to estimate the fractional order of the system
To deal with such a complex problem, we propose a new estimation algorithm for the simultaneous estimation of state variables, system parameters, and fractional order
Summary
Fractional calculus is a generalization of traditional differential calculus for cases where orders of differentiation and integration are real or even complex numbers. In [18], an advanced numerical optimization algorithm was used to obtain the value of the fractional order, and in [11], the dual estimation method was used to estimate the fractional order of the system To deal with such a complex problem, we propose a new estimation algorithm for the simultaneous estimation of state variables, system parameters, and fractional order. Such an algorithm will be formulated for one type of variable order definition. It is based on a modification (enlargement) of the classical dual estimation algorithm, which contains two estimation actions (one for states variables and another for system parameters).
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