Fractional Kalman Filter algorithm for states, parameters and order of fractional system estimation

This paper presents a generalization of the Kalman Filter for linear and nonlinear fractional order discrete state-space systems. The linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified Kalman Filter for linear case is called Fractional Kalman Filter and its nonlinear extension is named Extended Fractional Kalman Filter respectively. The background and motivation for using such techniques are given and the algorithms are derived and proved. The paper also shows a simple numerical example of linear state estimation. Finally, as an example of nonlinear estimation paper discusses the possibility of using these algorithms to parameters and fractional order estimation for fractional order systems. Numerical examples of the use of these algorithms in general nonlinear case are presented.