Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

In the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.