State Estimation Strategy for Fractional Order Systems with Noises and Multiple Time Delayed Measurements

The fractional order calculus can represent systems with high-order dynamics and complex non-linear phenomena using fewer coefficients. In this study the extended fractional Kalman filter is developed for the class of non-linear discrete-time fractional order systems using observations with multiple delays contaminated by additive white noise. For a wide class of practical applications, the time delay cannot be neglected. In the time delay integer order systems, a common approach is partial differential equation. This method is very difficult to solve. The authors' approach is applied the reorganised innovation technique. As a result of the reorganised innovation sequence, the Kalman filtering problem with multiple delayed measurements is converted to filter of a delay-free system. In the rest of paper, the covariance matrix of the prediction error of the states is presented in the form of the novel Riccati equations. Finally, the solution of the Kalman filtering problem is obtained by applying the re-organised innovation sequence and Riccati equations. A numerical example is given to illustrate the effectiveness of the proposed scheme.