Two New Fractional Order Kalman Filters for Linear Fractional Order Systems with Colored Measurement Noise

This paper presents two new Kalman filter for state estimation in fractional order systems using colored measurement noise, according to the importance of the state estimation especially in fractional order systems (FOSs). In these two novel filters, by expanding measurement differencing method, new auxiliary outputs will be defined. By defining these new auxiliary outputs, the fractional order system with colored measurement noise will be changed to a system with correlated process and measurement noises. Therefore, according to these new outputs, new state estimation algorithms will be proposed. The accuracy of these algorithms will be proved by some theorems. These two methods are easy to implement and can be easily extended to nonlinear systems. Finally, the precision of the proposed algorithms will be examined by using an appropriate and applicable example.