Reduced order Kalman filter for a continuous-time fractional-order system using fractional-order average derivative

This paper investigates two kinds of reduced order Kalman filters for a continuous-time fractional-order system with uncorrelated and correlated process and measurement noises. The fractional-order average derivative is adopted to enhance the discretization accuracy for the investigated continuous-time fractional-order system. The uncorrelated and correlated cases for the process and measurement noises are treated by the reduced order Kalman filters to achieve the robust estimation for a part of states of a fractional-order system. The truncation issue is considered to implement the practical application of the proposed state estimation algorithm. Finally, two examples for uncorrelated and correlated noises are offered to verify the effectiveness of the proposed reduced order Kalman filters.