On initial value problem for fractional-order Kalman filters of linear continuous-time fractional-order systems

To realize the state estimation of linear continuous-time fractional-order systems, the fractional-order Kalman filter (FOKF) is designed to solve problem on the initial value influence. By using the model transformation, an equivalent equation is obtained such that the state estimation of the transformed model is independent of the initial value. The dimension of the equivalent equation is the same as that of the original system, and the proposed FOKF algorithm based on equivalent equation can effectively reduce the initial value influence on the state estimation. Finally, the effectiveness of the solutions for initial value problem for FOKF is validated by the given simulation example.