Improved fractional Kalman filter for variable order systems

This paper presents generalization of the Improved Fractional Kalman Filter (ExFKF) for variable order discrete state-space systems. This generalization based on a linear discrete fractional variable order state-space system rewritten into a restricted infinite dimensional form. In order to demonstrate the effectiveness of the proposed algorithms, results of numerical experiments are presented. Proposed algorithm is compared with Variable Order Fractional Kalman Filter algorithm. More over, a special case when constant order Kalman Filter algorithm is used for estimation of variable order system is also studied. Results are compared in terms of estimation and smoothing actions.