The Finite Time State Observer and Its Cooperation with Kalman Filter Algorithm

W. Byrski and M. Pelc (Poland)


Integral Observers, Finite Time Observers, Deadbeat Observers, Kalman Filter.


The theory of an optimal integral Moving Window Observer for exact reconstruction of the state in finite time interval and its application for cooperation with Kalman Filter KF is presented. Exact reconstruction of real state is based on integral functional and finite time interval [0,T] measurement window. The use of MWO which reconstruct the state x(T) exactly (non asymptotically) is very valuable in control applications. However, because of time consuming calculations its use in on-line mode is possible for slow dynamic systems rather, e.g. in chemical processes. Hence, we present the new idea of only cyclic cooperation of MWO and KF. In this structure the main observer (KF) accomplishes the task of optimal filtering of the state but it does not guarantee the best state tracking. The results of exact state observation x(T) are used for first correction of state estimate (T)x~ =x(T) in KF. The state stabilization with e.g. LQR is based on use of KF. Hence, for t>T it makes possible the exact state reconstruction also. MWO as the special task in real time system is wake-up after any unexpected state disturbances for any ti>T and reconstructs the state x(ti+T). Application of cyclic corrections of initial estimate in KF by MWO and its comparison with both types of observers working separately in presence of disturbances is showed.

Important Links:

Go Back