On the structure of the Luenberger observer in discrete-time linear stochastic systems

The extended Luenberger observer is considered as an alternative to the Kalman filter for obtaining state estimates in discrete-time linear stochastic systems. In certain conditions both estimators have the same structure. It has been shown that the satisfaction of the Huddle equations [7], [9] is sufficient for the discrete extended Luenberger observer to be in the form of a Kalman filter; here we show necessity.