CONNECTION BETWEEN THE 3-BLOCK GENERALIZED RICCATI EQUATION AND THE STANDARD RICCATI EQUATION

In a recent paper, Nikoukbah et al. [1] developed a maximum likelihood descriptor Kalman filter the properties of which are governed by a th ree-block generalized Riccati difference equation (GRDE). The converge nce of this GRDE has been studied and the generalization of the eigenv ector approach to solving the associated generalized algebraic Riccati equation has been carried out. In this paper, we connect the GRDE to the standard Riccati equation to point out Nikoukhah's results from we ll-known results obtained in the standard Kalman filtering. Moreover, while the previous study made by [1] provides only sufficient conditio ns on the convergence and stability of the three-block descriptor Kalm an filter, the relationship established herein allows us to derive nec essary and sufficient conditions. In addition, several descriptor Kalm an filtering problems can be treated as in the standard case.