Kalman filtering and Riccati equations for descriptor systems

摘要

The theory of Kalman filtering is extended to the case of systems with descriptor dynamics. Explicit expressions are obtained for the descriptor Kalman filter allowing for the possible singularity of the observation noise covariance. The asymptotic behavior of the filter in the time-invariant case is studied; in particular, a method for constructing the solution of the algebraic descriptor Riccati equation is presented.