State Estimation for Systems With Packet Dropping and State Equality Constraints

We consider the linear estimation problem for systems with packet dropping and equality constraints in this brief, where two kinds of constrained estimators will be designed. First, the constrained state estimator is derived based on the projection method and the unconstrained linear minimum mean square error estimator, and the estimator gains can be yielded in terms of the solutions to a Ricatti equation and a Lyapunov equation. However, when referring to the infinite horizon state estimation, there is a need to consider the convergence of the Lyapunov equation. To meet the requirement of the convergence analysis, the condition that the system matrix is stable should be imposed. Then, in order to remove the restrict condition that the system matrix is stable, another constrained state estimator is designed based on the projection method and time-stamp technique, where the estimator gains can be yielded only in terms of the solutions to a Riccati equation. Finally, we give two numerical examples to show that the second constraint estimator is more effective compared with the first constraint estimator.