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The problem of reduced-order Optimal state estimation for linear systems with singular noise covariance matrix is studied. It is shown that the optimal estimator is somewhat different from the Kalman filter. The state estimator problem in the singular case can be cast as a constrained optimization problem. Solving this optimization problem yields the truly optimal estimator. The estimator derived here is of the form of the hybrid estimator of Fairman . However, the derivations here are somewhat more direct.