Kalman Filtering with State Constraints

The Kalman filter is the optimal minimum-variance state estimator for linear dynamic systems with Gaussian noise. In addition, the Kalman filter is the optimal linear state estimator for linear dynamic systems with non-Gaussian noise. For nonlinear systems various modifications of the Kalman filter (e.g., the extended Kalman filter, the unscented Kalman filter, and the particle filter) have been proposed as approximations to the optimal state estimator, which (in general) cannot be solved analytically. One reason that Kalman filtering is optimal for linear systems is that it uses all the available information about the system in order to obtain a state estimate.