On unscented Kalman filtering with state interval constraints

This paper addresses the state-estimation problem for nonlinear systems for the case in which prior knowledge is available in the form of interval constraints on the states. Approximate solutions to this problem are reviewed and compared with new algorithms. All the algorithms investigated are based on the unscented Kalman filter. Two illustrative examples of chemical processes are discussed. Numerical results suggest that the use of constrained unscented filtering algorithms improves the accuracy of the state estimates compared to the unconstrained unscented filter, especially when a poor initialization is set. Moreover, it is shown that the constrained filters that enforce the state interval constraint on both the state estimate and error covariance yield more accurate state estimates than the methods that enforce such constraint only on the state estimates.