Optimal State Estimation for Linear Systems with State Constraints

This paper considers the optimal strategies for constrained linear state estimation. Prior information for estimating state variables is often available in the form of inequality constraints on states. In the latest developments of optimal state estimation theory consideration of state constraints has been often neglected since constraints do not fit easily in the structure of the optimal filter, for example, the issue of state constraints being present has to be addressed adequately, for example nonnegativity of concentration. In order to address this issue and to extend previous developments on the accuracy of state estimation, this work develops the constrained optimal state estimation for finite-dimensional systems. Finally, a numerical example illustrating the proposed method is presented.