Constrained Dynamic Systems: Generalized Modeling and State Estimation

Due to physical laws or mathematical properties the states of some dynamic systems satisfy certain constraints, and taking advantage of such constraints generally will produce more accurate system models. This paper is concerned with dynamic modeling and state estimation of equality constrained systems. First, an effective framework for constrained dynamic modeling is proposed by which equality constraints and an original dynamics are optimally fused. In particular, modeling of linear and quadratic equality constrained dynamic systems is systematically investigated. Meanwhile, the effects of the original dynamics on the constructed dynamic model are analyzed. Next, properties of the constrained state estimation are presented, and in particular, the constrained minimum mean square error (CMMSE) estimator is proposed and its differences from the conventional constrained estimators are illustrated. Finally, the proposed modeling is assessed on benchmark scenarios of road-confined vehicle tracking. Simulation results demonstrate that the proposed CMMSE estimator outperforms the conventional constrained ones.