State Estimation for Equality-Constrained Nonlinear Systems

This paper addresses the state-estimation problem for nonlinear systems in a context where prior knowledge, in addition to the model and the measurement data, is available in the form of a nonlinear equality constraint. Then three suboptimal algorithms based on the unscented Kalman filter (UKF) are developed, namely, the equality-constrained unscented Kalman filter (ECUKF), the projected unscented Kalman filter (PUKF), and the measurement-augmented unscented Kalman filter (MAUKF). These methods are compared on three examples, including a quaternion-based attitude estimation problem, as well as a mechanical system and an idealized flow model, both involving conserved quantities. In addition to very closely satisfying a nonlinear equality constraint on the system, the proposed methods produce more precise and more informative estimates than the unconstrained estimates.