Unscented filtering 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 an equality constraint. Three novel suboptimal algorithms based on the unscented Kalman filter are developed, namely, the equality-constrained unscented Kalman filter, the projected unscented Kalman filter, and the measurement-augmented unscented Kalman filter. These methods are compared on two examples: a quaternion-based attitude estimation problem and an idealized flow model involving conserved quantities.