Implicit Augmented UKF and Its Application to the Stellar Refraction Navigation

Abstract

Stellar refraction navigation is an effective method for autonomous celestial navigation of satellites. Compared with the refraction apparent height, a better navigation performance can be achieved via the stellar refraction angle. Nevertheless, this causes the measurement model to become an implicit function, in which the measurements and states are restricted to implicit equations. The available filters, applied to a system with an implicit measurement model, are based on linearization, which needs to compute the Jacobian matrices and introduces linearization errors. In this paper, a type of unscented Kalman filter (UKF), referred to as an implicit augmented unscented Kalman filter (IAUKF), is proposed, in which the state is augmented via the measurement. The zero is regarded as the equivalent measurement vector for updating the estimation of the augmented state as well as its covariance matrix. The performance of the IAUKF is tested and demonstrated via simulation. Simulations reveal that the navigation performance of the IAUKF is better than that of the implicit extended Kalman filter (IEKF), the implicit augmented extended Kalman filter (IAEKF), the iterative IEKF, and the implicit UKF.