Constrained sigma points for attitude estimation

Abstract

The Kalman filter is considered as an optimal filter with the hypothesis of gaussian noise and linear model. For nonlinear model several approaches have been proposed and Unscented Kalman Filter (UKF) seems to be one of the most accurate. In this study, we wonder if an appropriate constraint can enhance the efficiency of UKF. We propose a new algorithm called Constrained Sigma Points (CGS) that constrained the sigma points with a nonlinear observer constraint. Here, our research is based on attitude estimation and the constraint is related to attitude. We evaluate its performance compared to the state of the art of non-linear fusion filters, i.e. Multiplicative Extended Kalman Filter (MEKF), UnScented QUaternion Estimator, Quaternion estimate (QUEST) and a nonlinear observer (CGO). Our results show that our algorithm leads to better results in term of accuracy with an effective duration of computation. In future works, we will determine how this new constraint can be generalised to different kind of nonlinear models.