Invariant Unscented Kalman filtering : A Parametric formulation study for Attitude Estimation

The invariant unscented Kalman filtering (IUKF), relies on a geometrical-based constructive method for designing filters dedicated to non-linear state estimation problems while preserving the physical invariances and systems symmetries. This can be achieved by using a geometrically adapted correction term based on an invariant output error. In this article, a special formulation of the attitude and heading estimation problem derives the invariant IUKF so that state and sigma-points are considered as a transformation group parameterization. The specific interest of this formulation is that only the invariant errors between the predicted state and the sigma-points must be known to determine the predicted outputs errors. As this is already computed during the prediction step, the computation complexity to find the covariance matrix of the invariant state estimation is greatly reduced