Efficient Bingham filtering based on saddlepoint approximations

In this paper, we address the problem of developing computationally efficient recursive estimators on the periodic domain of orientations using the Bingham distribution. The Bingham distribution is defined directly on the unit hypersphere. As such, it is able to describe both large and small uncertainties in a unified framework. In order to tackle the challenging computation of the normalization constant, we propose a method using its saddlepoint approximations and an approximate MLE based on the Gauss-Newton method. In a set of simulation experiments, we demonstrate that the Bingham filter not only outperforms both Kalman and particle filters, but can also be implemented efficiently.