Recursive Bingham Filter for Directional Estimation Involving 180 Degree Symmetry

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1 December 2014

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This work considers filtering of uncertain data defined on periodic domains, particularly the circle and the manifold of orientations in 3D space. Filters based on the Kalman filter perform poorly in this directional setting as they fail to take the structure of the underlying manifold into account. We present a recursive filter based on the Bingham distribution, which is defined on the considered domains. The proposed filter can be applied to circular filtering problems with 180 degree symmetry and to estimation of orientations in three dimensional space. It is easily implemented using standard numerical techniques and suitable for real-time applications. We evaluate our filter in a challenging scenario and compare it to a Kalman filtering approach adapted to the particular setting.