Optimal quantization of circular distributions

In this work, a new method for approximating circular probability distributions by a mixture of weighted discrete samples is proposed. Particularly, the wrapped normal distribution, the von Mises distribution, and the Bingham distribution are considered. The approximation approach is based on formulating a quantizer and a global optimality measure, which can be optimized directly. Furthermore, a relationship between the Bingham distribution and the von Mises distribution are formulated showing that it is sufficient to approximate a von Mises distribution with suitably chosen parameters in order to obtain an optimal approximation of the Bingham distribution. The resulting approximation is of particular interest for filtering applications, because the involved optimality measure gives rise to a general error estimate in propagation of uncertainties through nontrivial functions in the circular domain.