Deterministic approximation of circular densities with symmetric Dirac mixtures based on two circular moments

Circular estimation problems arise in many applications and can be addressed with the help of circular distributions. In particular, the wrapped normal and von Mises distributions are widely used in the context of circular problems. To facilitate the development of nonlinear filters, a deterministic sample-based approximation of these distributions with a so-called wrapped Dirac mixture distribution is beneficial. We propose a new closed-form solution to obtain a symmetric wrapped Dirac mixture with five components based on matching the first two circular moments. The proposed method is superior to state-of-the-art methods, which only use the first circular moment to obtain three Dirac components, because a larger number of Dirac components results in a more accurate approximation.