Toroidal Information Fusion Based on the Bivariate von Mises Distribution

Fusion of toroidal information, such as correlated angles, is a problem that arises in many fields ranging from robotics and signal processing to meteorology and bioinformatics. For this purpose, we propose a novel fusion method based on the bivariate von Mises distribution. Unlike most literature on the bivariate von Mises distribution, we consider the full version with matrix-valued parameter rather than a simplified version. By doing so. we are able to derive the exact analytical computation of the fusion operation. We also propose an efficient approximation of the normalization constant including an error bound and present a parameter estimation algorithm based on a maximum likelihood approach. The presented algorithms are illustrated through examples.