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 bioinfor-
matics. 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.