Bivariate angular estimation under consideration of dependencies using directional statistics

Gerhard Kurz, Igor Gilitschenski, Maxim Dolgov, Uwe D. Hanebeck

Abstract: Estimation of angular quantities is a widespread issue, but standard approaches neglect the true topology of the problem and approximate directional with linear uncertainties. In recent years, novel approaches based on directional statistics have been proposed. However, these approaches have been unable to consider arbitrary circular correlations between multiple angles so far. For this reason, we propose a novel recursive filtering scheme that is capable of estimating multiple angles even if they are dependent, while correctly describing their circular correlation. The proposed approach is based on toroidal probability distributions and a circular correlation coefficient. We demonstrate the superiority to a standard approach based on the Kalman filter in simulations.