The limit of gaussian distribution on curve manifold
I am reading the paper. In introduction, it said
In many applications, even simple estimation problems involving angular data are often considered as traditional linear or nonlinear estimation problems and handled with classical techniques such as the Kalman Filter , the extended Kalman Filter (EKF), or the unscented Kalman Filter (UKF) . In a circular setting, most traditional approaches to filtering suffer from assuming a Gaussian probability density at a certain point. They fail to take into account the periodic nature of the problem and assume a linear vector space instead of a curved manifold. This shortcoming can cause poor results, in particular when the angular uncertainty is large. In certain cases, the filter may even diverge.
My background is engineering, and I understand what Gaussian distribution in N-dimension means and the role of Gaussian distribution in Kalman filter. But I don't understand why Gaussian distribution fail to estimate angular data in its nature. It will be great if there are mathematical explanation and reference. Thank you.