Objeckt tracking - filter training (MOSSE)
The solution to the problem was, to rearrange the quadrants of the filter. After rearranging the quadrants, my filter looks like this: 



A lot more like the one in the paper. However, it still lacks in tracking precission.   To tweak this I played arround with the 2D gaussian. And obtained the filter below. Still not optimal but it's an improvement.



This is the formula for the 2D gaussian
$$
g_{i}(x,y) = e^{-\frac{(x-x_{i})^2+(y-y_{i})^2}{\sigma ^{2}}}
$$

In the paper I mentioned in the question, Bolme et al. used $\sigma = 2$. Instead of this I obtained $\sigma$ now dependent on the size of my template

$$
\sigma = \sqrt{{imgSize_{x} \cdot {imgSize_{y}}}} \cdot \frac{1}{16}
$$

like used by Galoogahi et al. (2015). Correlation Filters with Limited Boundaries