Figure 4.

Localization error depending on the starting point distance for one iteration. For each distance d_s the start position has been moved from the dipole into 100 random directions. The mean remaining distance d_r after one localization step is shown. The curves are plotted until the starting distance d_r where the localization was still stable from all 100 directions. To get the result after multiple iterative localization steps, the d_r-value has to be taken as the starting distance d_s of the following step. We used the inner moments up to the 3^rd order , , plotted in curves 3χ and the inner moments up to the 4^th order , , , plotted in curves 4χ. The outer moments which were used to model the disturbing fields were none (curves χ0), 2^nd order moments (curves χ2: homogeneous fields), 2^nd and 3^rd order moments (curves χ3: homogeneous and gradient fields), and 2^nd to 4^th order moments (curves χ4: external fields up to 2^nd order).