Figure 2.

Illustration of error metric between a model vector sets (solid lines) and an estimated vector (dashed). A cone of uncertainty (A) is calculated as the average angular distance between the estimated the K₀^th+1 closest directions (red dashed) to each vector j in the model set which sum to the corresponding partial fraction t_j. Other estimated directions (blue dotted) are not considered. The importance weighting (ζ₁,B) deemphasized direction with low partial fraction that may have high error (as indicated by line width) as these are less relevant to goodness of fit. Noise in the estimation process may introduce estimated direction with low partial fraction and high angular error which are still within the sharp cone of uncertainty and lead to unreasonable error measures. The fuzzy cone of uncertainty (ζ₂,C) weights the cone of uncertainty by the proportion of unexplained partial fraction (indicated by line width) up to or less than each angle, which reduces the impact of small, outlier contributions (such a the three small dashed vectors).