Linear Regression Fit

Two consecutive linear regression fits to the coordinates of the cell centers are used to get a 3D line that follows the trajectory of the candidate.

First the coordinates are sorted according to the size of the candidate in the coordinate direction. The coordinate corresponding to the maximum size is used as the ordinate for the first fit, the second biggest is used as the abscissa. For the second fit the ordinate is the projection of the cell onto the line obtained with the first fit. The abscissa is the third unused variable.

The fit algorithms take care of special cases where a candidate has no size in one or two coordinate directions.

The fits are performed eight times with all possible combinations of the following algorithms:

1. Energy weighted:
2. Cell size weighted:
3. Correction of the cell position based on the cell imbalance: where is the direction perpendicular to the WLS corresponding to positive cell energy imbalance.

Of those fitted lines the one with the best HitRatio is selected. To allow for problems with the fit accuracy the hit ratio is calculated using the blown up cell geometry.