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R. Frühwirth et al.
Track Road
The track road method starts out with a set of measurements that potentially
belong to the same track, typically one close to the vertex area, one far out in
the tracking detector, and one in the middle. The track model can then be used,
either exactly or approximately, if speed is an important issue, to interpolate between
the measurements and create a road around the hypothesized track. Measurements
inside the road are then collected. The number of measurements and the quality of
the subsequent track fit are used to determine whether the track candidate should be
kept or discarded.
Track Following
A track following procedure takes a track seed as a starting point. A seed is often a
short track segment, potentially including a constraint of the position of the vertex
region. Seeds can be generated at the inner part of the tracking detector, where the
measurements frequently are of very high precision, or at the outer part, where the
track density is lower. From the seed, the track is extrapolated to the next detector
unit. As for the track roads method, this can be done either with the full track model
or with an approximate, simplified model. The measurement closest to the predicted
track is included in the track candidate, and the track is extrapolated again.
Kalman Filter
The Kalman filter [24–26] can be regarded as a statistically optimal track following
procedure. It works by alternating prediction and update steps. Starting from
the seed, the track parameters and their covariance matrix are extrapolated to
the next detector unit containing a measurement, using the full track model. If
the measurement is compatible with the prediction, it is included in the track
candidate, and the track parameters and their covariance matrix are updated with
the information from the measurement. The procedure is repeated until too many
detector units without compatible measurements are traversed or the end of the
tracking detector is reached.
In the original formulation of the method, the measurement closest to the
predicted track is included in the track candidate [27]. However, if the density
of measurements is high, the closest measurement might originate from another
particle or from noise in the detector electronics. Including the wrong measurement
could therefore lead to a wrong subsequent prediction and ultimately to the loss of
the track. The currently most popular approach, the combinatorial Kalman filter,
avoids such losses by splitting the track candidate into several branches when
several compatible measurements are found after the prediction [28]. In order to
take into account detector inefficiencies an additional branch with a missing hit can
be generated.
R. Frühwirth et al.
Track Road
The track road method starts out with a set of measurements that potentially
belong to the same track, typically one close to the vertex area, one far out in
the tracking detector, and one in the middle. The track model can then be used,
either exactly or approximately, if speed is an important issue, to interpolate between
the measurements and create a road around the hypothesized track. Measurements
inside the road are then collected. The number of measurements and the quality of
the subsequent track fit are used to determine whether the track candidate should be
kept or discarded.
Track Following
A track following procedure takes a track seed as a starting point. A seed is often a
short track segment, potentially including a constraint of the position of the vertex
region. Seeds can be generated at the inner part of the tracking detector, where the
measurements frequently are of very high precision, or at the outer part, where the
track density is lower. From the seed, the track is extrapolated to the next detector
unit. As for the track roads method, this can be done either with the full track model
or with an approximate, simplified model. The measurement closest to the predicted
track is included in the track candidate, and the track is extrapolated again.
Kalman Filter
The Kalman filter [24–26] can be regarded as a statistically optimal track following
procedure. It works by alternating prediction and update steps. Starting from
the seed, the track parameters and their covariance matrix are extrapolated to
the next detector unit containing a measurement, using the full track model. If
the measurement is compatible with the prediction, it is included in the track
candidate, and the track parameters and their covariance matrix are updated with
the information from the measurement. The procedure is repeated until too many
detector units without compatible measurements are traversed or the end of the
tracking detector is reached.
In the original formulation of the method, the measurement closest to the
predicted track is included in the track candidate [27]. However, if the density
of measurements is high, the closest measurement might originate from another
particle or from noise in the detector electronics. Including the wrong measurement
could therefore lead to a wrong subsequent prediction and ultimately to the loss of
the track. The currently most popular approach, the combinatorial Kalman filter,
avoids such losses by splitting the track candidate into several branches when
several compatible measurements are found after the prediction [28]. In order to
take into account detector inefficiencies an additional branch with a missing hit can
be generated.