Kalman Filter Fit

In LHCb a track is a collection of a number of measurements and track states. In the Kalman filter fit procedure the measurements are added one by one into the fit, each time updating the fit in the local node. The Kalman filter needs to be initialised with a seed, an initial track state. The fit is iterated by using the state of iteration "n" as the seed of iteration "n+1". Mathematically the Kalman fit is the same as a least squares fit. The Kalman filter consists of the following sub-algorithms:

  • Seeding: determining the initial state and covariance before the fit starts
  • Prediction: predicting the trajectory (i.e. a state and covariance) in the plane of a measurement
  • Projection: updating the track state with the measurement of given plane
  • Smoothing: reversing the fit iteration from the last added measurement to the first measurement in order to obtain the full precision in each node.
The attractive feautures of the Kalman filter fit are:
  • Multiple scattering is implemented as a local kink in the trajectory at a material "wall". At a wall the covariance matrix of the track state is updated according to the expected mean scattering angle. The fit "fits" the size of the kink accordingly
  • Measurements can be added into the fit without redoing the fit
  • For tracks with many measurements, the Kalman filter is a fast procedure as it avoids large dimensional matrix inversions needed in global fits.
In LHCb the extended kalman filter is implemented, linearising the propagation and projection functions around a reference trajectory

-- MarcelMerk - 11 Apr 2005

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Topic revision: r6 - 2005-05-02 - MarcelMerk
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