Kalman Alignment: Kalman Filter Alignment

Kalman Alignment

This is a toy model with which you can simulate Kalman Filter Alignment. It consists of a simulation package, the kalman alignment algorithm, and a validation package. Multiple scattering is simulated, and it is possible to generate particles according to the cosmic muon spectrum.

Build instructions:

This package relies on two external libraries, namely CLHEP (http://proj-clhep.web.cern.ch/proj-clhep/) and ROOT (http://root.cern.ch/). You will first need to install these packages. Adjust the SConstruct and the event/Makefile and util/Makefile accordingly.

Currently two builder programs are used: SCons and make. First, you need to build two shared libraries. Go to the "event/" subdirectory and issue "make". Add the "event/" directory to your LD_LIBRARY_PATH. Go to the "util/" subdirectory and issue "make". Add the "util/" directory to your LD_LIBRARY_PATH. Go back to the main directory (where the Doxyfile and the SConstruct file reside). Run the SCons program by typing "scons" at the prompt. This will build all other programs. Run the simulation in the main directory with the command

simulation/simulation cfg/simulation.cfg

The program will simulate 10000 tracks in a misaligned detector, reconstruct the tracks, and show a display of all tracks. A file with all information necessary for the alignment of the detector is created, by default called "alignment_data.root". Open ROOT, load the shared library and open the alignment_data.root file. Then you can browse through it. An alternative is to use the event/event program to display the first 10 data records.

After running the simulation, it is time for alignment. Run the alignment program with

kfa/align cfg/align.cfg

This runs the Kalman Alignment algorithm over the previously created data file. After finishing, it has created another file named "alignment_result.root". This file contains for each alignment parameter its evolution, i.e. its value for each processed track. These histograms are named "hAliParXXX" where XXX is the number of the alignment parameter. In addition, the final values of the alignment parameters are saved in the histogram hLimits. The values in each bin correspond to the alignment parameter after processing all tracks. The bin number corresponds to the alignment parameter number.

Finally, you can validate whether the alignment procedure worked. Run the program

validation/validation cfg/validation.cfg

This will start the data-driven validation. The validation program will reprocess all tracks with the previously determined alignment parameters and compare the track chi^2 value before and after the alignment. The program creates three plots: A raw plot named "validation_1.pdf" and more refined plots "validation_2.pdf" and "validation_3.pdf". Looking at the latter ones is recommended. They shows a comparison between the track chi^2 before alignment and after alignment. The file "validation_2.pdf" shows the track chi^2 directly. After alignment, the mean chi^2 should correspond to the number of degrees of freedom of each track. For each crossed layer, the track has two hits. E.g. for the default detector with six layers there are twelve hits. Since the track has four parameters (no magnetic field is simulated), the number of degrees of freedom for the track is 2*6-4 = 8. So you should expect that after alignment the mean chi^2 is approximately eight. In practive it will be smaller since some tracks do not cross some detectors, so the number of hits is on average smaller than 2*6. You can see the number of deegrees of freedom in the "validation_1.pdf" histogram. The third histogram, "validation_3.pdf", shows the so-called "normalized" chi^2-distribution, i.e. the value "chi^2/ndof" where ndof is the number of degrees of freedom as above. After alignment it is expected to be close to unity.

You can configure the simulation, alignment and validation packages by editing the corresponding files in the cfg/ subdirectory.

Have fun!