1. Kalman filter for TPC calibration and alignment Marian Ivanov

2. TPC space point distortions (0) Sector  rotation, translation, scaling (?)  edge effect – r j ~ 1/d edge Inner and Outer field cage (FC) ~ 1/d fc Field distortions  Determined by FC misalignment, ROC misalignment, CE misalignment, resistor roads imperfection...  rotation, translation, scaling, tilting (r,phi,z)  edge effect Inner and Outer field cage ~ 1/d fc

3. TPC space point distortions- Z coordinate (1) Drift velocity  Global y dependence (pressure and temperature gradient) changing in time  mean drift velocity – change in time Trigger offset  Change in time  Different for different triggers

4. TPC calibration First approach  Attempt to calibrate effects separately (3 classes)  Data representation for different types of transformation (2-3 classes) Non linear transformation Problems:  Effects are correlated – should be fit together (Milipedde – why not)  Calibration not yet finished – data representation can change – potential problem with backward compatibility

5. New approach General (non linear) transformation class implemented – Ali(TPC)Transformation  Possible to represent any transformation Kalman fit for calibration/alignment implemented - Ali(TPC)kalmanFit  Fitting of tracks (planes) together with parameters of transformations  Transformation represented by set of the Ali(TPC)transformation The same transformation representation used in calibration and also in reconstruction and simulation

6. Ali(TPC)transformation (0) Main function:  virtual Double_t GetDeltaXYZ(Int_t coord, Int_t volID, Double_t param, Double_t x, Double_t y, Double_t z) Possible to register a user defined formulas without creating new class  Ali(TPC)transformation::RegisterFormula("TPCscalingROFC",(GenFun cG)(AliTPCTransformation::TPCscalingROFC)); Internal representation of transformation – pointers to the function  typedef Double_t (*GenFuncG)(const Double_t*,const Double_t*);  GenFuncG fFormulaX; //! x formula  GenFuncG fFormulaY; //! y formula  GenFuncG fFormulaZ; //! z formula

7. Ali(TPC)transformation (1) Make a transformation - (formulas found in the list of registered formulas) transformation = new AliTPCTransformation("tTPCDeltaLxIROCA", new TBits(maskInnerA), "TPClocaldLxdGX","TPClocaldLxdGY",0, 0); Set initial parameters transformation->SetParams(0,0.2,0,&fpar); Add it to the list of transformation kalmanFit->AddCalibration(transformation); Enable/disable transformation: SetActive(Bool_t )

8. Ali(TPC)transformation (3) Plane structure to for transformation representation currently used  Enough for TPC alignment/calibration  Assumption – transformation commute Possible extension - Hierarchical structure  To be done.  First priority finish the TPC calibration Still 3 weeks before the AliRoot frozen

9. Ali(TPC)kalmanFit – calibration and alignment Propagate calibration parameters in time (drift velocity, global y gradient) Propagate track parameters in space (track model+multiple scattering...) Parameter vector: x k = (x calib, x track ) Covariance: p k = (C calib, 0,0,C track ) x track and C track reset after each track H k matrix – transformation of the calibration and track (plane) parameters to the observation  space point (AliTrackPoint) Wikipedia (http://en.wikipedia.org/wiki/Kalman_filter)

10. Current status Calibration/alignment using kalman filter  Improved resolution by factor ~ 1.5, calibrating the Field distortions Main goal – reach width of pulls bellow 1.2  Expected to be achieved after adding of alignment parameters to the fit