Track fitting using kalman filter and smoother
Download
1 / 12

Track Fitting using Kalman Filter and Smoother - PowerPoint PPT Presentation


  • 114 Views
  • Uploaded on

Track Fitting using Kalman Filter and Smoother. S. Gorbunov DESY Zeuthen I. Kisel KIP , Uni-Heidelberg E. Kryshen SPbSPU, St. Petersburg. KIP. CBM Collaboration Meeting, GSI March 9-12, 2005. Contents. Analytic formula of track extrapolation Kalman Smoother routine.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Track Fitting using Kalman Filter and Smoother' - raja-everett


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Track fitting using kalman filter and smoother

Track Fitting using Kalman Filter and Smoother

S. Gorbunov DESY Zeuthen

I. KiselKIP, Uni-Heidelberg

E. KryshenSPbSPU, St. Petersburg

KIP

CBM Collaboration Meeting, GSI

March 9-12, 2005


Contents
Contents

  • Analytic formula of track extrapolation

  • Kalman Smoother routine

S. Gorbunov, I. Kisel, E. Kryshen


Extrapolation in magnetic field
Extrapolation in Magnetic Field

Differential equation of charged particle motion in a magnetic field

Along Z direction :

S. Gorbunov, I. Kisel, E. Kryshen


Analytic expression
Analytic Expression

Coefficients:

Equation of motion:

Extrapolation error:

S. Gorbunov, I. Kisel, E. Kryshen


Analytic expression features
Analytic Expression Features

  • Features :

  • The precision of extrapolation does not depend on a shape of the magnetic field.

  • One can cut off the higher-order terms in the series.

S. Gorbunov, I. Kisel, E. Kryshen


Analytic 3
Analytic 3

Example: Third order extrapolation in a homogeneous By field

Small parameter:

S. Gorbunov, I. Kisel, E. Kryshen


Coefficients in the analytic formula
Coefficients in the Analytic Formula

Analytic Light

Analytic 1

Analytic 2

Analytic 3

S. Gorbunov, I. Kisel, E. Kryshen


Performance of extrapolation
Performance of Extrapolation

S. Gorbunov, I. Kisel, E. Kryshen


Kalman filter scheme
Kalman Filter Scheme

Final result

rn,Cn

Initialization

r0,C0

Filtering

Kk= CkHTk(Vk+HkCkHTk)-1

rk+1= rk+Kk(mk-Hkrk)

Ck+1= (E-KkHk)Ck

Extrapolation

rk = Ak-1 rk-1

Ck = Ak-1Ck-1ATk-1+Qk

rk,Ck

Measurement

mk, Hk, Vk

Noise

Qk

rk,Ck

S. Gorbunov, I. Kisel, E. Kryshen


Kalman smoother scheme
Kalman Smoother Scheme

Final result

r0n,C0n

Extrapolation

r0k= Ak-1r0k+1

C0k= Ak-1C0k+1A-1Tk

Smoothing

Kk= Qk(Ck+Qk)-1

r0k= r0k+Kk(rk-r0k)

C0k= KkCk+(E-Kk)C0k(E-Kk)T

Noise

Qk

r0k+1,C0k+1

S. Gorbunov, I. Kisel, E. Kryshen


Kalman smoother
Kalman Smoother

  • Optimal track parameter estimation at each measurement

  • Optimal track parameter estimation between measurements

  • Detection and suppression of outliers

S. Gorbunov, I. Kisel, E. Kryshen


Summary
Summary

  • An analytic formula of extrapolation in magnetic field has been derived

  • A simplified formula is used in the KF fitter and CA track finder

  • Kalman smoother is ready for track fitting in presence of noise hits

  • Tracking is well tested and available

S. Gorbunov, I. Kisel, E. Kryshen


ad