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Fast Tracking of Strip and MAPS Detectors

Fast Tracking of Strip and MAPS Detectors. Joachim Gläß Computer Engineering, University of Mannheim Target application is trigger 1. do it fast 2. check precision Contents STS Tracking (Strip Detectors) Hough Transform MAPS Tracking Kalman Filter.

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Fast Tracking of Strip and MAPS Detectors

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  1. Fast Tracking of Strip and MAPS Detectors Joachim Gläß Computer Engineering, University of Mannheim Target application is trigger • 1. do it fast • 2. check precision • Contents • STS Tracking (Strip Detectors) • Hough Transform • MAPS Tracking • Kalman Filter October 7, 2004 CBM Collaboration Meeting

  2. 0.3 By x = z2 2 Pz 1 2 x 1 2 (z sinq – x cosq) = = Pz 0.3 By z2 Pz 0.3 By (z cosq + x sinq)2 STS TrackingHough Transform of Parabola <=> rotated by q (Px/Pz): Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  3. 1/Pz Py/Pz Px/Pz STS Tracking3-D Hough Transform • 3-D according to the three parameters of a track • bending 1/Pz, angles q and g (Px/Pz, Py/Pz) • Py/Pz detector slice corresponds to one 2-D Hough-histogram • 2-D Hough-histograms can be processed independently • Py/Pz planes are overlapping ( due to multiple scattering) Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  4. CNT D Q STS TrackingHardware Implementation Systolic processing of space points (1 hit/cycle) hit coordinates x, z LUT shift registers 1 bit/row start Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  5. CNT D Q STS TrackingHardware Implementation Systolic processing of space points (1 hit/cycle) hit coordinates x, z LUT shift registers 1 bit/row start Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  6. CNT D Q STS TrackingHardware Implementation Systolic processing of space points (1 hit/cycle) hit coordinates x, z LUT shift registers 1 bit/row start Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  7. STS TrackingHardware Implementation Systolic processing of space points (1 hit/cycle) one hit -> one curve hit coordinates x, z LUT shift registers 1 bit/row start Cell number of peak determines track parameters Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  8. STS TrackingSimulation Results • Efficiency • e: found tracks/all tracks with P > 1GeV/c • g: ghost tracks/processed tracks • i: identified tracks/processed tracks • 31 x 95 x 383 e: 95 %, g: 25 %, i: 45 % • 63 x 191 x 255 e: 93 %, g: 12 %, i: 65 % Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  9. STS TrackingSimulation Results • Precision of the reconstructed momentum • 63 x 191 x 255 Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  10. STS TrackingHardware Implementation • Processing speed (rough estimations) • Real-time tracking (emphasis is on fast) • 1 hit/cycle • e.g. 10 Gb/s link with 64 bit/hit => 150 x 106 hits/s 1 hit/cycle => 150 MHz • 1500 to 10000 hits/event => 10µs to 100µs • total number of processing units ca. 200 x 10 Gb/s links needed for STS => ca. 200 units Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  11. STS Tracking of Strip DetectorsHardware Implementation Processing of strip detector data one hit (x strip) -> one plane (horizontal) hit coordinates x, z LUT shift registers 1 bit/row start stop Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  12. STS Tracking of Strip Detectors Hardware Implementation Processing of strip detector data one hit (y strip) -> one plane(vertical) hit coordinates x, z LUT shift registers 1 bit/row start stop Logical AND gives same Hough Transform than intersection point of strips (+ all fakes given by strip layout) to do: angles other than 90°, especially small angles Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  13. MAPS TrackingKalman Filter Track Following • MAPS layer 1 and 2 (monolithic active pixel sensors) • high resolution < 10 µm • slow readout > 10 µs pile up of ca. 100 events • Kalman Filter track following • track hits from L3 – L5 as seed • later Hough transform • emphasis is on fast: process 1 track/cycle 100 µm Si 100 µm Si 100 µm Si Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  14. MAPS TrackingKalman Filter Track Following • y-z plane (non-bending) => straight line • y = m * z + c • start with m0 = y0/z0, c0=0 • predict position in previous layer yk = mk-1 * zk + ck-1 • measure position (distance predicted – real Dyk) • update estimate with measurement • yk, mk, ck are simple function of mk-1, ck-1 and Dyk • Dyk < 500 µm => needs few bits to code • noise and error covariance are chosen to „believe“ the latest measurement ^ ^ Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  15. MAPS TrackingKalman Filter Track Following • x-z plane (magnetic field) => parabola • x = a z2 + b z + c • start with a0, b0 from hits in layer 3, 4, 5 (or Hough-Transform), c0=0 • predict position in previous layer xk = ak-1 zk2 + bk-1 zk + ck-1 • measure position (distance predicted – real Dxk) • update estimate with measurement • xk, ak, bk, ck are simple functions of ak-1, bk-1, ck-1, Dxk • Dxk < 500 µm => needs few bits to code • noise and error covariance are chosen to „believe“ the latest measurement ^ ^ Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  16. MAPS TrackingSimulation Results • no binning of data • max distance 0.5 mm • nearest hit as function of PZ • tracks with lower momentum are worse • w/o pileup • 98% of nearest hits from same track • with pileup • no missing hits • less hits from same track (ca. 10 %) Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  17. hits from detector layer . . . . . . . . . . . . . . . . predicted position Dx, Dy of nearest hit . . . . . . . . . . . . . . . . . MAPS TrackingHardware Implementation • coefficients and parameters with 10 – 12 bit sufficient • no double precision floating point needed • old values -> LUTs -> adder -> LUT -> new value • associative hit memory Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

  18. Summary • Hough Transform • global algorithm • processing time ~ number of hits • possible implementation using FPGA and LUT • efficiency ca. 95% of tracks found • relatively high ghost rate • able to handle strip detectors • Kalman Filter • MAPS pile up ca. 100 min. bias events • w/o pile up ca. 98% of nearest hits from same track • with pile up ca. 88% of nearest hits from same track ca. 12 % of nearest hits from other events • possible implementation using FPGA and LUT • simple calculation • associative hit memory Joachim Gläß, Univ. Mannheim, Institute of Computer Engineering

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