A Hardware Track-Trigger for CMS pp 69-87 | Cite as
The Kalman Filter
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Abstract
The Kalman filter uses linear quadratic estimation to produce estimates of unknown variables from a series of uncertain measurements. It can therefore be used to fit and filter the track candidates produced by the Hough transform track finder. In addition, a simple duplicate removal algorithm is described. A mathematical derivation of the algorithm is provided, alongside a description of the FPGA firmware design. FPGA resource utilisation and latency are provided.
References
- 1.Frühwirth R (1987) Application of Kalman filtering to track and vertex fitting. Nucl Inst Meth A 262:444–450. https://doi.org/10.1016/0168-9002(87)90887-4
- 2.Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans ASME - J Basic Eng 35–45. https://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf
- 3.Gaylor DE, Lightsey EG (2003) GPS/INS Kalman filter design for spacecraft operating in the proximity of International Space Station, Aug 2003, AIAA Guidance, Navigation, and Control Conference and Exhibit. https://doi.org/10.2514/6.2003-5445
- 4.Bar-Shalom Y, Rong LX, Thiagalingam K (2001) Estimation with applications to tracking and navigation. Wiley, New York, pp 308–317. ISBN 978-0-471-41655-5Google Scholar
- 5.Einicke GA (2006) Optimal and robust noncausal filter formulations. IEEE Trans. Sign Process 54(3):1069–1077. https://doi.org/10.1109/TSP.2005.863042
- 6.Harvey AC (1994) Applications of the Kalman filter in econometrics. In Bewley T (ed) Advances in econometrics. Cambridge University Press pages, New York, 285f, ISBN 0-521-46726-8Google Scholar
- 7.Mankel R (2004) Pattern recognition and event reconstruction in particle physics experiments. Rep Prog Phys 67:553. https://doi.org/10.1088/0034-4885/67/4/R03
- 8.Strandlie A, Wittek W (2006) Derivation of Jacobians for the propagation of covariance matrices of track parameters in homogeneous magnetic fields. Nucl Inst nd Meth A 566(2):687–698. https://doi.org/10.1016/j.nima.2006.07.032
- 9.Innocente V, Nagy E (1993) Trajectory fit in presence of dense materials. Nucl Inst Meth Res Sect A 324(1–2):297–306Google Scholar
- 10.Strandlie A, Fr\(\ddot{\text{u}}wirth\) (2009) Track and vertex reconstruction: from classical to adaptive methods, Oct 2009. http://www.hephy.at/fileadmin/user_upload/Fachbereiche/ASE/Strandlie.pdf
- 11.Maxeler Technologies, MaxCompiler white paper, Feb 2011. https://www.maxeler.com/media/documents/MaxelerWhitePaperMaxCompiler.pdf
- 12.Summers SP (2018) Application of FPGAs to triggering in high energy physics, Mar 2018, Imperial College London Ph.D. Thesis, CERN-THESIS-2018-248Google Scholar
- 13.Summers SP, Rose A, Sanders P (2016) Using MaxCompiler for high level synthesis of trigger algorithms. JINST 12:C02015. https://doi.org/10.1088/1748-0221/12/02/C02015
- 14.Aggleton R et al (2017) An FPGA based track finder for the L1 trigger of the CMS experiment at the High Luminosity LHC. JINST 12:P12019. https://doi.org/10.1088/1748-0221/12/12/P12019
- 15.Xilinx Inc (2017) 7 series FPGAs data sheet: overview, Aug 2017, product specification, DS180 (v2.5)Google Scholar
- 16.Intel Corporation, Stratix V device overview, Oct 2015, SV51001Google Scholar
- 17.Cieri D (2018) Development of a L1 Track and Vertex Finder for the Phase II CMS experiment upgrade, Jan 2018, University of Bristol Ph.D. Thesis, CERN-THESIS-2018-045Google Scholar
- 18.Aggleton R et al (2017) A novel FPGA-based track reconstruction approach for the level-1 trigger of the CMS experiment at CERN, Sep 2017, 27th International Conference on Field Programmable Logic and Applications. https://doi.org/10.23919/FPL.2017.8056825
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