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Register a new userA parametrized Kalman filter for fast track fitting at LHCb
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Authors
Pierre Billoir
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We present an alternative implementation of the Kalman filter employed for track fitting within the LHCb experiment. It uses simple parametrizations for the extrapolation of particle trajectories in the field of the LHCb dipole magnet and for the effects of multiple scattering in the detector material. A speedup of more than a factor of four is achieved while maintaining the quality of the estimated track quantities. This Kalman filter implementation could be used in the purely software-based trigger of the LHCb upgrade.
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One of the most computationally challenging problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is determining the trajectory of charged particles during event reconstruction. Algorithms used at the LHC today rely on Kalman filtering, which builds physical trajectories incrementally while incorporating material effects and error estimation. Recognizing the need for faster computational throughput, we have adapted Kalman-filter-based methods for highly parallel, many-core SIMD architectures that are now prevalent in high-performance hardware. In this paper, we discuss the design and performance of the improved tracking algorithm, referred to as mkFit. A key piece of the algorithm is the Matriplex library, containing dedicated code to optimally vectorize operations on small matrices. The physics performance of the mkFit algorithm is comparable to the nominal CMS tracking algorithm when reconstructing tracks from simulated proton-proton collisions within the CMS detector. We study the scaling of the algorithm as a function of the parallel resources utilized and find large speedups both from vectorization and multi-threading. mkFit achieves a speedup of a factor of 6 compared to the nominal algorithm when run in a single-threaded application within the CMS software framework.
We describe the Hybrid seeding, a standalone pattern recognition algorithm aiming at finding charged particle trajectories for the LHCb upgrade. A significant improvement to the charged particle reconstruction efficiency is accomplished by exploiting the knowledge of the LHCb magnetic field and the position of energy deposits in the scintillating fibre tracker detector. Moreover, we achieve a low fake rate and a small contribution to the overall timing budget of the LHCb real-time data processing.
In the context of track fitting problems by a Kalman filter, the appropriate functional forms of the elements of the random process noise matrix are derived for tracking through thick layers of dense materials and magnetic field. This work complements the form of the process noise matrix obtained by Mankel[1].
This article describes a new charged-particle track fitting algorithm designed for use in high-speed electronics applications such as hardware-based triggers in high-energy physics experiments. Following a novel technique designed for fast electronics, the positions of the hits on the detector are transformed before being passed to a linearized track parameter fit. This transformation results in fitted track parameters with a very linear dependence on the hit positions. The approach is demonstrated in a representative detector geometry based on the CMS detector at the Large Hadron Collider. The fit is implemented in FPGA chips and optimized for track fitting throughput and obtains excellent track parameter performance. Such an algorithm is potentially useful in any high-speed track-fitting application.
A Kalman filter package has been developed for reconstructing muon ($mu^pm$) tracks (coming from the neutrino interactions) in ICAL detector. Here, we describe the algorithm of muon track fitting, with emphasis on the error propagation of the elements of Kalman state vector along the muon trajectory through dense materials and inhomogeneous magnetic field. The higher order correction terms are included for reconstructing muon tracks at large zenith angle $theta$ (measured from the perpendicular to the detector planes). The performances of this algorithm and its limitations are discussed.
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