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Input-adaptive QMC-Kalman filters for track fitting

Authors:
Rodolfo G. Esteves
Christiane Lemieux
Michael McCool

Keywords: Nonlinear dynamic systems; quasi-Monte Carlo (QMC); Kalman filter (KF)

Abstract:
On-line track reconstruction is one of the bottlenecks of the pattern recognition task in High-Energy Physics (HEP). This problem has been traditionally divided into the sub-tasks of track finding and track fitting. The latter involves estimating the state of a particle inside a detector moving under the influence of a magnetic field. For the last twenty or so years the most popular solution to the track fitting problem has been the Kalman filter (KF). It is well known that the KF is only guaranteed to compute the optimal estimator if the dynamics of the system are linear and subject to Gaussian noise. However, these conditions are not met in the track fitting problem, in particular, the dynamics are strongly non-Gaussian due to effects such as multiple Coulomb scattering and energy loss. A proposed solution is the “Gaussian sum filter” (GSF) which runs a bank of KFs to estimate each of the modes of the noise distributions, modelled here as a mixture of Gaussians. But this solution is limited by the fact that the GSF uses the same distribution for every input dataset. To address this issue, we present in this paper the Input-adaptive KF (IAKF), which makes use of the dynamic code generation features in Intel’s ArBB parallel framework to create a GSF that matches the given (observation) noise distribution. The IAKF further deals with non-linearity by having the GSF drive, instead of KFs, the recently proposed Quasi-Monte Carlo KF (QMC-KF), a generalization of the sigma-point KF family. Numerical results are shown to validate the performance of the IAKF. The generated code is not only tailored to the data, but takes advantage of several levels of parallelism in multi-core processors.

Pages: 9 to 14

Copyright: Copyright (c) IARIA, 2011

Publication date: September 25, 2011

Published in: conference

ISSN: 2308-4146

ISBN: 978-1-61208-156-4

Location: Rome, Italy

Dates: from September 25, 2011 to September 30, 2011