arXiv subjects
Publications and source records attributed to T. Todorov.
We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper ``asymptotic function'', similar to but different from J. F. Colombeau's algebras of new generalized functions.
The bremsstrahlung energy loss distribution of electrons propagating in matter is highly non Gaussian. Because the Kalman filter relies solely on Gaussian probability density functions, it might not be an optimal reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF) algorithm for electron track reconstruction in the CMS tracker has therefore been developed. The basic idea is to model the bremsstrahlung energy loss distribution by a Gaussian mixture rather than a single Gaussian. It is shown that the GSF is able to improve the momentum resolution of electrons compared to the standard Kalman filter. The momentum resolution and the quality of the estimated error are studied with various types of mixture models of the energy loss distribution.