Robust Fitting Algorithm Research Articles

Particle size determination: An undergraduate lab in Mie scattering

A technique for determining the size of microscopic spherical particles using light scattering is presented as an undergraduate physics lab. Scatterer size is determined from angular scattering distribution measurements of laser light scattered from a dilute suspension of latex spheres with diameters of 4.99±0.05 and 6.038±0.045 μm. Previous experiments of this type used approximate theoretical corrections and required the construction of specialized sample cells to minimize complicating effects. As a significant improvement to these, we generate angular scattering distributions from Mie theory and, using an accurate numerical procedure, correct these distributions for Snell’s law and foreshortening effects. Scatterer size is then determined using a fast, robust fitting algorithm to compare these corrected angular scattering distributions to measured angular scattering distributions. We fit the scatter from a solution of 6.04-μm-diam spheres to spheres of 5.95±0.11 μm diameter, and that from a solution of 4.99-μm spheres to 4.85±0.15 μm. Additionally, scattering data for a 2:1 mixture of spheres of diameters 4.99 and 6.04 μm are taken, and after numerical adjustment for Snell’s law and foreshortening effects, good agreement with theory is obtained.

Phase-space prediction of chaotic time series

We report on improved phase-space prediction of chaotic time series. We propose a new neighbour-searching strategy which corrects phase-space distortion arising from noise, finite sampling time and limited data length. We further establish a robust fitting algorithm which combines phase-space transformation, weighted regression and singular value decomposition least squares to construct a local linear prediction function. The scaling laws of prediction error in the presence of noise with various parameters are discussed. The method provides a practical iterated prediction approach with relatively high prediction performance. The prediction algorithm is tested on maps (Logistic, Hénon and Ikeda), finite flows (Rössler and Lorenz) and a laser experimental time series, and is shown to give a prediction time up to or longer than five times the Lyapunov time. The improved algorithm also gives a reliable prediction when using only a short training set and in the presence of small noise.

A new robust fitting algorithm for vertex reconstruction in the CERES experiment

In this paper we report on the application of a robust approach based on a reweighted least squares method for the vertex reconstruction of the CERES/NA45 experiment at the CERN SPS for the case of 160 GeV/u Pb+Au collisions and compare its performance with the presently used algorithm based on the minimization of summed Gaussian weights. In the CERES/NA45 experiment a doublet of cylindrical silicon drift detectors (SDD) is used for vertex reconstruction and tracking. The vertex reconstruction algorithm has to cope with a background-contaminated environment. Furthermore, in the case of ultrarelativistic heavy-ion collisions where high event multiplicities occur ( dn ch dη ⋍ 500 ), the probability of confusing hits from close or intersecting tracks is high. The algorithm needs to provide the precise vertex location even at high occupancies, at a reasonable speed. Our findings are that the robust iterative procedure presented here is about an order of magnitude faster than approaches using standard minimization packages, at a comparable or slightly better accuracy.