Adaptive Smoothing Tractor Spline For Trajectory...

documentclass{article} % use amsart instead of article for AMSLaTeX format usepackage{geometry} % See geometry.pdf to learn the layout options. There are lots. geometry{left=1.5cm,right=1.5cm,top=1.5cm,bottom=1.5cm} usepackage{graphicx} usepackage{amssymb} usepackage{indentfirst} usepackage{amsmath} usepackage{amsthm} usepackage{subfigure} usepackage{siunitx} ewtheorem{theorem}{Theorem} ewtheorem{lemma}{Lemma} usepackage{rotating} usepackage{lscape} usepackage{natbib} providecommand{keywords}[1]{ extbf{ extit{Keywords: }} #1} itle{Adaptive Smoothing Tractor Spline for Trajectory Reconstruction} author{Zhanglong Cao, Matthew Parry} %author{Zhanglong Cao,$^1$ Matthew Parry,$^1$ %affil{$^1$University of Otago} %affil{$^1$University of Otago/ Department of Mathematics and Statistics / New Zealand}} date{} % Activate to display a given date or no date egin{document} maketitle egin{abstract} Trajectory of a vehicular system can be reconstructed from noisy position data. Smoothing spline is an efficient method of reconstructing smoothing curves. In conventional smoothing spline, the objective function minimizes errors of observed position points with a penalty term, who has a single parameter that controls the smoothness of reconstruction. Adaptive smoothing spline extends single parameter to a function varying in different domains and adapting the change of roughness. In this paper, using Hermite Spline, we