Paper Info
Title
Connection between differential geometry and estimation theory for polynomial nonlinearity in 2D
Abstract
A relationship between differential geometry and estimation theory was lacking until the work of Bates and Watts in the context of nonlinear parameter estimation. They used differential geometry based curvature measures of nonlinearity (CMoN), namely, the parameter-effects and intrinsic curvatures to quantify the degree of nonlinearity of a general multi-dimensional nonlinear parameter estimation problem. However, they didn't establish a relationship between CMoN and the curvature in differential geometry. We consider a polynomial curve in two dimensions and for the first time show analytically and through Monte Carlo simulations that affine mappings with positive slopes exist among the logarithm of the curvature in differential geometry, Bates and Watts CMoN, and mean square error.
Year
DOI
Venue
2010
10.1109/ICIF.2010.5712084
Fusion
Keywords
Field
DocType
degree of nonlinearity,mean square error,polynomial nonlinearity,curvature measures of nonlinearity,differential geometry,parameter-effects curvature,cmon,polynomial curve,monte carlo simulation,multidimensional nonlinear parameter estimation,crameár-rao lower bound,estimation theory,extrinsic curvature,curvature measures-of-nonlinearity,monte carlo methods,parameter-effect,polynomials,mean square error methods,intrinsic curvature,geometry,lower bound,estimation,parameter estimation,noise measurement,two dimensions
Affine transformation,Nonlinear system,Polynomial,Mathematical analysis,Artificial intelligence,Estimation theory,Logarithm,Geometry,Gaussian curvature,Computer vision,Curvature,Differential geometry,Mathematics
Conference
ISBN
Citations 
PageRank 
978-0-9824438-1-1
2
0.42
References 
Authors
0
4
Name
Order
Citations
PageRank
Mahendra Mallick1449.55
Sanjeev Arulampalam214219.13
Yanjun Yan3309.73
Aditya Mallick420.42