Circular Curve-Fitting Method for Field Surveying Data with Correlated Noise
Publication: Journal of Surveying Engineering
Volume 144, Issue 4
Abstract
The horizontal alignment geometric parameter is an important basis for road management, safety analysis, and railway maintenance. Therefore, the identification of horizontal curve features is of great importance. Least squares is most common method currently used to estimate the parameter. By comparing different approaches of least squares, this paper outlines the drawbacks of algebraic fitting and presents an analysis of the connection and limitation of other forms of least squares. After showing the presence of correlated noise in sampled data points and based on the maximum likelihood estimation theory, the paper shows the derivation of a generic curve-fitting method, which was also applied to circular curve fitting. Experimental results showed that the proposed fitting method was capable of estimating circular curve parameters and the precision of them in all circumstances by specifying stochastic models. The geometric meaning of the fitting results was connected with the corresponding stochastic models. The estimated parameters varied by stochastic models, leading to different alignment identifications. An in-depth understanding of curve fitting was provided that explains that only the proper stochastic model could meet the maximum likelihood principle, and thus, achieved the best fit.
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Acknowledgments
The authors acknowledge Professor William Young for editing the manuscript. The project was sponsored by the National Natural Science Foundation of China (Grant 51678574). The first author thanks the China Scholarship Council (Grant 201706375006) for financially supporting his studies at the University of Maryland.
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Published In
Journal of Surveying Engineering
Volume 144 • Issue 4 • November 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Aug 3, 2017
Accepted: May 10, 2018
Published online: Sep 13, 2018
Published in print: Nov 1, 2018
Discussion open until: Feb 13, 2019
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