Circular Curve-Fitting Method for Field Surveying Data with Correlated Noise

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.