- ISSN 0258-2724
- CN 51-1277/U
- EI Compendex
- Scopus
- Indexed by Core Journals of China, Chinese S&T Journal Citation Reports
- Chinese S&T Journal Citation Reports
- Chinese Science Citation Database
| Citation: | SONG Zhanfeng, GUO Jiejia, LI Jun. Fitting a Straight-Line to Data Points with Correlated Noise Between Coordinate Components under Constraints[J]. Journal of Southwest Jiaotong University, 2021, 56(6): 1283-1289. doi: 10.3969/j.issn.0258-2724.20200120
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Straight-line fitting has received extensive attention both in curve fitting research and engineering practice. The methods of ordinary least squares and orthogonal least squares fitting ignore the existence of the observation error correlation. The coordinate pairs of surveying points, obtained by a total station in railway realignment, not only have different levels of precision but also have correlated noise. Meanwhile, straight-line fitting is usually under constraints in the realignment. Thus, a straight-line fitting model was derived based on the maximum likelihood estimation and Lagrange conditional extremum theory, considering constraints and correlated noise between coordinate components, and a Gauss-Newton algorithm was presented to search for the optimum. The method was tested with the field surveying data. Experimental results show that the proposed fitting method is capable of estimating straight-line parameters and their precisions in all circumstances by specifying stochastic models. When considering correlated noise, the precision of estimated parameters improve 9.2% with a constraint and improve 2.7% without constraints, respectively. The Gauss-Newton algorithm takes only 6 and 3 iteration times with a constraint and without constraints respectively, for locating the optimum straight-line.
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