Total Least Squares Spiral Curve Fitting
by Thomas G. Davis, (Visiting Prof., Dept. of Civ. and Envir. Engrg., Univ. of South Florida, Tampa, FL 33620)
Journal of Surveying Engineering, Vol. 125, No. 4, November 1999, pp. 159-176, (doi 10.1061/(ASCE)0733-9453(1999)125:4(159))
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| Document type: |
Journal Paper |
| Abstract: |
A rapidly convergent algorithm for fitting clothoids to measured points is developed and tested. The second-order, reduced Hessian method, broadly applicable to the class of scalable, C² parametrizations, is orthogonal distance regression with four-parameter similarity transformations. The local parameters, or state variables, are implicitly eliminated, and second-order solutions are rigorously computed in the model parameter space (rank ≤4). The algorithm is further distinguished from earlier works by the inclusion of approximation procedures that yield very good starting values. Additionally, a strong connection between the Helmert transformation and the total least-squares problem is established, and a fixed point method is suggested. |
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