Total Least Squares Algorithms for Fitting 3d Straight Lines

To address the problem of fitting a 3D straight line, the TLS method based on the Lagrange function is used to solve it. The number of parameter to be estimated is decreased from six to four by changing the standard equation of the straight line into the projective equation of it. The problem of fitting a 3D straight line is converted to the problem of fitting two 2D straight lines with errors in both coordinates. And then the total least square (TLS) and least square (LS) method are employed to fit the two 2D straight line. A simulated example is carried out to demonstrate the effectiveness and applicability of proposed algorithms.