Abstract: For the problem of fitting the independent variables with error, orthogonal distance least squares and weighted total least squares two independent approaches can be employed to solve it. However, the weighted total least square is unlike orthogonal distance least squares. It does not taking into account the orthogonal geometry information, namely, the line segment consisted of observation point and fitted point is vertical to fitted object. Aimed to solve this problem, a nonlinear equality constrained total least squares adjustment model is proposed, in which total least squares is combined with orthogonal geometry information that has been transformed into a nonlinear equality constraints function with unknown corrected errors. After the function model and the nonlinear equality constraints function are linearized, the Lagrange multiplier method is introduced to derive the calculation formula for estimating parameter and assessing accuracy. Two iterative algorithms are given correspondingly. The suggested method and the designed algorithm are tested by the example of fitting a straight-line. The results show that, ①the proposed model and the iterative algorithm are feasible; ②compared with weighted least squares and weighted total least squares, the sum square of orthogonal distance from the measured point to the fitted line calculated by the new method is the smallest value; ③this orthogonal distance is equal to the distance from the measured point to the corrected point calculated by the suggested method, and the other two methods are not like this.

Key words: nonlinear, equality constraints, total least squares, orthogonal distance, straight-line fit