On weighted total least squares adjustment for solving the nonlinear problems

In the classical geodetic data processing, a non- linear problem always can be converted to a linear least squares adjustment. However, the errors in Jacob matrix are often not being considered when using the least square method to estimate the optimal parameters from a system of equations. Furthermore, the identity weight matrix may not suitable for each element in Jacob matrix. The weighted total least squares method has been frequently applied in geodetic data processing for the case that the observation vector and the coefficient matrix are perturbed by random errors, which are zero mean and statistically in- dependent with inequality variance. In this contribution, we suggested an approach that employ the weighted total least squares to solve the nonlinear problems and to mitigate the affection of noise in Jacob matrix. The weight matrix of the vector from Jacob matrix is derived by the law of nonlinear error propagation. Two numerical examples, one is the triangulation adjustment and another is a simulation experiment, are given at last to validate the feasibility of the developed method.