On weighted total least squares adjustment for solving the nonlinear problems

Abstract

Abstract:In the classical geodetic data processing, a nonlinear 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 coe cient matrix are perturbed by random errors, which are zero mean and statistically independent 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 a ection 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.

Solving the Coupled Aerodynamic and Thermal Problem for Modeling the Air Distribution Devices with Perforated Plates

“…Due to the fundamentals of the least square method [24], the unknown parameters C and n are determined by the data from the matrix of planning a three-factor experiment (Table 4) using the procedure of minimizing the following error function: It should be noted that there are the following disadvantages of the obtained dependence. Firstly, the Equation (5) is linear and does not correspond to the physical peculiarities of the problem, the theory of dimensions, and the influence of the area S on the air velocity V is neglected.…”

“…Due to the fundamentals of the least square method [24], the unknown parameters C and n are determined by the data from the matrix of planning a three-factor experiment (Table 4) using the procedure of minimizing the following error function:…”