Free network adjustment: Minimum inner constraints and Pseudo-inverse approaches - Carvajal Rodríguez, Felipe Andrés; Barbosa de Medeiros, Leandro Ítalo; Klein, Ivandro; Koenig Veiga, Luis Augusto (UD y la Geomática, 2020)
The least squares technique is a classic procedure to compute the coordinates of a geodetic network. Different approaches of this method have been development to perform the least squares adjustment and thus solve the linearized system that relates the observations (internal geometry) and the reference system (external geometry). The free adjustment is a model that not use fix coordinates in the design matrix, thus the solution does not have connection with referential system or datum. Therefore, the rank deficiency problem or datum defect, which in terms of linear algebra defines a singular matrix in the system of normal equations, must be solve. Two mainly approaches of free adjustment are used to solve a geodetic network, the minimum inner constraints and pseudo-inverse technique. Both models provide results in an arbitrary reference system, therefore, the S-transformation is a typical procedure to transform the result to a known datum. This paper presents a review of both methods and the methodology necessary to perform a free network adjustment. Finally, an example was presented to analyze the equivalence between both methods. The results obtained was compare with an estimation realize through the constrained adjustment.