Free network adjustment: Minimum inner constraints and Pseudo-inverse approaches

Ajuste de red libre: Enfoques de condiciones internas mínimas y pseudo inversa

Palabras clave: Mínimos cuadrados, ajuste libre de redes, restricción mínima interna, Pseudo-inversa, Transformación S. (en_US)
Palabras clave: Least squares, Free adjustment networks, Minimum inner constrains, Pseudo-inverse, S- transformation. (es_ES)

Resumen (en_US)

El método de los mínimos cuadrados es un procedimiento clásico para calcular las coordenadas de una red geodésica. Se pueden utilizar diferentes modelos para realizar el ajuste por mínimos cuadrados y así resolver el sistema linealizado que relaciona las observaciones (geometría interna) y el sistema de referencia (geometría externa). Uno de los métodos es el ajuste libre, el cual es un modelo que no utiliza coordenadas fijas en la matriz de diseño, por lo que la solución no tiene conexión con el sistema de referencia o datum. Por lo tanto, el problema de la deficiencia de rango o datum, que en términos de alegra lineal define una matriz singular para el sistema de ecuaciones normales que tiene que ser resuelto. Para ajustar una red geodésica mediante este método se utilizan principalmente dos enfoques de ajuste libre, la técnica de restricción mínima interna y la técnica pseudo inversa. Ambos modelos proporcionan resultados en un sistema de referencia arbitrario, por lo que la S-transformación es un procedimiento típico para transformar los resultados a un datum o sistema de referencia conocido. En este trabajo se presenta una revisión de ambos métodos y la metodología necesaria para realizar un ajuste de red libre. Finalmente se presentó un ejemplo para analizar la equivalencia entre ambos métodos. Los resultados obtenidos se compararon con una estimación realizada a través del modelo de ajuste injuncionado.

Resumen (es_ES)

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.

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Cómo citar
Carvajal Rodríguez, F. A., Barbosa de Medeiros, L. Ítalo, Klein, I., & Koenig Veiga, L. A. (2020). Ajuste de red libre: Enfoques de condiciones internas mínimas y pseudo inversa. UD Y La geomática, (15). https://doi.org/10.14483/23448407.16309
Publicado: 2020-09-10
Sección
Artículo de revisión