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Articles

1966: Vol. XLIII, No. 2

Step Adjustment of Conditioned Observations

Submitted
August 11, 2015
Published
2015-06-19

Abstract

In an article published in the review Engenharia (São Paulo, January 1948) M. A. Machado, engineer at the Geographical and Geological Institute of the State of São Paulo, presented a method of adjusting the geometric figures of triangulation making it possible to obtain by a simple and elegant procedure results which are in perfect agreement with those given by the least squares method. The general principle on which this method is based will not however be found in this article. By studying the mathematics of the adjustment of normally distributed observations, so well set out by Tienstra and based on entirely new ideas, we finally found a way to generalize the Machado method. In this article we shall not comment upon the basic ideas introduced by Tienstra. We prefer to follow a mathematical development based on the classical theory established by Gauss and Legendre. It will be noticed, however, that some points are common to this article and the Tienstra theory, with the exception that Tienstra used the Ricci calculus notation whereas we have adopted the standard matrix notation.