A note on the use of Gauss' formulas in non-linear goedetic adjustment.

Abstract

The theory of adjustment is usually expounded by algebraic and analytical methods. It is well known, however, that the theory of linear adjustment can be represented simply and directly, using geometric reasoning, as properties of linear spaces. In Geodesy, geometric reasoning was already advocated by Tienstrat (1948), who used the Ricci calculus. Generalizing, the theory of non-linear adjustment can then be represented as properties of curved manifolds. In this note we show the principal role played by Gauss' formulas, known from differential geometry, in Gauss' method of least-squares. In particular we show the significance of AMS 1980 subject classification: 62P99, 62F10, 86A30.