CHALLENGING THE LOGIC OF LEAST-SQUARES METHODS FOR GEODETIC ESTIMATION PROBLEMS

Least-squares estimation methods are perhaps the most widely used tool in all fields of geodetic research. Nevertheless, their prevailing use is not often complemented by a widespread objective view of their rudiments. Within the standard formalism of the least-squares estimation theory there are actually several paradoxical and curious issues which are seldom explicitly formulated. The aim of this expository paper is to present some of these issues and to discuss their implications for geodetic data analysis and parameter estimation problems. « De tous les principes qu’on peut proposer pour cet objet, je pense qu’il n’en est pas de plus general, de plus exact, ni d’une application plus facile que celui qui consiste à rendre minimum la somme de carrés des erreurs. » Adrien-Marie Legendre [1805