# La G\'eom\'etrie de Compensation Non-Lin\'eaire - Le Probl\`eme Spatial d'Intersection dans l'Option de la G\'eod\'esie Tridimensionnelle

## TL;DR

This paper extends the application of non-linear adjustment methods to 3D geodetic trilateration, demonstrating how least squares can be used to determine an unknown point's coordinates from known distances in three-dimensional space.

## Contribution

It adapts the non-linear adjustment approach to 3D trilateration, providing a practical example in geodesy for coordinate determination.

## Key findings

- Effective application of least squares in 3D trilateration
- Demonstrated method for coordinate estimation from distance measurements
- Extended previous planar models to three-dimensional cases

## Abstract

In an article, E. Grafarend and B. Schaffrin studied the geometry of non-linear adjustment of the planar trisection problem using the Gauss Markov model and the method of the least squares. This paper develops the same method working on an example of the determination of a point by trilateration in the three-dimensional geodetic option for determining the coordinates $(x, y, z)$ of an unknown point from measurements known distances to $n$ points.