Ambiguities in a Problem in Planar Geodesy

TL;DR

This paper investigates a planar geodesy problem using complex algebraic geometry, focusing on conditions for unique or multiple solutions in determining relative positions from known viewing angles.

Contribution

It characterizes all scenarios where the problem admits multiple solutions, advancing understanding of ambiguities in planar geodesy.

Findings

Identifies conditions leading to multiple solutions

Provides a complete classification of ambiguous cases

Enhances methods for solving geodesic positioning problems

Abstract

This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative position when the viewing angles between target points seen from measure points are known. In particular, we determine all situations in which there is more than one solution.