Journal of Nonlinear Science

, Volume 27, Issue 1, pp 99–157

The Algebro-geometric Study of Range Maps

  • Marco Compagnoni
  • Roberto Notari
  • Andrea Alessandro Ruggiu
  • Fabio Antonacci
  • Augusto Sarti
Article

Abstract

Localizing a radiant source is a problem of great interest to many scientific and technological research areas. Localization based on range measurements is at the core of technologies such as radar, sonar and wireless sensor networks. In this manuscript, we offer an in-depth study of the model for source localization based on range measurements obtained from the source signal, from the point of view of algebraic geometry. In the case of three receivers, we find unexpected connections between this problem and the geometry of Kummer’s and Cayley’s surfaces. Our work also gives new insights into the localization based on range differences.

Keywords

Source localization model Range maps Kummer’s surfaces Applied algebraic geometry 

Mathematics Subject Classification

14J99 14P10 51K99 94A12 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Marco Compagnoni
    • 1
  • Roberto Notari
    • 1
  • Andrea Alessandro Ruggiu
    • 2
  • Fabio Antonacci
    • 3
  • Augusto Sarti
    • 3
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Department of MathematicsLinköping UniversityLinköpingSweden
  3. 3.Dipartimento di ElettronicaInformazione e Bioingegneria, Politecnico di MilanoMilanItaly

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