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.

The Algebro-geometric Study of Range Maps

COMPAGNONI, MARCO;NOTARI, ROBERTO;ANTONACCI, FABIO;SARTI, AUGUSTO
2016-01-01

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.
2016
Applied algebraic geometry; Kummer’s surfaces; Range maps; Source localization model; Modeling and Simulation; Engineering (all); Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1001754
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