The algebro-geometric study of range maps
This work addresses source localization, a critical issue in technologies like radar and sonar, but appears incremental as it focuses on algebraic geometry insights without claiming broad practical improvements.
The paper tackles the problem of localizing a radiant source using range measurements, revealing unexpected connections between the three-receiver case and the geometry of Kummer's and Cayley's surfaces, and provides new insights into range difference-based localization.
Localizing a radiant source is a widespread problem to many scientific and technological research areas. E.g. localization based on range measurements stays at the core of technologies like radar, sonar and wireless sensors networks. In this manuscript we study in depth 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 gives new insights also on the localization based on range differences.