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2D Triangulation of Signals Source by Pole-Polar Geometric Models

1
Web Engineering and Early Testing (IWT2) research group, Departamento de Lenguajes y Sistemas Informáticos, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Seville, Spain
2
Departamento de Informática Centro de Tecnologia, Universidade Estadual de Maringá, Av. Colombo, 5790 - Jd. Universitário, Maringá 87020-900, Brazil
3
Departamento de Lenguajes y Sistemas Informáticos, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Seville, Spain
*
Author to whom correspondence should be addressed.
Sensors 2019, 19(5), 1020; https://doi.org/10.3390/s19051020
Received: 10 December 2018 / Revised: 18 February 2019 / Accepted: 19 February 2019 / Published: 27 February 2019
(This article belongs to the Special Issue Signal and Information Processing in Wireless Sensor Networks)
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Abstract

The 2D point location problem has applications in several areas, such as geographic information systems, navigation systems, motion planning, mapping, military strategy, location and tracking moves. We aim to present a new approach that expands upon current techniques and methods to locate the 2D position of a signal source sent by an emitter device. This new approach is based only on the geometric relationship between an emitter device and a system composed of m 2 signal receiving devices. Current approaches applied to locate an emitter can be deterministic, statistical or machine-learning methods. We propose to perform this triangulation by geometric models that exploit elements of pole-polar geometry. For this purpose, we are presenting five geometric models to solve the point location problem: (1) based on centroid of points of pole-polar geometry, PPC; (2) based on convex hull region among pole-points, CHC; (3) based on centroid of points obtained by polar-lines intersections, PLI; (4) based on centroid of points obtained by tangent lines intersections, TLI; (5) based on centroid of points obtained by tangent lines intersections with minimal angles, MAI. The first one has computational cost O ( n ) and whereas has the computational cost O ( n l o g n ) where n is the number of points of interest. View Full-Text
Keywords: signal processing; 2D point location; computational geometry; pole-polar geometry signal processing; 2D point location; computational geometry; pole-polar geometry
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MDPI and ACS Style

Montanha, A.; Polidorio, A.M.; Dominguez-Mayo, F.J.; Escalona, M.J. 2D Triangulation of Signals Source by Pole-Polar Geometric Models. Sensors 2019, 19, 1020.

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