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 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 and whereas has the computational cost where is the number of points of interest.
Highlights
Signals can be of various natures, including sound waves, visible and non-visible light, or other electromagnetic spectrum energies
Three experimental cases are chosen to show the results produced by the application of the proposed geometric models: (1) one that produces the worst result; (2) one that produces result with intermediate precision; and (3) one that generates more accurate result
Three experimental cases are chosen to show the results produced by the application of the CHC—Convex Hull Centroid Model
Summary
Signals can be of various natures, including sound waves, visible and non-visible light, or other electromagnetic spectrum energies (radio waves or radar waves, for instance). The position of a signal emitter or receiver device can be estimated (located) by triangulating the signal data that it sends/acquires. The signal data comprise: the nature of the own signal (as light (electromagnetic energy), sound and vibration); its intrinsic attributes (such as power, frequency, and amplitude); its extrinsic attributes (as the time when the signal arrives at each particular receiver; the strength and the propagation angle of a signal acquired at each particular receiver). We propose to perform this triangulation by geometric models that explore elements of pole-polar geometry. We are presenting five geometric models to solve the point location problem: (1) based on centroid of a set of polar-points (PPC); (2) based on a convex hull region defined by a set of interest
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