Related papers: Global Positioning on Earth
We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This…
This paper gives a complete description of the solutions of the global positioning problem, emphasizing the under-determined case. We show that the solutions form a quadric, which may degenerate in various ways. Perhaps more surprisingly,…
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true…
Global navigation satellite systems use appropriate satellite constellations to get the coordinates of an user -close to Earth- in an almost inertial reference system. We have simulated both GPS and GALILEO constellations. Uncertainties in…
In the context of relativistic positioning, the coordinates of a given user may be calculated by using suitable information broadcast by a 4-tuple of satellites. Our 4-tuples belong to the Galileo constellation. Recently, we estimated the…
Source localization is widely used in many areas including GPS, but the influence of possible noises is not so negligible. Many optimization methods are attempted to alleviate different kinds of noises. Needless to say the stability of the…
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…
The Global Positioning System (GPS) is a U.S. space-based radionavigation system that provides reliable positioning, navigation, and timing services to civilian users on a continuous worldwide basis -- freely available to all. GPS provides…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
Modern global navigation satellite system receivers can access signals from several satellite constellations (including GPS, GLONASS, Galileo, BeiDou). Once these constellations are all fully operational, a typical receiver can expect to…
Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be…
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating…
Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can…
The five libration points of a sun-planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent…
In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how to configure 5 points on a sphere such that the mutual distance sum attains the maximum. It is conjectured that the sum of distances is…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
This work focuses on the study of the reconfiguration strategies available for uniformly distributed satellite constellations and slotting architectures. Particularly, this manuscript deals with the cases of reducing, maintaining, and also…
We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a space-time around Earth, described by a perturbed…
The project SYPOR wishes to use the global navigation satellite system GALILEO as an autonomous relativistic positioning system for the Earth. Motivations and a sketch of the basic concepts underlying the project are presented. For non…
If $G$ is a graph, then $X\subseteq V(G)$ is a general position set if for every two vertices $v,u\in X$ and every shortest $(u,v)$-path $P$, it holds that no inner vertex of $P$ lies in $X$. In this note we propose three algorithms to…