Related papers: Global Positioning on Earth
Using ideas of sphere packing problem we estimate the number of solid moons that can be packed inside the Earth, assuming that both the Moon and the Earth are perfect sphere.
We consider the 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative…
A general position set S is a set S of vertices in G(V,E) such that no three vertices of S lie on a shortest path in G. Such a set of maximum size in G is called a gpset of G and its cardinality is called the gp-number of G denoted by…
The characterization of global solutions to the obstacle problems in $\mathbb{R}^N$, or equivalently of null quadrature domains, has been studied over more than 90 years. In this paper we give a conclusive answer to this problem by proving…
Global mobile robot localization is the problem of determining a robot's pose in an environment, using sensor data, when the starting position is unknown. A family of probabilistic algorithms known as Monte Carlo Localization (MCL) is…
Satellite imagery solutions are widely used to study and monitor different regions of the Earth. However, a single satellite image can cover only a limited area. In cases where a larger area of interest is studied, several images must be…
This paper considers the localization problem in a 5G-aided global navigation satellite system (GNSS) based on real-time kinematic (RTK) technique. Specifically, the user's position is estimated based on the hybrid measurements, including…
We solve the problem of determining the pose of known shapes in $\mathbb{R}^3$ from their unoccluded silhouettes. The pose is determined up to global optimality using a simple yet under-explored property of the area-of-silhouette: its…
A flat Universe model supported by recent observations has 18 possible choices for its overall topology. To detect or exclude these possibilities is one of the most important tasks in modern cosmology, but it has been very difficult for…
A fundamental assumption in the so-called "global polytropic model" is hydrostatic equilibrium for a system of planets or statellites. By solving the Lane-Emden differential equation for such a system in the complex plane, we find…
In this paper, we study the global well-posedness and scattering of 3D defocusing, cubic Schr\"odinger equation. Recently, Dodson [arXiv:2004.09618] studied the global well-posedness in a critical Sobolev space $\dot{W}^{11/7,7/6}$. In this…
The location determination in obstructed area can be very challenging especially if Global Positioning System are blocked. Users will find it difficult to navigate directly on-site in such condition, especially indoor car park lot or…
It is well known that the P3P problem could have 1, 2, 3 and at most 4 positive solutions under different configurations among its 3 control points and the position of the optical center. Since in any real applications, the knowledge on the…
Low Earth orbit (LEO) satellites offer a promising alternative to global navigation satellite systems for precise positioning; however, their relatively low altitudes make them more susceptible to orbital perturbations, which in turn…
Satellite imagery is increasingly used to complement traditional data collection approaches such as surveys and censuses across scientific disciplines. However, we ask: Do all places on earth benefit equally from this new wealth of…
Let $X$ be a vertex subset of a graph $G$. Then $u, v\in V(G)$ are $X$-positionable if $V(P)\cap X \subseteq \{u,v\}$ holds for any shortest $u,v$-path $P$. If each two vertices from $X$ are $X$-positionable, then $X$ is a general position…
We present a novel technique to estimate the 6D pose of objects from single images where the 3D geometry of the object is only given approximately and not as a precise 3D model. To achieve this, we employ a dense 2D-to-3D correspondence…
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…
Global Navigation Satellite Systems (GNSS)-based positioning plays a crucial role in various applications, including navigation, transportation, logistics, mapping, and emergency services. Traditional GNSS positioning methods are…
Relativistic positioning systems are interesting {\em technical objects} for applications around the Earth and in the Solar system. But above all else, they are basic {\em scientific objects} allowing developing relativity from its own…