Related papers: Global Positioning on Earth
Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function…
An interstellar communication network benefits from relay nodes placed in the gravitational lenses of stars. The signal gains are of order $10^{9}$ with optimal alignment, allowing for GBits connections at kW power levels with meter-sized…
We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere. However, there exist both special and ordinary central…
The non-linearities of the dynamics of Earth artificial satellites are encapsulated by two formal integrals that are customarily computed by perturbation methods. Standard procedures begin with a Hamiltonian simplification that removes…
Navigation of a mobile robot is conditioned on the knowledge of its pose. In observer-based localisation configurations its initial pose may not be knowable in advance, leading to the need of its estimation. Solutions to the problem of…
This work proposes an adaptation of the Facility Location Problem for the optimal placement of on-orbit servicing depots for satellite constellations in high-altitude orbit. The high-altitude regime, such as Medium Earth Orbit (MEO), is a…
One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…
In object-based Simultaneous Localization and Mapping (SLAM), 6D object poses offer a compact representation of landmark geometry useful for downstream planning and manipulation tasks. However, measurement ambiguity then arises as objects…
Current GNSS systems rely on global reference frames which are fixed to the Earth (via the ground stations) so their precision and stability in time are limited by our knowledge of the Earth dynamics. These drawbacks could be avoided by…
We conduct a systematic survey of the regions in which distant satellites can orbit stably around the four giant planets in the solar system, using orbital integrations of up to $10^9$ yr. In contrast to previous investigations, we use a…
A deterministic attitude estimator for a rigid body under an attitude dependent potential is studied. This estimator requires only a single direction measurement to a known reference point at each measurement instant. The measurement cannot…
We show that the equations underlying the $GW$ approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact,…
Determining the precise geographic location of an image at a global scale remains an unsolved challenge. Standard image retrieval techniques are inefficient due to the sheer volume of images (>100M) and fail when coverage is insufficient.…
Path planning algorithms for unmanned aerial or ground vehicles, in many surveillance applications, rely on Global Positioning System (GPS) information for localization. However, disruption of GPS signals, by intention or otherwise, can…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
In a reference frame fixed to the solar system's center of mass, a satellite's energy will change as it is deflected by a planet. But a number of satellites flying by Earth have also experienced energy changes in the Earth-centered frame --…
The use of four Lagrange points of the Sun/Earth system for fundamental physics experiments in space is presented. L1, L2, L4 and L5 rotating rigidly together with the Earth form a natural reference frame at the scale of the inner solar…
We solve the stabilization problem on the $n-$sphere in the presence of conic constraints. We use the stereographic projection to map this problem to the classical navigation problem on $\mathbb{R}^n$ in the presence of spherical obstacles.…
Positioning problem can be solved with several approaches in 5G. This paper introduces RT (Ray Tracing) technique for small-cell Outdoor positioning and tracking for systems with distributed architecture with multipath processing gain.…
This paper presents a unified theory for the power of a point with respect to generalized spheres (spheres, horospheres, and hyperspheres) in $n$-dimensional hyperbolic space $\mathbf{H}^n$. By extending the classical secant theorem, we…