Related papers: The Relativistic framework of Positioning systems
Measurements of the position of a relativistic particle is considered in the framework of the Restricted-Path-Integral (RPI) approach. The amplitude describing such a measurement is shown to be exponentially small outside the light cone of…
The propagation time of a signal, emitted by a moving along an elliptical orbit satellite from the GPS (or GLONASS) satellite confi gurations is a very important ingredient of the theory, based on the formalism of the null cone and…
We discuss a new formalism for light propagation which can be used within the regime of validity of geometric optics, but with no limitation on the scales of interest: from inside the Galaxy to the ultra-large scales of cosmology. One of…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained…
Observing artificial satellites is a relatively new and unique branch of astronomy that is very interesting and dynamic. One specific aspect of observing these objects is that although they appear amongst the celestial background, as…
Trajectory prediction and planning in autonomous driving are highly challenging due to the complexity of predicting surrounding agents' movements and planning the ego agent's actions in dynamic environments. Existing methods encode map and…
All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined like it happens for Fermi coordinates both in special and general relativity. As a consequence, it is not known how…
All experiments to date are in remarkable agreement with the predictions of Einstein's theory of gravity, General Relativity. Besides the classical tests, involving light deflection, orbit precession, signal delay, and the gravitational…
Positioning using Global Navigation Satellite Systems (GNSS) typically requires several seconds of continuous signal reception from satellites in Medium Earth Orbit (MEO). This requirement poses challenges for applications where receivers…
We consider the geometry of four spatial displacements, arranged in cyclic order, such that the relative motion between neighbouring displacements is a pure rotation. We compute the locus of points whose homologous images lie on a circle,…
The irregular satellites of the giant planets are believed to have been captured during the evolution of the solar system. Knowing their physical parameters, such as size, density, and albedo is important for constraining where they came…
Relative localization between autonomous robots without infrastructure is crucial to achieve their navigation, path planning, and formation in many applications, such as emergency response, where acquiring a prior knowledge of the…
We consider a robust and self-reliant (or "egoistic") variation of the rigid body localization (RBL) problem, in which a primary rigid body seeks to estimate the pose (i.e., location and orientation) of another rigid body (or "target"),…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
Global Positioning System (GPS) satellites are essential for providing accurate navigation and timing information worldwide. Operating in medium Earth orbit (MEO), these satellites must maintain precise Earth-pointing attitudes to transmit…
In this work, we use real quaternions and the basic concept of the final speed of light in an attempt to enhance the standard description of special relativity. First, we demonstrate that it is possible to introduce a quaternion time domain…
The relativistic theories of light propagation are generalized by introducing two new parameters $\varsigma$ and $\eta$ in the second post-Newtonian (2PN) order, in addition to the parameterized post-Newtonian parameters $\gamma$ and…
Deviation equation: Second order differential equation for the 4-vector which measures the distance between reference points on neighboring world lines in spacetime manifolds. Relativistic geodesy: Science representing the Earth (or any…
Several space missions that will use atomic clocks on board of an Earth-orbiting satellite are planned for the near future, such as the Atomic Clock Ensemble in Space (ACES) or the Space Optical Clock on the ISS (I-SOC). The increasing…