Related papers: Relativistic Positioning Systems: Numerical Simula…
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic…
This paper delves into critical concepts and meticulous calculations pertinent to Simultaneous Localization and Mapping (SLAM), with a focus on error analysis and Jacobian matrices. We introduce various types of errors commonly encountered…
Satellite tracking involves sending electromagnetic signals to Earth. Both the orbit of the spacecraft and the electromagnetic signals themselves are affected by the curvature of spacetime. The arrival time of the pulses is compared to the…
This paper proposes a sampling-based motion planner that employs a dual quaternion representation to generate smooth, collision-free six-degree-of-freedom pose trajectories for satellite rendezvous and docking under keep-out zone…
This work focuses on the generation of non-self-intersecting relative trajectories, and their applications to satellite constellation design, slotting architectures, and Space Traffic Management. To that end, this paper introduces two…
With the increase in global positioning service demands and the requirement for more precise positioning, assisting existing medium and high orbit satellite-enabled positioning systems with low Earth orbit (LEO) satellites has garnered…
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…
To perform precise and accurate photometric catalogue cross-matches -- assigning counterparts between two separate datasets -- we need to describe all possible sources of uncertainty in object position. With ever-increasing time baselines…
Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here we show that the irregular and…
A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an…
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…
In urban environments, global navigation satellite system (GNSS) positioning is often compromised by signal blockages and multipath effects caused by buildings, leading to significant positioning errors. To address this issue, this study…
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…
We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…
We give a summary of recent results on spatial and velocity biases in cosmological models. Progress in numerical techniques made it possible to simulate halos in large volumes with a such accuracy that halos survive in dense environments of…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and…
The Doppler technique measures the reflex radial motion of a star induced by the presence of companions and is the most successful method to detect exoplanets. If several planets are present, their signals will appear combined in the radial…
The technique of mutual approximations accurately gives the central instant at the maximum apparent approximation of two moving natural satellites in the sky plane. This can be used in ephemeris fitting to infer the relative positions…
State-of-the-art object pose estimation methods are prone to generating geometrically infeasible pose hypotheses. This problem is prevalent in dexterous manipulation, where estimated poses often intersect with the robotic hand or are not…