Related papers: A relativistic and autonomous navigation satellite…
Low Earth orbit (LEO) satellite constellations play a pivotal role in sixth-generation (6G) wireless networks by providing global coverage, massive connections, and huge capacity. In this paper, we present a novel LEO satellite…
Global localization is a critical problem in autonomous navigation, enabling precise positioning without reliance on GPS. Modern global localization techniques often depend on dense LiDAR maps, which, while precise, require extensive…
This paper reviews the recent mathematical progresses made on the study of the orbital stability properties for the gravitational Vlasov-Poisson system. We present in details the paper of Lemou, M\'ehats and Rapha\"el (Inventiones 2011) and…
In order to do relativistic gravimetry one needs to define a system of null coordinates for a given constellation of satellites. We present here three methods in order to find the null coordinates of an event in a Schwarzschild geometry. We…
This paper surveys a number of recent developments in modern Global Navigation Satellite Systems (GNSS) and investigates the possible impact on autonomous driving architectures. Modern GNSS now consist of four independent global satellite…
The "Breakthrough Starshot" aims at sending near-speed-of-light cameras to nearby stellar systems in the future. Due to the relativistic effects, a trans-relativistic camera naturally serves as a spectrograph, a lens, and a wide-field…
The Backlund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensional dynamical systems. It has recently been used to study…
As emerging massive constellations are intended to provide seamless connectivity for remote areas using hundreds of small low Earth orbit (LEO) satellites, new methodologies have great importance to study the performance of these networks.…
Natural (such as lunar) occultations have long been used to study sources on small angular scales, while coronographs have been used to study high contrast sources. We propose launching the Big Occulting Steerable Satellite (BOSS), a large…
This article provides a review on X-ray pulsar-based navigation (XNAV). The review starts with the basic concept of XNAV, and briefly introduces the past, present and future projects concerning XNAV. This paper focuses on the advances of…
In a previous paper, using ergodic theory, Lo [1] derived a simple definite integral that provided an estimate of the view periods of ground stations to satellites. This assumes the satellites are in circular orbits with non-repeating…
The recent surge in interest in autonomous driving stems from its rapidly developing capacity to enhance safety, efficiency, and convenience. A pivotal aspect of autonomous driving technology is its perceptual systems, where core algorithms…
Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called "relativistic corrections", computed with the required precision using the Post-(Post-)Newtonian formalism. The current…
R-RoMulOC is a freely distributed toolbox which aims at making easily available to the users different optimization-based methods for dealing with uncertain systems. It implements both deterministic LMI-based results, that provide…
With the rapid expansion of low Earth orbit (LEO) constellations, thousands of satellites are now in operation, many equipped with onboard GNSS receivers capable of continuous orbit determination and time synchronization. This development…
We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…
Satellites are not randomly distributed around their central galaxies but show polar and planar structures. In this paper, we investigate the axis-asymmetry or lopsidedness of satellite galaxy distributions around isolated galaxies in a…
A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time…
Advanced civilizations capable of interstellar travel, if they exist, are likely to have advanced propulsion methods. Spaceships moving at high speeds would leave a particular signature which could be detected from Earth. We propose a…
Recent advances in space technology provide an opportunity for small satellites to be launched in cislunar space. However, tracking these small satellites still depends on ground-based operations. Autonomous navigation could be a possible…