Related papers: Geometric Solution to the Angles-Only Initial Orbi…
We consider the problem of recovering the initial value, from the trace on the light cone, of the solution of an initial value problem for the wave equation. When the space is odd dimensional, we show that the map from the initial value to…
A novel fast multi-impulse optimization method for long-duration perturbed orbit rendezvous is proposed. First, based on the analytically estimated impulses, the terminal rendezvous deviation with precise dynamics model can be predicted.…
We investigate the behaviour of two recent methods for the computation of preliminary orbits. These methods are based on the conservation laws of Kepler's problem, and enable the linkage of very short arcs of optical observations even when…
We present a novel 3D odometry method that recovers the full motion of a vehicle only from a Doppler-capable range sensor. It leverages the radial velocities measured from the scene, estimating the sensor's velocity from a single scan. The…
The existing techniques for measuring high-dimensional pure states of light in the orbital angular momentum (OAM) basis either involve a large number of single-pixel data acquisitions and substantial postselection errors that increase with…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
In this paper, we introduce a novel numerical method for reconstructing the trajectory within three-dimensional space, where both the emission moment and spatial location of the point source are unknown. Our approach relies solely on…
This article is a study about the existence and the uniqueness of solutions of a specific quadratic first-order ODE that frequently appears in multiple reconstruction problems. It is called the \emph{planar-perspective equation} due to the…
A moment approach for orbit determinations of an astrometric binary with low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with a short orbital period such as Cyg-X1 and…
In order to avoid collisions with space debris, the near Earth orbit must be continuously scanned by either ground- or spaced-based facilities. For the low Earth orbit, radar telescopes are the workhorse for this task, especially due to…
We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on…
Monocular 3D object detection is of great significance for autonomous driving but remains challenging. The core challenge is to predict the distance of objects in the absence of explicit depth information. Unlike regressing the distance as…
A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic deviation…
An ortho-radial grid is described by concentric circles and straight-line spokes emanating from the circles' center. An ortho-radial drawing is the analog of an orthogonal drawing on an ortho-radial grid. Such a drawing has an unbounded…
We present the novel concept of an Advanced de-Inclination Device (AID). This technique holds the promise of instantaneously solving almost all issues concerning the observed projection of astronomical sources on the plane of the sky. Along…
Head pose estimation plays a vital role in various applications, e.g., driverassistance systems, human-computer interaction, virtual reality technology, and so on. We propose a novel geometry based algorithm for accurately estimating the…
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…