Related papers: Global Positioning: the Uniqueness Question and a …
This paper describes an investigation of the source of geospatial error in digital surface models (DSMs) constructed from multiple satellite images. In this study the uncertainty in surface geometry is separated into two spatial components;…
Satellite imagery solutions are widely used to study and monitor different regions of the Earth. However, a single satellite image can cover only a limited area. In cases where a larger area of interest is studied, several images must be…
We introduce a new concept -- termed "planarity" -- which aims to quantify planar structure in galaxy satellite systems without recourse to the number or thickness of planes. We use positions and velocities from the Gaia EDR3 to measure…
The goal of this paper is to estimate directly the rotation and translation between two stereoscopic images with the help of five homologous points. The methodology presented does not mix the rotation and translation parameters, which is…
Standalone Global Navigation Satellite Systems (GNSS) are known to provide positioning accuracy of a few meters in open sky conditions. This accuracy can drop significantly when the line-of-sight (LOS) paths to some GNSS satellites are…
The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…
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…
This paper addresses the question: how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of N, n, m are…
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 consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the…
The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…
Studied here is the effect of the presence of symmetry groups in a system of algebraic equations on the numerical resolution with fixed-point algorithms. It is proved that the symmetries imply two important properties of the system: the…
The algebraic geometry of a universal algebra $\mathbf{A}$ is defined as the collection of solution sets of term equations. Two algebras $\mathbf{A}_1$ and $\mathbf{A}_2$ are called algebraically equivalent if they have the same algebraic…
This paper is dedicated to the global well-posedness issue of the compressible Oldroyd-B model in the whole space $\R^d$ with $d\ge2$. It is shown that this set of equations admits a unique global solution in a certain critical Besov space…
A linearly constrained framework in $\mathbb{R}^d$ is a point configuration together with a system of constraints which fixes the distances between some pairs of points and additionally restricts some of the points to lie in given affine…
The problem of uniqueness of universal formulae for (quantum) dimensions of simple Lie algebras is investigated. We present generic functions, which multiplied by a universal (quantum) dimension formula, preserve both its structure and its…
We propose an approach to estimate the 6DOF pose of a satellite, relative to a canonical pose, from a single image. Such a problem is crucial in many space proximity operations, such as docking, debris removal, and inter-spacecraft…
Motivated by secure wireless networking, we consider the problem of placing fixed localizers that enable mobile communication devices to prove they belong to a secure region that is defined by the interior of a polygon. Each localizer views…