Related papers: Localization from Pseudoranges: Quadrics and Duali…
We study obstructed deformation problems for two-dimensional residual Galois representations arising from weight~$2$ newforms of level~$N$. Using Poitou-Tate duality, we isolate local and global sources of obstructions and give concrete…
We consider the sensor network localization problem, which is closely related to multidimensional scaling and Euclidean distance matrix completion. Given a ground truth configuration of $n$ points in $\mathbb{R}^\ell$, we observe a subset…
The location determination in obstructed area can be very challenging especially if Global Positioning System are blocked. Users will find it difficult to navigate directly on-site in such condition, especially indoor car park lot or…
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…
Worldwide image geo-localization aims to infer the geographic location of an image captured anywhere on Earth, spanning street, city, regional, national, and continental scales. Existing methods rely on visual features that are sensitive to…
The localization problem in a wireless sensor network is to determine the coordination of sensor nodes using the known positions of some nodes (called anchors) and corresponding noisy distance measurements. There is a variety of different…
This paper proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally…
We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem…
Planar markers are useful in robotics and computer vision for mapping and localisation. Given a detected marker in an image, a frequent task is to estimate the 6DOF pose of the marker relative to the camera, which is an instance of planar…
The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities…
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…
Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal…
We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing)…
LiDAR-based localization serves as a critical component in autonomous systems, yet existing approaches face persistent challenges in balancing repeatability, accuracy, and environmental adaptability. Traditional point cloud registration…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with $\ell_\tau$-norms proposing two different methodologies: 1) by a new second order cone mixed…
Re-localizing a camera from a single image in a previously mapped area is vital for many computer vision applications in robotics and augmented/virtual reality. In this work, we address the problem of estimating the 6 DoF camera pose…
This paper presents a method for motion planning under uncertainty to deal with situations where ambiguous data associations result in a multimodal hypothesis on the robot state. In the global localization problem, sometimes referred to as…
In many applications of autonomous mobile robots the following problem is encountered. Two maps of the same environment are available, one a prior map and the other a sensor map built by the robot. To benefit from all available information…
This paper discusses consistent flag bicolorings of maps and maniplexes, in their own right and as generalizations of orientations and pseudo-orientations. Furthermore, a related doubling concept is introduced, and relationships between…