Related papers: Dual Quaternion SE(3) Synchronization with Recover…
The control of free-floating robots requires dealing with several challenges. The motion of such robots evolves on a continuous manifold described by the Special Euclidean Group of dimension 3, known as SE(3). Methods from finite horizon…
Vision-based 3D human motion capture from videos remains a challenge in computer vision. Traditional 3D pose estimation approaches often ignore the temporal consistency between frames, causing implausible and jittery motion. The emerging…
The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles $\theta_1,...,\theta_n$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \mod 2\pi$. Of…
This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the tracking error of the normalized Euclidean distance meeting predefined transient and…
This work investigates Bayesian stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation. While asymptotic analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum…
Nowadays, we have seen that dual quaternion algorithms are used in 3D coordinate transformation problems due to their advantages. 3D coordinate transformation problem is one of the important problems in geodesy. This transformation problem…
Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…
Three-dimensional (3D) Ultrasound (US) can facilitate diagnosis, treatment planning, and image-guided therapy. However, current studies rarely provide a comprehensive evaluation of volumetric accuracy and reproducibility, highlighting the…
This paper investigates the problem of pose synchronization for multiple rigid body systems evolving on the matrix Lie group $\SE(3)$. We propose a distributed hybrid feedback control scheme with global asymptotic stability guarantees using…
This paper addresses the problem of motion synchronization (or averaging) and describes a simple, closed-form solution based on a spectral decomposition, which does not consider rotation and translation separately but works straight in…
Quaternion kinematical differential equation (QKDE) plays a key role in navigation, control and guidance systems. Although explicit symplectic geometric algorithms (ESGA) for this problem are available, there is a lack of a unified way for…
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and…
Due to its significance as a subroutine, in this work, we consider the coherent version of the quantum phase estimation problem, where given an arbitrary input state and black-box access to unitaries $U$ and controlled-$U$, the goal is to…
Rotation group $\mathcal{SO}(d)$ synchronization is an important inverse problem and has attracted intense attention from numerous application fields such as graph realization, computer vision, and robotics. In this paper, we focus on the…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Dynamical decoupling is a long-established and effective way to suppress unwanted interactions in qubit systems, enabling advances in fields ranging from quantum metrology to quantum computing. For general qudit systems, however, comparable…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…