English
Related papers

Related papers: Attitude Quaternion Estimation Using a Spectral Pe…

200 papers

This paper introduces a novel idea for representation of individuals using quaternions in swarm intelligence and evolutionary algorithms. Quaternions are a number system, which extends complex numbers. They are successfully applied to…

Neural and Evolutionary Computing · Computer Science 2013-06-11 Iztok Fister , Iztok Fister

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

Optimization and Control · Mathematics 2023-06-05 Hongyi Li , Zhen Peng , Chengwei Pan , Di Zhao

We consider the problem of distributed attitude estimation of multi-agent systems, evolving on $SO(3)$, relying on individual angular velocity and relative attitude measurements. The interaction graph topology is assumed to be an undirected…

Systems and Control · Electrical Eng. & Systems 2024-05-17 Mouaad Boughellaba , Abdelhamid Tayebi

A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…

Optimization and Control · Mathematics 2026-03-17 Haoming Shen , Yang Zeng , Baoyu Zhou

The hand-eye calibration problem is an important application problem in robot research. Based on the 2-norm of dual quaternion vectors, we propose a new dual quaternion optimization method for the hand-eye calibration problem. The dual…

Robotics · Computer Science 2022-09-19 Zhongming Chen , Chen Ling , Liqun Qi , Hong Yan

This paper addresses the global exponential attitude tracking of a spacecraft when gyro measurements are corrupted by bias. Based on contraction analysis, an exponentially convergent nonlinear observer is designed first to estimate the gyro…

Systems and Control · Electrical Eng. & Systems 2020-07-09 Eduardo Espíndola-López , Yu Tang Xu

Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…

Numerical Analysis · Mathematics 2016-11-16 Silvia Noschese , Lothar Reichel

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…

Machine Learning · Statistics 2021-10-26 Yuxin Chen , Yuejie Chi , Jianqing Fan , Cong Ma

Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET…

Image and Video Processing · Electrical Eng. & Systems 2023-06-09 Tin Vlašić , Tomislav Matulić , Damir Seršić

Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…

Computer Vision and Pattern Recognition · Computer Science 2025-06-16 Yinlong Liu , Tianyu Huang , Zhi-Xin Yang

We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…

Statistics Theory · Mathematics 2025-07-11 Yihan Zhang , Hong Chang Ji , Ramji Venkataramanan , Marco Mondelli

The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix…

Numerical Analysis · Mathematics 2024-03-01 Peng-Ling Wu , Kit Ian Kou , Hongmin Cai , Zhaoyuan Yu

We address several estimation problems in quantum optics by means of the maximum-likelihood principle. We consider Gaussian state estimation and the determination of the coupling parameters of quadratic Hamiltonians. Moreover, we analyze…

Quantum Physics · Physics 2009-11-06 G. Mauro D'Ariano , Matteo G. A. Paris , Massimiliano F. Sacchi

In this paper we present several additions to the quaternion QR algorithm, including algorithms for eigenvector computation and eigenvalue reordering. A key outcome of the eigenvalue reordering algorithm is that the aggressive early…

Numerical Analysis · Mathematics 2025-11-05 Zhigang Jia , Meiyue Shao , Yanjun Shao

This paper presents a numerical algorithm for computing 6-degree-of-freedom free-final-time powered descent guidance trajectories. The trajectory generation problem is formulated using a unit dual quaternion representation of the rigid body…

Optimization and Control · Mathematics 2020-09-01 Taylor P. Reynolds , Michael Szmuk , Danylo Malyuta , Mehran Mesbahi , Behcet Acikmese , John M. Carson

Recently, deep space exploration, especially focusing on halo orbits, the periodic orbits of the Moon, has been widely studied. The spacecraft in halo orbits performs periodic orbital motion, which affects the attitude motion by periodic…

Earth and Planetary Astrophysics · Physics 2025-05-02 Yuta Hayashi , Mai Bando , Shinji Hokamoto

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…

Optimization and Control · Mathematics 2016-04-05 Patrick Holmes , Shreyas Kousik , Shankar Mohan , Ram Vasudevan

We present two quaternion-based sliding variables for controlling the orientation of a manipulator's end-effector. Both sliding variables are free of singularities and represent global exponentially convergent error dynamics that do not…

Robotics · Computer Science 2024-12-30 Brett T. Lopez , Jean-Jacques Slotine

From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

Numerical Analysis · Mathematics 2025-10-20 Veit Elser