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In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group affine and…

Robotics · Computer Science 2023-01-23 Lubin Chang

The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…

Numerical Analysis · Mathematics 2022-02-17 Dieter Armbruster , Michael Herty , Giuseppe Visconti

The ensemble Kalman filter (EnKF) has become a standard methodology for state estimation in high-dimensional systems, yet its various stochastic and deterministic formulations often appear conceptually disconnected. In this paper, a unified…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Jin Won Kim

This paper addresses the challenges in learning-based monocular positioning by proposing VKFPos, a novel approach that integrates Absolute Pose Regression (APR) and Relative Pose Regression (RPR) via an Extended Kalman Filter (EKF) within a…

Computer Vision and Pattern Recognition · Computer Science 2025-02-03 Jian-Yu Chen , Yi-Ru Chen , Yin-Qiao Chang , Che-Ming Li , Jann-Long Chern , Chih-Wei Huang

This paper proposes an $SE_2(3)$ based extended Kalman filtering (EKF) framework for the inertial-integrated state estimation problem. The error representation using the straight difference of two vectors in the inertial navigation system…

Robotics · Computer Science 2021-03-15 Yarong Luo , Chi Guo , Shengyong You , Jianlang Hu , Jingnan Liu

The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…

Numerical Analysis · Mathematics 2022-07-27 Neil K. Chada

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…

Machine Learning · Computer Science 2023-02-01 Ashesh Chattopadhyay , Ebrahim Nabizadeh , Eviatar Bach , Pedram Hassanzadeh

An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector) which assigns importance weights to describe non-Gaussian distribution. The weights are obtained by…

Computation · Statistics 2009-07-20 Jan Mandel , Jonathan D. Beezley

The phase-field approach to brittle fracture provides a continuum framework for modeling crack initiation and propagation without explicit representation of discrete crack surfaces, provided the spatial discretization is fine enough to…

Computational Engineering, Finance, and Science · Computer Science 2026-03-11 Lucas Hermann , Ralf Jänicke , Knut Andreas Meyer , Ulrich Römer

Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…

Robotics · Computer Science 2023-10-04 Xiaoyu Ye , Fujun Song , Zongyu Zhang , Rui Zhang , Qinghua Zeng

Autonomous surface vessels (ASVs) are increasingly vital for marine science, offering robust platforms for underwater mapping and inspection. Accurate state estimation, particularly of vehicle pose, is paramount for precise seafloor…

Robotics · Computer Science 2025-06-13 Derek Benham , Easton Potokar , Joshua G. Mangelson

This paper illustrates the way for estimating position and orientation of a vehicle with an Extended Kalman Filter (EKF). For this purpose a non-linear model is designed and an adaptive calculation of measurement noise covariance matrix is…

Systems and Control · Electrical Eng. & Systems 2021-08-26 Reiner Marchthaler

Millimeter-wave (mmWave) communication is a promising technology to meet the ever-growing data traffic of vehicular communications. Unfortunately, more frequent channel estimations are required in this spectrum due to the narrow beams…

Signal Processing · Electrical Eng. & Systems 2019-11-06 Sina Shaham , Matthew Kokshoorn , Ming Ding , Zihuai Lin , Mahyar Shirvanimoghaddam

In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…

Numerical Analysis · Mathematics 2024-09-26 Simon Weissmann , Neil K. Chada , Xin T. Tong

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…

Numerical Analysis · Mathematics 2022-04-06 Michael Herty , Elisa Iacomini , Giuseppe Visconti

This paper describes a novel method for the estimation of the trajectory curve and orientation of a rigid body moving along a railway track. Compared to other recent developments in the literature, the presented approach has the significant…

Computational Engineering, Finance, and Science · Computer Science 2022-03-15 J. González-Carbajal , Pedro Urda , Sergio Muñoz , José L. Escalona

In millimeter-wave (mmWave) systems, beamforming is needed to overcome harsh channel environments. As a promising beamforming solution, lens antenna array (LAA) implementation can provide a cost-effective solution without notable…

Signal Processing · Electrical Eng. & Systems 2020-11-03 Liza Afeef , Murat Karabacak , Hüseyin Arslan

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…

Machine Learning · Computer Science 2026-04-30 Xin T. Tong , Yanyan Wang , Liang Yan

Several variations of the Kalman filter algorithm, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in science and engineering applications. In this paper, we introduce two algorithms of…

Optimization and Control · Mathematics 2018-10-11 Wei Kang , Liang Xu

In this paper, we consider the collaborative attitude estimation problem for a multi-agent system. The agents are equipped with sensors that provide directional measurements and relative attitude measurements. We present a bottom-up…

Systems and Control · Electrical Eng. & Systems 2024-07-23 Yixiao Ge , Behzad Zamani , Pieter van Goor , Jochen Trumpf , Robert Mahony