相关论文: Equivariant filter (EqF): A general filter design …

Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…

In this paper, a self-calibration approach for eye-in-hand robots using SLAM is considered. The goal is to calibrate the positioning of a robotic arm, with a camera mounted on the end-effector automatically using a SLAM-based method like…

Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they…

In this paper we address the inconsistency of the EKF-based SLAM algorithm that stems from non-observability of the origin and orientation of the global reference frame. We prove on the non-linear two-dimensional problem with point…

Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman…

An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an open problem in many cases. In this paper, we observe that…

Consistent localization of cooperative multi-robot systems during navigation presents substantial challenges. This paper proposes a fault-tolerant, multi-modal localization framework for multi-robot systems on matrix Lie groups. We…

A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law…

In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of $n\in\mathbb{N}$ robots in the $\mathcal{OBLOT}$ model and analyze their collective $\mathcal{F}$sync dynamics using of…

In this work, we introduce the Equivariance Seeker Model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances…

Recent work has shown impressive localization performance using only images of ground textures taken with a downward facing monocular camera. This provides a reliable navigation method that is robust to feature sparse environments and…

This paper introduces an innovative approach to Simultaneous Localization and Mapping (SLAM) using the Unscented Kalman Filter (UKF) in a dynamic environment. The UKF is proven to be a robust estimator and demonstrates lower sensitivity to…

Simultaneous localization and mapping (SLAM) is a method that constructs a map of an unknown environment and localizes the position of a moving agent on the map simultaneously. Extended Kalman filter (EKF) has been widely adopted as a low…

Graph-structured data jointly contain discrete topology and continuous geometry, which poses fundamental challenges for generative modeling due to heterogeneous distributions, incompatible noise dynamics, and the need for equivariant…

A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…

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…

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…

This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…

Kalman Filtering problems often have inherent and known constraints in the physical dynamics that are not exploited despite potentially significant gains (e.g., fixed speed of a motor). In this paper, we review existing methods and propose…

This paper proposes a novel approach to improve the performance of the extended Kalman filter (EKF) for the problem of mobile robot localization. A fuzzy logic system is employed to continuous-ly adjust the noise covariance matrices of the…