Related papers: Subspace Tracking with Dynamical Models on the Gra…

In this paper, a robust RGB-D SLAM system is proposed to utilize the structural information in indoor scenes, allowing for accurate tracking and efficient dense mapping on a CPU. Prior works have used the Manhattan World (MW) assumption to…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…

This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is…

When robots are able to see and respond to their surroundings, a whole new world of possibilities opens up. To bring these possibilities to life, the robotics industry is increasingly adopting camera-based vision systems, especially when a…

We introduce a method for constructing reduced-order models directly from videos of dynamical systems. The method uses a non-intrusive tracking to isolate the motion of a user-selected part in the video of an autonomous dynamical system. In…

This letter presents a versatile trajectory planning pipeline for aerial tracking. The proposed tracker is capable of handling various chasing settings such as complex unstructured environments, crowded dynamic obstacles and multiple-target…

A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise in the form of Krylov subspaces in matrix…

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance…

In this paper, we develop an algorithm for joint handover and beam tracking in millimeter-wave (mmWave) networks. The aim is to provide a reliable connection in terms of the achieved throughput along the trajectory of the mobile user while…

This paper proposes the use of subspace tracking algorithms for performing MIMO channel estimation at millimeter wave (mmWave) frequencies. Using a subspace approach, we develop a protocol enabling the estimation of the right (resp. left)…

Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to reduce the computational costs and preserve the benign…

Autonomous agents rely on sensor data to construct representations of their environments, essential for predicting future events and planning their actions. However, sensor measurements suffer from limited range, occlusions, and sensor…

This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…

In this paper, we introduce a novel method to capture visual trajectories for navigating an indoor robot in dynamic settings using streaming image data. First, an image processing pipeline is proposed to accurately segment trajectories from…

There is extensive literature on accelerating first-order optimization methods in a Euclidean setting. Under which conditions such acceleration is feasible in Riemannian optimization problems is an active area of research. Motivated by the…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

Tracking algorithms such as the Kalman filter aim to improve inference performance by leveraging the temporal dynamics in streaming observations. However, the tracking regularizers are often based on the $\ell_p$-norm which cannot account…

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…

We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions…