Related papers: Nonlinear Explicit Stochastic Attitude Filter on S…
This paper studies nonlinear observer design for rigid-body extended pose estimation using inertial measurements and generic exteroceptive sensing. The estimation problem is formulated as a cascade architecture that separates translational…
We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…
Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…
In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon,…
It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to…
This paper presents global tracking strategies for the attitude dynamics of a rigid body. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
This paper addresses the problem of Visual-Inertial Odometry (VIO) for rigid body systems evolving in three-dimensional space. We introduce a novel matrix Lie group structure, denoted SE_{3+n}(3), that unifies the pose, gravity, linear…
This is the last part of four series papers, aiming at stabilization for signal-input-signaloutput (SISO) linear finite-dimensional systems corrupted by general input disturbances. A new observer, referred to as Extended Dynamics Observer…
Despite the numerous applications that may be expeditiously modelled by counting processes, stochastic filtering strategies involving Poisson-type observations still remain somewhat poorly developed. In this work, we propose a Monte Carlo…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a compact and connected matrix Lie group without boundary, e.g. SO(n) and SE(n), in the presence of real-valued observations. This…
In this paper, a new probability distribution, referred to as the matrix Fisher-Gaussian (MFG) distribution, is proposed on the nonlinear manifold $\mathrm{SO}(3)\times\mathbb{R}^n$. It is constructed by conditioning a (9+n)-variate…
Nonlinear pose (\textit{i.e,} attitude and position) filters are characterized with simpler structure and better tracking performance in comparison with other methods of pose estimation. A critical factor when designing a nonlinear pose…
Nonlinear observer design for systems whose state space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…