Related papers: On Deterministic Attitude Observers on the Special…
In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in…
This technical note aims to introduce geometric controllers to roboticists for aligning \emph{3D robots} with non-constant 3D vector fields. This alignment entails the control of the robot's 3D attitude. We derive with excessive detail all…
We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields…
This article presents an extended state observer for vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The extended state observer is applicable to a rotorcraft aerial vehicle with a fixed plane of…
Smoothing is a specialized form of Bayesian inference for state-space models that characterizes the posterior distribution of a collection of states given an associated sequence of observations. Ramgraber et al. (2023) proposes a general…
In this paper we propose a novel method for estimating rigid body motion by modeling the object state directly in the space of the rigid body motion group SE(2). It has been recently observed that a noisy manoeuvring object in SE(2)…
We derive an exact deterministic nonlinear observer to compute the continuous state of an inertial navigation system based on partial discrete measurements, the so-called strapdown problem. Nonlinear contraction is used as the main analysis…
In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…
This article presents a tracking control framework enhanced by an extended state observer for a rotorcraft aerial vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The system is considered as an…
Motivated by drone autonomous navigation applications we address a novel problem of velocity-aided attitude estimation by combining two linear velocity components measured in a body-fixed frame and a linear velocity component measured in an…
This report proposes a discrete time observer for the continuous time rigid body kinematics on the rotation group $\mathbb{S}\mathbb{O}(3)$. The work draws on two research schools - one by Chang based on feedback integrators for systems…
Inertial-based navigation refers to the navigation methods or systems that have inertial information or sensors as the core part and integrate a spectrum of other kinds of sensors for enhanced performance. Through a series of papers, the…
Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in interesting and complicated nonlinear dynamics when studying…
We introduce the first direct policy search algorithm which provably converges to the globally optimal $\textit{dynamic}$ filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial…
We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to…
This work is concerned with robust filtering of nonlinear sampled-data systems with and without exact discrete-time models. A linear matrix inequality (LMI) based approach is proposed for the design of robust $H_{\infty}$ observers for a…
This paper presents a novel cascade nonlinear observer framework for inertial state estimation. It tackles the problem of intermediate state estimation when external localization is unavailable or in the event of a sensor outage. The…
Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coarse (uniform noise). The expected smoothness (ES) condition…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…