Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2209.03564

Constructive Equivariant Observer Design for Inertial Velocity-Aided Attitude

Pieter van Goor·Tarek Hamel·Robert Mahony
View original source ↗Read source document ↗Export metadata ↓

Abstract

Inertial Velocity-Aided Attitude (VAA), the estimation of the velocity and attitude of a vehicle using gyroscope, accelerometer, and inertial-frame velocity (e.g. GPS velocity) measurements, is an important problem in the control of Remotely Piloted Aerial Systems (RPAS). Existing solutions provide limited stability guarantees, relying on local linearisation, high gain design, or assuming specific trajectories such as constant acceleration of the vehicle. This paper proposes a novel non-linear observer for inertial VAA with almost globally asymptotically and locally exponentially stable error dynamics. The approach exploits Lie group symmetries of the system dynamics to construct a globally valid correction term. To the authors' knowledge, this construction is the first observer to provide almost global convergence for the inertial VAA problem. The observer performance is verified in simulation, where it is shown that the estimation error converges to zero even with an extremely poor initial condition.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pieter van Goor, Tarek Hamel, Robert Mahony. 2026-01-16. Constructive Equivariant Observer Design for Inertial Velocity-Aided Attitude. https://doi.org/10.1016/j.ifacol.2023.02.059

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Observability and parameter estimation of a generic model for aggregated distributed energy resources

We propose a novel framework for estimating the parameters of an aggregated distributed energy resources (DER A) model. First, we introduce a rigorous method to determine whether all model parameters are estimable. When they are not, our approach identifies the subset of parameters that can be estimated. The proposed framework offers new insights into the number and specific parameters that can be reliably estimated based on commonly available measurements. It also highlights the limitations of calibrating such models. Second, we introduce a Kalman filtering method to calibrate the DER A model. Since we account for nonlinear effects such as saturation and deadbands, we develop a specific mechanism to handle smoothing functions within the Kalman filter. Specifically, we consider the extended and the unscented Kalman filter. We demonstrate the effectiveness of the proposed framework on a modified IEEE 34-node distribution feeder with inverter- based resources. Our findings align with the North American Electric Reliability Corporation's parameterization guideline and underscore the importance of model calibration in accurately capturing the collective dynamics of distributed energy resources installed on distribution systems.

eess.SY↗
arXiv2026

Salted Fisher Information for Hybrid Systems

Discrete events change how parameter-influence propagates in hybrid systems. Prevailing Fisher information for- mulations assume that sensitivities evolve smoothly according to continuous-time variational equations and therefore neglect the sensitivity updates induced by discrete events. This paper derives a Fisher information matrix formulation compatible with hybrid systems. To do so, we use the saltation matrix, which encodes the first-order transformation of sensitivities induced by discrete events. We call the resulting formulation the salted Fisher information matrix (SFIM). The proposed framework unifies continuous information accumulation during flows with discrete updates at event times. We also show that hybrid persistence of excitation is sufficient for the SFIM to be positive definite

eess.SY↗
arXiv2026

Min-Max Grassmannian Optimization for Online Subspace Tracking

We propose GeRoST (Geometrically Robust Subspace Tracking), an online subspace tracking algorithm that models uncertainty in a subspace using a Grassmannian ball. We derive an exact scalar dual for the worst-case subspace problem, establish conditions for a unique worst-case subspace and a Riemannian gradient, and characterize the minimum radius needed to cover a dimensional extension of the target subspace. Each update uses either a spectral direction computed in a reduced subspace or the gradient of the window reconstruction loss. Our numerical experiments show that GeRoST achieves lower mean post-fault prediction error than GREAT in system identification. In video separation, it achieves higher precision and a better precision--recall balance, as measured by the F$_1$ score, than both GREAT and GRASTA at the reported thresholds, with lower recall and longer runtime.

eess.SY↗