Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.12328

The Iterative Equivariant Filter

Pieter van Goor·James Richard Forbes
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents the iterative equivariant filter (IterEqF). The iterative extended Kalman filter (IterEKF) replaces the standard EKF correction step with an iterative correction step that is the Gauss-Newton solution to a nonlinear weighted least squares problem. The standard equivariant filter (EqF) exploits and respects the underlying symmetry of state estimation problems posed on homogeneous spaces and Lie groups. The motivation behind the IterEqF is to combine the features of both the IterEKF and the EqF, thus leading to a high-performance state estimation solution that is well suited to navigation problems. This paper derives the iteration procedure for the IterEqF update step and shows how the intrinsic nonlinearity of the approach naturally results in a `reset' of the filter's covariance into new coordinates. Monte-Carlo simulations of range-based localisation for a mobile robot demonstrate the improvement in performance relative to a standard EqF, especially during the transient convergence.

Explore related subjects

eess.SYcs.ROcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pieter van Goor, James Richard Forbes. 2026-09-11. The Iterative Equivariant Filter. https://arxiv.org/abs/2609.12328

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

KEEP EXPLORING

Related papers

arXiv2026

Simultaneous state estimation and control for nonlinear systems subject to bounded disturbances

In this work, we address the output--feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimisation-based problem that simultaneously estimates the state trajectory and computes future control inputs. It minimises a criterion that involves finite backward and forward horizons with respect to the unknown initial state, measurement noises and control input variables.The main novelty of this work relies on linking the lengths of the forward and backward windows with the closed-loop stability, assuming detectability and decoding sufficient conditions to assure system stabilizability. It leads to a formulation that does not require to be a Control Lyapunov Function for the terminal cost of the controller. Simulation examples are carried out to compare the performance of solving simultaneously and independently the estimation and control problems. Furthermore, the examples show how the controller influences the length of the estimation window through its gain.

eess.SY↗
arXiv2026

On finite-horizon approximation of an infinite-horizon feedback Nash equilibrium in discrete-time LQ games

Computing feedback Nash equilibria (FNEs) in infinite-horizon discrete-time linear-quadratic (LQ) dynamic games remains computationally challenging. Inspired by model predictive control (MPC) in single-agent optimal control, we address this challenge with a finite-horizon strategy for approximating one such FNE. The finite-horizon strategy is as follows. Each player $i$ has an individual prediction horizon $T^i$. At each stage, player $i$ envisions an auxiliary $T^i$-stage game, computes its unique FNE, and implements only the first-stage control. Our main results are as follows. First, we give parameter conditions that guarantee geometric convergence of the coupled Riccati iteration to a stabilizing solution. Second, under these conditions, the finite-horizon strategies stabilize the system, and each player's total cost converges to the limiting FNE cost as all prediction horizons tend to infinity. Third, we derive an explicit upper bound on this cost gap that decreases geometrically with the shortest prediction horizon. This bound tells us how long the prediction horizons need to be for a given accuracy. The strategy is tractable and implementable, as it avoids directly solving the coupled algebraic Riccati equations of the infinite-horizon game.

eess.SY↗
arXiv2026

Closed Loop Reference Optimization for Extrusion Additive Manufacturing

Various defects occur during material extrusion additive manufacturing processes that degrade the quality of the 3D printed parts and lead to significant material waste. This motivates feedback control of the extrusion process to mitigate defects and prevent print failure. We propose a linear quadratic regulator (LQR) for closed-loop control with force feedback to provide accurate width tracking of the extruded filament. Furthermore, we propose preemptive optimization of the reference force given to the LQR that accounts for the performance of the LQR and generates the optimal reference for the closed loop extrusion dynamics and machine constraints. Simulation results demonstrate the improved tracking performance and response time. Experiments on a Fused Filament Fabrication 3D printer showcase a root mean square error improvement of 39.57% compared to tracking the unmodified reference as well as an 83.7% shorter settling time.

eess.SY↗