Invariant EKF

EKF: Extended Kalman Filter

Ask about this topic

Momentum

1 paper in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28
View on map

Latest papers 10

All topics
CardsList
Sep 25, 2026cs.RO

Accuracy Evaluation of INS/ZUPT Filtering Methods Based on Different Geometric Error Definitions

Geometric filters have recently been introduced to improve the accuracy and consistency of inertial-based integrated navigation systems. Error states were defined through specific group operations, introducing state correlations in error definition, which were lacked in the additive error used by a conventional indirect Kalman filter. The desirable consistent filtering models can be obtained based on specific geometric errors. For zero-velocity measurements expressed in the reference frame, this paper derives left-error process and measurement models from invariant filtering, two-frame-group filtering, and equivariant filtering. Importantly, a new group operation is introduced for the left tangent-group equivariant error. The analysis shows that the two-frame-group invariant extended Kalman filter (TFG-IEKF) and the tangent-group equivariant filter (TG-EqF) do not offer a significant consistency advantage over the invariant extended Kalman filter (IEKF). Experiments with an INS/ZUPT measurement system show that, under small initial attitude errors, the conventional indirect extended Kalman filter (EKF) achieves loop-closure position errors below 0.1%0.1\% of the traveled distance, while the three geometric filters achieve comparable positioning accuracy.

Wei Ouyang, Jiale Han, Yarong Luo +1

School of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China · School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai 200240, China · School of Robotics, Wuhan University, Wuhan 430072, China

Invariant EKFInertial Navigation
AskPDF
Aug 3, 2026cs.RO

Residual-Based Adaptive Kalman Filtering for Legged Robot State Estimation

State estimation is a key component in model-based control of walking robots and, more broadly, applicable wherever hidden variables must be inferred. The Kalman filter is widely used to estimate floating-base position and velocity by fusing multiple sensing modalities. However, tuning noise parameters is challenging and typically requires expert knowledge. Moreover, fixed noise parameters are unsuitable for varying gaits and environments. We propose an online adaptation strategy for the process noise covariance matrix Q and the measurement noise covariance matrix R. Specifically, we introduce a filter residual and innovation-based covariance adaptation method for legged robot state estimation and evaluate it against a baseline approach relying on IMU and foot force measurements. The proposed adaptation is implemented within an Invariant Extended Kalman Filter (InEKF) fusing IMU and leg kinematics. Experiments on indoor and outdoor datasets with a Unitree Go2 quadruped show that adapting R is sufficient and improves accuracy by 25% for the trotting gait compared to the fixed-tuned InEKF. Finally, the proposed residual-based adaptation achieves comparable performance to the foot force approach, without requiring foot force measurements or additional parameter tuning.

Mihaela Popescu, Dennis Mronga, Shivesh Kumar +1

Legged RoboticsKalman FilteringEnsemble Kalman FilteringRobot State EstimationInvariant EKFMultimodal Sensor Fusion
AskPDF
Jul 3, 2026cs.RO

Derivations of Error-State Kalman Filter Kinematics for Globally Applicable Aided Inertial Navigation Systems

Global navigation systems require state estimation algorithms that handle Earth's curvature, Earth's rotation, and gravitational variations. These factors can typically be neglected in local navigation algorithms for robots, drones, etc. In classical error-state Kalman Filtering (ESKF) the error state dynamics are trajectory-dependent. Invariant ESKFs utilize Lie Group symmetries to represent the error, which can render error propagation trajectory-independent for group-affine systems. Choosing between a standard filter (where position and velocity errors are defined additively in the navigation frame), a left-invariant filter (where errors are represented in the body frame) and a right-invariant filter (where errors are represented in the navigation/world frame) depends on system dynamics and sensor configuration. This note presents the mathematical formulas for four classical and invariant ESKFs for globally applicable aided inertial navigation systems. It is intended to serve as a systematic reference for comparison and implementation.

Antonia Hager, Torleiv H. Bryne

Airbus Central Research and Technology, Taufkirchen, Germany · Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway

Kalman FilteringLie Group MethodsInvariant EKFInertial Navigation
AskPDF
Jun 30, 2026cs.RO

Iterated Invariant EKF for 3D Landmark-Aided Inertial Navigation

Inertial navigation systems aided by three-dimensional landmark measurements constitute a fundamental problem in robotic perception and state estimation. Classical SO(3)-based Extended Kalman Filter (SO(3)-EKF) approaches provide practical solutions, but suffer from the false observability problem, in which the filter becomes overconfident in unobservable directions, leading to degraded estimation performance. The Invariant EKF (IEKF) addresses this limitation by reformulating the system dynamics as a group-affine system on a Lie group, although its measurement update does not fully satisfy certain state compatibility properties. More recently, the Iterated Invariant EKF (IterIEKF) was proposed to further improve the IEKF by ensuring, in the low-noise regime, that the estimated state remains on the observed state manifold while the uncertainty is confined to its tangent space. In this work, we formulate and apply the IterIEKF to landmark-based inertial 3D localization for the first time. Through numerical simulations, we show that the proposed approach outperforms the classical SO(3)-EKF, the Iterated SO(3)-EKF, and the IEKF in terms of both estimation accuracy and consistency.

Hilton Marques Souza Santana, João Carlos Virgolino Soares, Marco Antonio Meggiolaro

Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil · Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia, Genova, Italy

Invariant EKFInertial Navigation
AskPDF
Jun 23, 2026cs.RO

Invariant Kalman filtering for extended pose estimation in multi-IMU articulated rigid-body systems

Accurate extended pose estimation (orientation, velocity, and position) for IMU-instrumented articulated rigid-body systems is a key challenge in robotics and human motion analysis. The invariant extended Kalman filter (IEKF) addresses this problem for a single rigid body with convergence guarantees and consistency under unobservability, but extending these properties to articulated systems is nontrivial: inter-body pose coupling prevents a direct application, and incorporating joint kinematic constraints within the invariant framework remains an open problem. To address this gap, we introduce the relative L-extended pose, a Lie group representation for kinematic-tree systems. With one IMU per body, it yields group-affine dynamics and allows joint constraints to be expressed in invariant form. We incorporate these constraints as noise-free pseudo-measurements within an iterated IEKF (IterIEKF), thereby preserving the convergence and consistency guarantees of invariant filtering. Validated on both a UR5e robot and a human leg, the proposed IterIEKF outperforms all EKF, IterEKF, and absolute-pose IterIEKF baselines. It converges faster, exhibits lower run-to-run variability, and consistently achieves the lowest RMSE, with reductions of at least 50% compared to the second-best filter across all scenarios considered in this work.

Sven Goffin, Cédric Schwartz, Silvère Bonnabel +2

Department of Electrical Engineering and Computer Science, University of Liège, Belgium · Department of Physical Activity and Rehabilitation Sciences, University of Liège, Belgium · Department of Mathematics and Systems, Mines Paris – PSL, France +1

3D Human Pose EstimationHuman Pose EstimationRobot State EstimationInvariant EKFInertial Navigation
AskPDF
Jun 21, 2026cs.RO

Invariant Stochastic Filtering on SE(3) for Inertial-Encoder State Estimation of Serial Rigid Manipulators

An invariant extended Kalman filter (IEKF) is developed for state estimation of serial rigid manipulators with an arbitrary number of links, formulated entirely within the Lie group SE(3). The group-affine property of the kinematic equations makes the linearised error dynamics autonomous, so the Riccati equation governs the true error covariance rather than a local approximation. A physically separated noise model treats gyroscope and accelerometer channels independently: the accelerometer provides translational twist via gravity-compensated integration, yielding a measurement covariance that scales with the sample interval in exact analogy with process noise discretisation; a state-dependent Coriolis noise term captures gyroscope noise propagating through the nonlinear dynamics, vanishing at rest and growing with twist magnitude. The filter is structured as a modular chain of per-link IEKFs in which the predicted covariance of each link depends on its predecessor only through the Adjoint-transformed posterior, giving linear computational cost in link count. Exponential ultimate boundedness in mean square is established via a Lie algebra Lyapunov function, with per-link bounds chained through the Adjoint operator norm to yield a stability certificate that is modular and scalable to arbitrary chain length. Numerical results validate the design.

S. Yaqubi, J. Mattila

Department of Automation Technology and Mechanical Engineering, Tampere University, Korkeakoulunkatu 6, 33720 Tampere, Finland

Robot State EstimationInvariant EKF
AskPDF
Jun 17, 2026cs.RO

Proprioceptive Invariant State Estimation for Humanoid Robots on Non-Inertial Ground

This paper presents an invariant extended Kalman filtering (InEKF) approach for real-time state estimation of humanoid robots operating on non-inertial ground using only onboard proprioceptive sensing. The proposed approach estimates the robot's base position and velocity relative to the moving ground frame without requiring direct measurements of ground motion or externally mounted sensors. By exploiting kinematic constraints at the stance foot through foot-mounted IMUs, the filter accounts for ground-induced nonlinearities in the process and measurement models while remaining fully proprioceptive. The estimator is formulated to admit a right-invariant measurement model, enabling favorable error dynamics under large initial uncertainties. Observability analysis establishes conditions under which the robot's relative base position and velocity are observable with respect to the non-inertial ground frame. Experiments with the Digit humanoid robot standing and squatting atop a swaying and pitching ground showcase a 96% speedup in convergence rate and an 80% reduction in position estimate errors over existing InEKFs. Walking experiments on a uni-axially rotating ground achieve an average estimation error of less than 9 cm for an initial error of up to 1 m.

Falak Mandali, Zijian He, Yan Gu

Purdue University, West Lafayette, IN 47907, USA.

Robot State EstimationInvariant EKF
AskPDF
May 14, 2026cs.RO

CoCo-InEKF: State Estimation with Learned Contact Covariances in Dynamic, Contact-Rich Scenarios

Robust state estimation for highly dynamic motion of legged robots remains challenging, especially in dynamic, contact-rich scenarios. Traditional approaches often rely on binary contact states that fail to capture the nuances of partial contact or directional slippage. This paper presents CoCo-InEKF, a differentiable invariant extended Kalman filter that utilizes continuous contact velocity covariances instead of binary contact states. These learned covariances allow the method to dynamically modulate contact confidence, accounting for more nuanced conditions ranging from firm contact to directional slippage or no contact. To predict these covariances for a set of predefined contact candidate points, we employ a lightweight neural network trained end-to-end using a state-error loss. This approach eliminates the need for heuristic ground-truth contact labels. In addition, we propose an automated contact candidate selection procedure and demonstrate that our method is insensitive to their exact placement. Experiments on a bipedal robot demonstrate a superior accuracy-efficiency tradeoff for linear velocity estimation, as well as improved filter consistency compared to baseline methods. This enables the robust execution of challenging motions, including dancing and complex ground interactions -- both in simulation and in the real world.

Michael Baumgartner, David Müller, Agon Serifi +4

ETH Zurich, Switzerland · Disney Research, Switzerland

Legged RoboticsRobot State EstimationInvariant EKF
AskPDF
May 12, 2026cs.RO

A Proprioceptive-Only Benchmark for Quadruped State Estimation: ATE, RPE, and Runtime Trade-offs Between Filters and Smoothers

We compare three state-of-the-art proprioceptive state estimators for quadruped robots: MUSE [1], the Invariant Extended Kalman Filter (IEKF) [2], and the Invariant Smoother (IS) [3], on the CYN-1 sequence of the GrandTour Dataset [4]. Our goal is to give practitioners clear guidance on accuracy and computation time: we report long-term accuracy (Absolute Trajectory Error, ATE), short-term accuracy (translational and rotational Relative Pose Error, RPE), and per-update computation time on a fixed hardware/software stack. On this dataset, RPEs are broadly similar across methods, while IEKF and IS achieve a lower ATE than MUSE. Runtime results highlight the accuracy-latency trade-offs across the three approaches. In the discussion, we outline the evaluation choices used to ensure a fair comparison and analyze factors that influence short-horizon metrics. Overall, this study provides a concise snapshot of accuracy and cost, helping readers choose an estimator that fits their application constraints, with all evaluation code and documentation released open-source at https://github.com/iit-DLSLab/state_estimation_benchmark for full reproducibility.

Ylenia Nisticò, João Carlos Virgolino Soares, Joan Solà +1

Dynamic Legged Systems (DLS) Lab, Istituto Italiano di Tecnologia, 16163 Genova, Italy · Institut de Rob`otica i Inform`atica Industrial - CSIC, 08028 Barcelona, Spain

State TrackingRobot State EstimationInvariant EKF
AskPDF
Apr 16, 2026cs.RO

Iterated Invariant EKF for Quadruped Robot Odometry

Kalman filter-based algorithms are fundamental for mobile robots, as they provide a computationally efficient solution to the challenging problem of state estimation. However, they rely on two main assumptions that are difficult to satisfy in practice: (a) the system dynamics must be linear with Gaussian process noise, and (b) the measurement model must also be linear with Gaussian measurement noise. Previous works have extended assumption (a) to nonlinear spaces through the Invariant Extended Kalman Filter (IEKF), showing that it retains properties similar to those of the classical Kalman filter when the system dynamics are group-affine on a Lie group. More recently, the counterpart of assumption (b) for the same nonlinear setting was addressed in [1]. By means of the proposed Iterated Invariant Extended Kalman Filter (IterIEKF), the authors of that work demonstrated that the update step exhibits several compatibility properties of the classical linear Kalman filter. In this work, we introduce a novel open-source state estimation algorithm for legged robots based on the IterIEKF. The update step of the proposed filter relies solely on proprioceptive measurements, exploiting kinematic constraints on foot velocity during contact and base-frame velocity, making it inherently robust to environmental conditions. Through extensive numerical simulations and evaluation on real-world datasets, we demonstrate that the IterIEKF outperforms the vanilla IEKF, the SO(3)-based Kalman Filter, and its iterated variant in terms of both accuracy and consistency.

Hilton Marques Souza Santana, João Carlos Virgolino Soares, Sven Goffin +4

Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia, Genoa, Italy. · Department of Mechanical Engineering, Pontifical Catholic University of Rio de Janeiro, Brazil. · Department of Electrical Engineering and Computer Science, University of Liège, Belgium. +1

Robot State EstimationInvariant EKF
AskPDF