mlsanityData to 7 Oct 2026

Quaternion kinematics for the error-state Kalman filter

arXiv 1711.02508 ↗First posted 3 Nov 2017cs.ROcited by 30

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Abstract (arXiv)

This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the rotation group and its Lie structure, with formulations using both quaternions and rotation matrices. It makes special attention in the definition of rotation perturbations, derivatives and integrals. It provides numerous intuitions and geometrical interpretations to help the reader grasp the inner mechanisms of 3D rotation. The whole material is used to devise precise formulations for error-state Kalman filters suited for real applications using integration of signals from an inertial measurement unit (IMU).

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Nov 2017.

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Citing papers per year: 2021: 1; 2022: 3; 2023: 6; 2024: 7; 2025: 10; 2026: 3.

30 papers.

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  1. 2025VGGT-SLAM: Dense RGB SLAM Optimized on the SL(4) Manifoldcited by 130
  2. 2021Comparing Representations in Tracking for Event Camera-based SLAMcited by 23
  3. 2025ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generationcited by 10
  4. 2023SchurVINS: Schur Complement-Based Lightweight Visual Inertial Navigation Systemcited by 5
  5. 2022CUAHN-VIO: Content-and-Uncertainty-Aware Homography Network for Visual-Inertial Odometrycited by 4
  6. 2023EDI: ESKF-based Disjoint Initialization for Visual-Inertial SLAM Systemscited by 4
  7. 2023Continuous Pose for Monocular Cameras in Neural Implicit Representationcited by 4
  8. 2024Legged Robot State Estimation With Invariant Extended Kalman Filter Using Neural Measurement Networkcited by 3
  9. 2024Traj-LIO: A Resilient Multi-LiDAR Multi-IMU State Estimator Through Sparse Gaussian Processcited by 2
  10. 2025Novel computational workflows for natural and biomedical image processing based on hypercomplex algebrascited by 2
  11. 2025Improving Monocular Visual-Inertial Initialization with Structureless Visual-Inertial Bundle Adjustmentcited by 2
  12. 2025MagShield: Towards Better Robustness in Sparse Inertial Motion Capture Under Magnetic Disturbancescited by 2
18 more
  1. 2022Sleep Posture One-Shot Learning Framework Using Kinematic Data Augmentation: In-Silico and In-Vivo Case Studiescited by 1
  2. 2023Multi-Visual-Inertial System: Analysis, Calibration and Estimationcited by 1
  3. 2024Enhancing Visual Inertial SLAM with Magnetic Measurementscited by 1
  4. 2024Reinforcement Learning with Lie Group Orientations for Roboticscited by 1
  5. 2025SSPINNpose: A Self-Supervised PINN for Inertial Pose and Dynamics Estimationcited by 1
  6. 2022An Improved Multi-State Constraint Kalman Filter for Visual-Inertial Odometrycited by 0
  7. 2023Locking On: Leveraging Dynamic Vehicle-Imposed Motion Constraints to Improve Visual Localizationcited by 0
  8. 2023High-accuracy Vision-Based Attitude Estimation System for Air-Bearing Spacecraft Simulatorscited by 0
  9. 2024Multi-Robot Relative Pose Estimation in SE(2) with Observability Analysis: A Comparison of Extended Kalman Filtering and Robust Pose Graph Optimizationcited by 0
  10. 2024Sky-GVIO: an enhanced GNSS/INS/Vision navigation with FCN-based sky-segmentation in urban canyoncited by 0
  11. 2024Tightly-Coupled, Speed-aided Monocular Visual-Inertial Localization in Topological Mapcited by 0
  12. 2025KN-LIO: Geometric Kinematics and Neural Field Coupled LiDAR-Inertial Odometrycited by 0
  13. 2025HDVIO2.0: Wind and Disturbance Estimation with Hybrid Dynamics VIOcited by 0
  14. 2025Aleatoric Uncertainty from AI-based 6D Object Pose Predictors for Object-relative State Estimationcited by 0
  15. 2025Adaptive Covariance and Quaternion-Focused Hybrid Error-State EKF/UKF for Visual-Inertial Odometrycited by 0
  16. 2026Observability Conditions and Filter Design for Visual Pose Estimation via Dual Quaternionscited by 0
  17. 2026SubSplat: High-Resolution Pixel-aligned 3DGS via Sub-pixel Gaussian Reparameterizationcited by 0
  18. 2026QuacamFM: Quaternion-Constrained Flow Matching for Camera Pose Estimationcited by 0