An Invariant Extended H<sub>∞</sub> Filter

Lavoie, Marc-Antoine; Arsenault, Jonathan; Forbes, James Richard

doi:10.1109/cdc40024.2019.9029289

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…We note that there has been some preliminary work in this direction. In particular, Lavoie et al have proposed an invariant extended H∞ filter for Lie groups [27]. Noting the similarities and crucial differences between the Extended Kalman Filter (EKF) and its invariant counterpart, the IEKF, the authors consider an analogous relationship between the Extended H∞ Filter and its potential invariant counterpart.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear $H_{\infty}$ Filtering on the Special Orthogonal Group $SO(3)$ using Vector Directions

Aslam¹,

Haydar²

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

Nonlinear $H_{\infty}$ Filtering on the Special Orthogonal Group $SO(3)$ using Vector Directions

Aslam¹,

Haydar²

2022

Preprint

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“…Therefore, the invariant-EKF can be viewed as the correction step of error state in the body frame but the SE 2 (3) based EKF executes the correction of error state in the navigation frame. Remark 3 Our SE 2 (3) based EKF can be used in H ∞ filtering similar to the invariant extended H ∞ filter[14].…”

mentioning

confidence: 99%

$SE_2(3)$ based Extended Kalman Filtering and Smoothing Framework for Inertial-Integrated Navigation

Luo,

Guo,

You

et al. 2021

Preprint

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The error representation using the straight difference of two vectors in the inertial navigation system may not be reasonable as it does not take the direction difference into consideration. Therefore, we proposed to use the SE 2 (3) matrix Lie group to represent the state of the inertial-integrated navigation system which consequently leads to the common frame error representation. With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed frame, respectively, the corresponding extending Kalman filter (EKF), terms as SE 2 (3)-EKF has also been derived. It provides a new perspective on the geometric EKF with a more sophisticated formula for the inertial-integrated navigation system. Furthermore, we propose a SE 2 (3)-based smoothing algorithm based on the SE 2 (3)-based EKF.

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A Novel Sensor Fusion Method Based on Invariant Extended Kalman Filter for Unmanned Aerial Vehicle

Zhou

Chen

Liu

et al. 2021

2021 IEEE International Conference on Robotics and Biomimetics (ROBIO)

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An Invariant Extended H_∞ Filter

Cited by 4 publications

References 16 publications

Nonlinear $H_{\infty}$ Filtering on the Special Orthogonal Group $SO(3)$ using Vector Directions

Nonlinear $H_{\infty}$ Filtering on the Special Orthogonal Group $SO(3)$ using Vector Directions

$SE_2(3)$ based Extended Kalman Filtering and Smoothing Framework for Inertial-Integrated Navigation

A Novel Sensor Fusion Method Based on Invariant Extended Kalman Filter for Unmanned Aerial Vehicle

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An Invariant Extended H∞ Filter

Cited by 4 publications

References 16 publications

Nonlinear $H_{\infty}$ Filtering on the Special Orthogonal Group $SO(3)$ using Vector Directions

Nonlinear $H_{\infty}$ Filtering on the Special Orthogonal Group $SO(3)$ using Vector Directions

$SE_2(3)$ based Extended Kalman Filtering and Smoothing Framework for Inertial-Integrated Navigation

A Novel Sensor Fusion Method Based on Invariant Extended Kalman Filter for Unmanned Aerial Vehicle

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An Invariant Extended H_∞ Filter