# Nonlinear Stochastic Attitude Filters on the Special Orthogonal Group 3: Ito and Stratonovich

@article{Hashim2019NonlinearSA, title={Nonlinear Stochastic Attitude Filters on the Special Orthogonal Group 3: Ito and Stratonovich}, author={Hashim A. Hashim and Lyndon J. Brown and Kenneth A. McIsaac}, journal={IEEE Transactions on Systems, Man, and Cybernetics: Systems}, year={2019}, volume={49}, pages={1853-1865} }

This paper formulates the attitude filtering problem as a nonlinear stochastic filter problem evolved directly on the Special Orthogonal Group 3 (<inline-formula> <tex-math notation="LaTeX">${\mathbb {SO}}(3)$ </tex-math></inline-formula>). One of the traditional potential functions for nonlinear deterministic complimentary filters is studied and examined against angular velocity measurements corrupted with noise. This paper demonstrates that the careful selection of the attitude potential…

## 42 Citations

Nonlinear Explicit Stochastic Attitude Filter on SO(3)

- Mathematics2018 IEEE Conference on Decision and Control (CDC)
- 2018

The proposed stochastic filter evolved on the Special Orthogonal Group (3) guarantees that errors in the Rodriguez vector and estimates steer very close to the neighborhood of the origin and that the errors are semi-globally uniformly ultimately bounded in mean square.

Guaranteed Performance of Nonlinear Attitude Filters on the Special Orthogonal Group SO(3)

- EngineeringIEEE Access
- 2019

Two novel nonlinear attitude filters evolved directly on the special orthogonal group SO, able to ensure prescribed measures of transient and steady-state performance are proposed, providing good attitude estimates with superior convergence properties and can be applied to measurements obtained from low-cost inertial measurement units.

Nonlinear Stochastic Position and Attitude Filter on the Special Euclidean Group 3

- MathematicsJ. Frankl. Inst.
- 2019

Nonlinear Attitude and Pose Filters with Superior Convergence Properties

- Mathematics
- 2019

In this thesis, several deterministic and stochastic attitude filtering solutions on the special orthogonal group SO(3) are proposed. Firstly, the attitude estimation problem is approached on the…

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

- MathematicsInternational Journal of Robust and Nonlinear Control
- 2020

Two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group SO(3) with the tracking error of the normalized Euclidean distance meeting predefined transient and steady-state characteristics are introduced.

Nonlinear Stochastic Estimators on the Special Euclidean Group SE(3) Using Uncertain IMU and Vision Measurements

- MathematicsIEEE Transactions on Systems, Man, and Cybernetics: Systems
- 2021

Two novel robust nonlinear stochastic full pose estimators on the Special Euclidean Group $\mathbb {SE}(3)$ are proposed using the available uncertain measurements to consider the group velocity vectors to be contaminated with constant bias and Gaussian random noise.

Neural-Adaptive Stochastic Attitude Filter on SO(3)

- EngineeringIEEE Control Systems Letters
- 2022

This letter proposes a novel stochastic nonlinear neural-adaptive-based filter on $SO(3)$ for the attitude estimation problem. The proposed filter produces good results given measurements extracted…

Nonlinear Filter for Simultaneous Localization and Mapping on a Matrix Lie Group Using IMU and Feature Measurements

- EngineeringIEEE Transactions on Systems, Man, and Cybernetics: Systems
- 2022

This paper proposes a computationally cheap geometric nonlinear SLAM filter algorithm structured to mimic the nonlinear motion dynamics of the true SLAM problem posed on the matrix Lie group of SLAMn (3).

Guaranteed Performance of Nonlinear Pose Filter on SE(3)

- Engineering2019 American Control Conference (ACC)
- 2019

This paper presents a novel nonlinear pose filter evolved directly on the Special Euclidean Group SE with guaranteed characteristics of transient and steady-state performance and remarkable convergence properties such that it can be fitted with measurements obtained from low-cost measurement units.

Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping

- MathematicsIEEE Control Systems Letters
- 2021

A geometric nonlinear observer algorithm for Simultaneous Localization and Mapping (SLAM) developed on the Lie group of $\mathbb {SLAM}_{n}(3)$ is proposed andumerical results reveal effectiveness of the proposed observer.

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