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

Abstract

This paper formulates the pose estimation problem as nonlinear stochastic filter kinematics evolved directly on the Special Euclidean Group SE(3). Proposed filter guarantees that the errors present in position and Rodriguez vector estimates are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and that they converge to small neighborhood of the origin in probability. Simulation results show the robustness and effectiveness of the proposed filter in presence of high levels of noise and bias associated with the velocity vector as well as body-frame measurements. Keywords: Pose estimator, pose observer, attitude estimate, control, estimator, observer, Nonlinear stochastic pose filter, stochastic differential equations, Brownian motion process, Ito, Stratonovich, Wong Zakai, unit-quaternion, special orthogonal group, homogeneous transformation matrix, complimentary filter, Euler angles, Angle-axis, mapping, Parameterization, Representation, Robust, Multiplicative Extended Kalman Filter, Unscented Kalman Filter, Particle filter, KF, EKF, IEKF, UKF, MEKF, partial derivative, small, dynamics, equilibrium, asymptotic, covariance, expected value, zero, unknown, time-varying, global, semi-global, stable, stability, uncertain, Gaussian, colored, white, noise, vectorial measurement, vector measurement, translational velocity, angular velocity, singular value decomposition, rotational matrix, identity, deterministic, comparison, inertial frame, rigid body, three dimensional, 3D, space, adjoint, Lie group, projection, landmark, feature, Gyroscope, micro electromechanical systems, Inertial measurement units, sensor, IMUs, Fixed, moving, orientation, Roll, Pitch, Yaw, SVD, UAVs, QUAV, unmanned, underwater vehicle, robot, Robotic System, Spacecraft, quadrotor, quadcopter, integral, advantage, disadvantage, Comparative study, Review, Overview, Survey, autonomous, xyz, axis, SO(3), SE(3).

Journal of the Franklin Institute. arXiv admin note: text overlap with arXiv:1810.03130

References in corpus (3)

• Nonlinear Stochastic Attitude Filters on the Special Orthogonal Group 3: Ito and Stratonovich
• Adaptive synchronisation of unknown nonlinear networked systems with prescribed performance
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Cited by in corpus (7)

• Nonlinear Pose Filters on the Special Euclidean Group SE(3) with Guaranteed Transient and Steady-state Performance
• Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping
• Special Orthogonal Group SO(3), Euler Angles, Angle-axis, Rodriguez Vector and Unit-Quaternion: Overview, Mapping and Challenges
• Guaranteed Performance of Nonlinear Attitude Filters on the Special Orthogonal Group SO(3)
• Attitude Determination and Estimation using Vector Observations: Review, Challenges and Comparative Results
• Guaranteed Performance of Nonlinear Pose Filter on SE(3)
• Outlier-robust Kalman filters with mixture correntropy