Kenneth McIsaac

Hashim A. Hashim, Lyndon J. Brown, Kenneth McIsaac

Two nonlinear stochastic complimentary filters are developed on SO(3). They guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood of the origin. Simulation results are presented to illustrate the effectiveness of the proposed filters considering high level of uncertainties in angular velocity as well as body-frame vector measurements. Keywords: Attitude estimate, Attitude estimator, Attitude observer, Attitude filter, Nonlinear stochastic filter, stochastic differential equations, Brownian motion process, Ito, Stratonovich, Wong Zakai, Rodriguez vector, unit-quaternion, special orthogonal group 3, Euclidean, Euler angles, Angle-axis, Mapping, Parameterization, Representation, Robust, Invariant, Kalman Filter, Extended Kalman Filter, Multiplicative Extended Kalman Filter, Unscented Kalman Filter, Particle Filter, KF, EKF, MEKF, IEKF, first, second, Partial derivative, operator, probability, small, error, dynamics, kinematics, equilibrium, asymptotic, covariance, mean square, expected value, zero, unknown, time-varying, global, semi-global, stable, stability, uncertain, white noise, Gaussian noise, colored noise, bias, vectorial, vector measurement, angular velocity, singular value decomposition, bounded, rotational matrix, identity, deterministic, orientation, body frame, comparison, inertial frame, rigid body, three dimensional, 3D, space, Attitude Control, Lie algebra, Lie group, projection, Gyroscope, Inertial measurement units, micro electromechanical systems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV, SVD, Fixed, Moving, Vehicles, Robot, Robotic System, Spacecraft, submarine, Underwater vehicle, Problem, advantage, integral, integration, passive complementary filter, Disadvantage, autonomous, Review, Overview, Survey, comparative study, pose, SDEs, SE(3), SO(3).

Hashim A. Hashim, Lyndon J. Brown, Kenneth McIsaac

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).