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

TL;DR

This paper introduces two nonlinear stochastic attitude filters on SO(3) that ensure bounded errors and convergence in the presence of high uncertainties, validated through simulations.

Contribution

The paper develops novel stochastic filters on SO(3) that guarantee bounded errors and convergence, addressing high uncertainty scenarios in attitude estimation.

Findings

Errors are semi-globally uniformly ultimately bounded in mean square.

Filters converge to a small neighborhood of the true attitude.

Simulation results demonstrate effectiveness under high uncertainties.

Abstract

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).