Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory

Area of Science:

• Robotics and Control Systems
• Aerospace Engineering
• Computer Science

Background:

• Attitude estimation is crucial for navigation and control.
• Traditional Kalman filters struggle with the non-Euclidean geometry of attitude representations.
• Unit quaternions are a common method for representing attitude, but require specialized filter treatments.

Purpose of the Study:

• To develop a novel framework for attitude estimation using manifold theory.
• To define mean and covariance for distributions of unit quaternions on manifolds.
• To create and evaluate non-linear Kalman filter algorithms for attitude estimation.

Main Methods:

• Utilized concepts from manifold theory to define statistical moments (mean, covariance) for unit quaternion distributions.
• Developed non-linear Kalman filter variants based on these manifold-aware definitions.
• Conducted simulations to assess the accuracy and performance of the proposed algorithms.

Main Results:

• The developed manifold-based Kalman filters demonstrated accurate attitude estimation.
• A clear best-performing attitude estimator was identified based on simulation results and a defined performance metric.
• The new viewpoint naturally integrates multiplicative updates and covariance correction steps.

Conclusions:

• Manifold theory provides a natural and effective framework for attitude estimation with unit quaternions.
• The proposed non-linear Kalman filters offer improved accuracy for attitude estimation problems.
• The study successfully identified and validated an optimal attitude estimation algorithm.