Particle Filter with Stable Embedding for State Estimation of the Rigid Body Attitude System on the Set of Unit Quaternions

This paper presents a novel method for state esti- mation of rigid body attitude system evolving on the manifold S3, which is crucial in robotics and drone applications. We introduce a particle filter with stable embedding that extends the system into Euclidean space while ensuring stability of the manifold. Our particle filter with stable embedding enables accurate state estimation by maintaining estimated state values in close proximity to the manifold, while requiring significantly fewer computational resources than the standard exponential- map-based method that keeps state estimates on the manifold. Furthermore, our method facilitates the application of usual techniques designed for particle filters in Euclidean spaces, to the manifold system, as is, without any modification. The accuracy and the efficiency of our particle filter are confirmed both by simulation and by real drone experiments.