A quaternion particle filter based on hyper-hemisphere sampling for robot attitude estimation

With the increasing demand for high-precision attitude estimation in robotics, achieving an optimal balance between computational efficiency and estimation accuracy remains a critical challenge in quaternion-based sensor fusion. Existing quaternion particle filters often compromise performance or precision by relying on parametric manifold uncertainty models. Aiming at this limitation, this paper proposes a novel Hyper-Hemisphere Quaternion Particle Filter (HHQPF) for deterministic sampling to fuse IMU data and estimate gyroscope bias. First, we apply a Dirac mixture to generate deterministic samples nonparametrically on the hypersphere, modeling unit quaternion manifold uncertainty efficiently. Then, leveraging the double-covering property of the S³ rotation group, we project these hyper-hemisphere samples onto the unit quaternion manifold via exponential mapping for discrete Bayesian processing. Finally, this deterministic sampling scheme is integrated into the Gaussian particle filter framework. Validation via simulations and real IMU data shows HHQPF achieves accuracy equivalent to unscented quaternion estimators (USQUE) and genetic algorithm-based particle filters (GA-QPF), but at significantly lower computational cost. HHQPF executes single steps 43% faster than GA-QPF with identical particle counts (e.g. 500 particles), demonstrating strong potential for efficient real-time robotic attitude estimation.