Deterministic Von Mises–Fisher Sampling on the Sphere Using Fibonacci Lattices

We propose a von Mises–Fisher sampling scheme using Fibonacci lattices to generate high-quality deterministic samples on the sphere. Key idea is an orthogonal inverse transform to map uniform low-discrepancy or quasi-random samples, ideally from Fibonacci lattices, to the sphere. The proposed new sampling method can be applied in assumed density Riemannian particle filters and controllers. Compared to random sampling, it produces well-separated, locally homogeneous samples, yielding superior convergence in numerical applications. The advantage over UKF-like sampling schemes is the free choice of the number of samples.