Nonlinear von Mises–Fisher Filtering Based on Isotropic Deterministic Sampling

Abstract

We present a novel deterministic sampling approach for von Mises–Fisher distributions of arbitrary dimensions. Following the idea of the unscented transform, samples of configurable size are drawn isotropically on the hypersphere while preserving the mean resultant vector of the underlying distribution. Based on these samples, a von Mises–Fisher filter is proposed for nonlinear estimation of hyperspherical states. Compared with existing von Mises–Fisher-based filtering schemes, the proposed filter exhibits superior hyperspherical tracking performance.