Deterministic Gaussian Sampling With Generalized Fibonacci Grids

Abstract

We propose a simple and efficient method to obtain unweighted deterministic samples of the multivariate Gaussian density. It allows to place a large number of homogeneously placed samples even in high-dimensional spaces. There is a demand for large high-quality sample sets in many nonlinear filters. The Smart Sampling Kalman Filter (S2KF), for example, uses many samples and is an extension of the Unscented Kalman Filter (UKF) that is limited due to its small sample set. Generalized Fibonacci grids have the property that if stretched or compressed along certain directions, the grid points keep approximately equal distances to all their neighbors. This can be exploited to easily obtain deterministic samples of arbitrary Gaussians. As the computational effort to generate these anisotropically scalable point sets is low, generalized Fibonacci grid sampling appears to be a great new source of large sample sets in high-quality state estimation.