Linear Regression Kalman Filtering Based on Hyperspherical Deterministic Sampling

Nonlinear filtering based on Gaussian densities is commonly performed using so-called Linear Regression Kalman Filters (LRKFs). These filters rely on sample-based approximations of Gaussian densities. We propose a novel sampling scheme that is based on decomposing the problem of sampling a multivariate Gaussian into sampling a univariate Gaussian and sampling uniformly on the surface of a hypersphere. The proposed sampling scheme has significant advantages compared to existing methods because it produces a user-selectable number of samples with uniform, nonnegative weights and it does not require any numerical optimization. We evaluate the novel method in simulations and provide comparisons to multiple state-of-the-art approaches.