Deterministic Sampling on the Circle Using Projected Cumulative Distributions

We propose a method for deterministic sampling of arbitrary continuous angular probability density functions. With deterministic sampling, good estimation results can be obtained with a much smaller number of samples than with the commonly used random sampling. The Unscented Kalman Filter also uses deterministic sampling, but takes a very small number of samples. Our method can draw an arbitrary number of deterministic samples, improving the quality of state estimation. Conformity between the continuous density function (reference) and the Dirac mixture density, i.e., sample locations (approximation), is established by minimizing the distance of the cumulatives of dozens of univariate projections. In other words, we compare density functions in Radon space.