Deterministic Sampling on the Circle using Projected Cumulative Distributions

TL;DR

This paper introduces a novel deterministic sampling method for circular angular densities that improves state estimation accuracy by using multiple samples, surpassing the limitations of existing minimal-sample approaches like the Unscented Kalman Filter.

Contribution

The proposed method allows for arbitrary numbers of deterministic samples on the circle, optimizing sample placement by minimizing cumulative differences in projected densities.

Findings

Enhanced state estimation accuracy with fewer samples

Flexible sampling size beyond minimal sample sets

Effective approximation of continuous densities on the circle

Abstract

We propose a method for deterministic sampling of arbitrary continuous angular density functions. With deterministic sampling, good estimation results can typically be achieved with much smaller numbers of samples compared to the commonly used random sampling. While the Unscented Kalman Filter uses deterministic sampling as well, it only takes the absolute minimum number of samples. Our method can draw arbitrary numbers of deterministic samples and therefore improve 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 difference of the cumulatives of many univariate projections. In other words, we compare cumulatives of probability densities in the Radon space.