Deterministic Sampling on the Torus for Bivariate Circular Estimation

Many modern approaches to nonlinear filtering employ sample-based density approximations. These approximations are generated via random (Monte Carlo methods) or deterministic sampling [say, the unscented Kalman filter (UKF)]. The advantages of deterministic techniques are their reproducibility and that they require fewer samples. While the UKF is designed for real vector spaces, we present an approach for deterministic sampling applicable to two-dimensional periodic manifolds. This approach employs five weighted samples and matches trigonometric moments and a circular-circular correlation coefficient.