In this paper, we present libDirectional, a MATLAB library for directional statistics and
directional estimation. It supports a variety of commonly used distributions on the unit circle …

In estimation, control, and machine learning under uncertainties, latent variables are usually
described by a probability density function (pdf). The optimal reconstruction of a continuous …

(KIT) as part of the Programm zur Förderung der industriellen Gemeinschaftsforschung (IGF)
project 18798 N. First and foremost, I am utterly grateful to my Ph. D. advisor Uwe D …

Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state
belief using incomplete information from noisy sensors. To render the state estimation …

While estimation problems on periodic manifolds are inherently nonlinear, filters can benefit
from the boundedness of the domain. In this paper, we describe how densities on the unit …

The parameter space of nonnegative trigonometric sums (NNTS) models for circular data is
the surface of a hypersphere; thus, constructing regression models for a circular-dependent …

We extend the core operation of non-parametric belief propagation (NBP), also known as
multi-scale sequential Gibbs sampling, to approximate products of kernel density estimated …

For manifolds with topologies that strongly differ from the standard topology of R n, using
common filters created for linear domains can yield misleading results. While there is a lot of …

Estimation for multiple correlated quantities generally requires considering a domain whose
dimension is equal to the sum of the dimensions of the individual quantities. For multiple …

Estimation of periodic quantities such as angles or phase values is a common problem.
However, standard approaches, for example the Kalman filter and extensions thereof, have …