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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 difficulties when estimating periodic quantities. To address this problem, circular filtering algorithms have been proposed but they are limited to just a single angle. In order to deal with multiple, possibly correlated angles,...
While nonlinear filtering for circular quantities is closely related to nonlinear filtering on linear domains, the underlying manifold enables the development of novel filters that take advantage of the boundedness of the domain. Previously, we introduced Fourier filters that approximate the density or its square root using Fourier series. For these filters, we proposed filter steps for arbitrary...
We propose a novel measurement update procedure for orientation estimation algorithms that are based on directional statistics. This involves consideration of two scenarios, orientation estimation in the 2D plane and orientation estimation in three-dimensional space. We make use of the von Mises distribution and the Bingham distribution in these scenarios. In the derivation, we discuss directional...
Recursive filtering with multimodal likelihoods and transition densities on periodic manifolds is, despite the compact domain, still an open problem. We propose a novel filter for the circular case that performs well compared to other state-of-the-art filters adopted from linear domains. The filter uses a limited number of Fourier coefficients of the square root of the density. This representation...
We introduce a novel probability distribution on the group of rigid motions SE(2) and we refer to this distribution as the partially wrapped normal distribution. Describing probabilities on SE(2) is of interest in a wide range of applications, for example, robotics, autonomous vehicles, or maritime navigation. We derive some important properties of this novel distribution and propose an estimation...
In this paper, we address the problem of developing computationally efficient recursive estimators on the periodic domain of orientations using the Bingham distribution. The Bingham distribution is defined directly on the unit hypersphere. As such, it is able to describe both large and small uncertainties in a unified framework. In order to tackle the challenging computation of the normalization constant,...
This work proposes a novel way to represent uncertainty on the Lie group of rigid-body motions in the plane. This is achieved by using dual quaternions for representation of a planar rigid-body motion and proposing a probability distribution from the exponential family of distributions that inherently respects the underlying structure of the representation. This is particularly beneficial in scenarios...
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