Directional statistics and filtering using libDirectional

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, such as the von Mises, wrapped normal, and wrapped Cauchy distributions. Furthermore, various distributions on higher-dimensional manifolds such as the unit hypersphere and the hypertorus are available. Based on these distributions, several recursive filtering algorithms in libDirectional allow estimation on these manifolds. The functionality is implemented in a clear, well-documented, and object-oriented structure that is both easy to use and easy to extend

Dual Quaternion Sample Reduction for SE(2) Estimation

We present a novel sample reduction scheme for random variables belonging to the SE(2) group by means of Dirac mixture approximation. For this, dual quaternions are employed to represent uncertain planar transformations. The Cramér–von Mises distance is modified as a smooth metric to measure the statistical distance between Dirac mixtures on the manifold of planar dual quaternions. Samples of reduced size are then obtained by minimizing the probability divergence via Riemannian optimization while interpreting the correlation between rotation and translation. We further deploy the proposed scheme for nonparametric modeling of estimates for nonlinear SE(2) estimation. Simulations show superior tracking performance of the sample reduction-based filter compared with Monte Carlo-based as well as parametric model-based planar dual quaternion filters

Multitarget Tracking Using Orientation Estimation for Optical Belt Sorting

In optical belt sorting, accurate predictions of the bulk material particles’ motions are required for high-quality results. By implementing a multitarget tracker tailored to the scenario and deriving novel motion models, the predictions are greatly enhanced. The tracker’s reliability is improved by also considering the particles’ orientations. To this end, new estimators for directional quantities based on orthogonal basis functions are presented and shown to outperform the state of the art

Econometric Methods of Signal Extraction

The Wiener-Kolmogorov signal extraction filters, which are widely used in econometric analysis, are constructed on the basis of statistical models of the processes generating the data. In this paper, such models are used mainly as heuristic devices that are to be specified in whichever ways are appropriate to ensure that the filters have the desired characteristics. The digital Butterworth filters, which are described and illustrated in the paper, are specified in this way. The components of an econometric time series often give rise to spectral structures that fall within well-defined frequency bands that are isolated from each other by spectral dead spaces. We find that the finite-sample Wiener-Kolmogorov formulation lends itself readily to a specialisation that is appropriate for dealing with band-limited components.Signal extraction, Linear filtering, Frequency-domain analysis, Trend estimation