Directional Statistics and Filtering Using <b>libDirectional</b>

Kurz, Gerhard; Gilitschenski, Igor; Pfaff, Florian; Drude, Lukas; Hanebeck, Uwe D.; Haeb‐Umbach, Reinhold; Siegwart, Roland

doi:10.18637/jss.v089.i04

Cited by 26 publications

(14 citation statements)

References 59 publications

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“…Since the predictive prior distribution resulting from the mixture components is non-parametric we used a discrete circular filter to approximate the distributions in this simulation. The discrete filter is based on a grid of weighted Dirac components equally distributed along the circle (Kurz et al, 2016;Kurz, Gilitschenski, & Hanebeck, 2013) and was implemented with libDirectional toolbox for Matlab (Kurz, Gilitschenski, Pfaff, & Drude, 2015). Because in the unidimensional circular state space of orientations the quality of approximation is only given by the number of components, we felt that 10,000 Dirac components can adequately approximate a distribution of a circular variable.…”

Section: Model Parametersmentioning

confidence: 99%

Visual recency bias is explained by a mixture model of internal representations

Kalm

Norris

2017

Preprint

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Human bias towards more recent events is a common and well-studied phenomenon. Recent studies in visual perception have shown that this recency bias persists even when past events contain no information about the future. Reasons for this suboptimal behaviour are not well understood and the internal model that leads people to exhibit recency bias is unknown. Here we use a well-known orientation estimation task to frame the human recency bias in terms of incremental Bayesian inference. We show that the only Bayesian model capable of explaining the recency bias relies on a weighted mixture of past states. Furthermore, we suggest that this mixture model is a consequence of participants' failure to infer a model for data in visual short term memory, and reflects the nature of the internal representations used in the task. 0

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Section: Model Parametersmentioning

confidence: 99%

Visual recency bias is explained by a mixture model of internal representations

Kalm

Norris

2017

Preprint

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“…The PF, ProgSE2BF, and S3F are part of the latest version of libDirectional [ 28 ]. For the UKF-M, we use the implementation of [ 13 ].…”

Section: Discussionmentioning

confidence: 99%

The State Space Subdivision Filter for Estimation on SE(2)

Pfaff

Hanebeck

2021

Sensors

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The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.

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“…Ball et al (2008) introduced Brownian motion and Ornstein-Uhlenbeck processes on the shape space of R 2 . Kurz et al (2019) provided an overview of various recursive filtering algorithms involving a variety of circular, toroidal, and spherical distributions. Analogues of the Kalman filter based on the vMF and Bingham distributions on S d were proposed by Chiuso and Picci (1998) and Kurz et al (2014), respectively.…”

Section: Continuous-time Processesmentioning

confidence: 99%

“…An overview of many such packages was given by Pewsey (2018). Relevant packages written in other languages include CircStat (Berens 2009) and PyCircStat (Sinz et al 2018) for data on S 1 , libDirectional (Kurz et al 2019) for data on T d and S d , Mocapy++ for constructing probabilistic models of biomolecular structure (Paluszewski and Hamelryck 2010), and the promising geomstats (Miolane et al 2020) for manifold-valued data.…”

Section: Softwarementioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

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Directional Statistics and Filtering Using libDirectional

Cited by 26 publications

References 59 publications

Visual recency bias is explained by a mixture model of internal representations

Visual recency bias is explained by a mixture model of internal representations

The State Space Subdivision Filter for Estimation on SE(2)

Recent advances in directional statistics

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