Kernel density estimation and goodness-of-fit test in adaptive tracking

17 pagesInternational audienceWe investigate the asymptotic properties of a recursive kernel density estimator associated with the driven noise of a linear regression in adaptive tracking. We provide an almost sure pointwise and uniform strong law of large numbers as well as a pointwise and multivariate central limit theorem

Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting approach is proposed to construct the Likelihood Probability Density Function (Li-PDF) by using a comparably small number of so-called fulcrums. The likelihood of particles is thereby analytically inferred, explicitly or implicitly, based on the Li-PDF instead of directly computed by utilizing the observation, which can significantly reduce the computation and enables real time filtering. The proposed approach guarantees the estimation quality when an appropriate fitting function and properly distributed fulcrums are used. The details for construction of the fitting function and fulcrums are addressed respectively in detail. In particular, to deal with multivariate fitting, the nonparametric kernel density estimator is presented which is flexible and convenient for implicit Li-PDF implementation. Simulation comparison with a variety of existing approaches on a benchmark 1-dimensional model and multi-dimensional robot localization and visual tracking demonstrate the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a draft/preprint of one paper submitted to the IEEE Transaction

Recent advances in directional statistics

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 (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, aeronautics, 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. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Space Use And Habitat Selection By Bobcats In Southeastern Kentucky

Population estimation and trend analyses are critically important for sustainable harvest and management of many species. The bobcat (Lynx rufus) plays important ecological and economic roles in Kentucky as a furbearer and mesopredator. I conducted a study of the bobcat in southeastern Kentucky as a twenty year follow-up to research conducted in the same study area. I radio-collared five (4F, 1M) bobcats and assessed space and habitat use patterns. Mean annual minimum convex polygon (MCP) home range size for all bobcats was 14.7 km2 (n = 5, SE = 3.9 km2), and 22.2 km2 (n = 5, SE = 7.5 km2) using the adaptive kernel (AK) method. Mean female annual home range size was 17.4 km2 (MCP, n = 4, SE = 3.9 km2) and 27.4 km2 (AK, n = 4, SE = 7.5). Mean female-female home range overlap was 29.1% (MCP, n = 6, SE= 8.7), and female-male overlap was 17.1% (MCP, n = 4, SE = 7.0). Mean female-female core area overlap was 10.5% (MCP, n = 6, SE = 10.5), and female-male 12.1% (MCP, n = 4, SE = 12.1). Bobcats (all bobcats pooled) used forest in proportion to availability at the study area spatial scale, used open habitat more than expected, but avoided active mines (P \u3c 0.001). Movement rate (x = 0.12 km/hr) of a single GPS-collared male bobcat was lower during midday than during the morning, late afternoon, or nighttime periods. Also, more locations were recorded in forested habitat than expect based on habitat available within the home range, which contradicts the trend seen in the VHF data analysis, possibly indicating VHF data were not reliable in assessing habitat selection