3,890 research outputs found

    Kernel density estimation on the Siegel space applied to radar processing

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    Main techniques of probability density estimation on Riemannian manifolds are reviewed in the case of the Siegel space. For computational reasons we chose to focus on the kernel density estimation. The main result of the paper is the expression of Pelletier's kernel density estimator. The method is applied to density estimation of reflection coefficients from radar observations

    Computing distances and geodesics between manifold-valued curves in the SRV framework

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    This paper focuses on the study of open curves in a Riemannian manifold M, and proposes a reparametrization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. to define a Riemannian metric on the space of immersions M'=Imm([0,1],M) by pullback of a natural metric on the tangent bundle TM'. This induces a first-order Sobolev metric on M' and leads to a distance which takes into account the distance between the origins in M and the L2-distance between the SRV representations of the curves. The geodesic equations for this metric are given and exploited to define an exponential map on M'. The optimal deformation of one curve into another can then be constructed using geodesic shooting, which requires to characterize the Jacobi fields of M'. The particular case of curves lying in the hyperbolic half-plane is considered as an example, in the setting of radar signal processing

    Emitter Location Finding using Particle Swarm Optimization

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    Using several spatially separated receivers, nowadays positioning techniques, which are implemented to determine the location of the transmitter, are often required for several important disciplines such as military, security, medical, and commercial applications. In this study, localization is carried out by particle swarm optimization using time difference of arrival. In order to increase the positioning accuracy, time difference of arrival averaging based two new methods are proposed. Results are compared with classical algorithms and Cramer-Rao lower bound which is the theoretical limit of the estimation error

    Density estimation and modeling on symmetric spaces

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    In many applications, data and/or parameters are supported on non-Euclidean manifolds. It is important to take into account the geometric structure of manifolds in statistical analysis to avoid misleading results. Although there has been a considerable focus on simple and specific manifolds, there is a lack of general and easy-to-implement statistical methods for density estimation and modeling on manifolds. In this article, we consider a very broad class of manifolds: non-compact Riemannian symmetric spaces. For this class, we provide a very general mathematical result for easily calculating volume changes of the exponential and logarithm map between the tangent space and the manifold. This allows one to define statistical models on the tangent space, push these models forward onto the manifold, and easily calculate induced distributions by Jacobians. To illustrate the statistical utility of this theoretical result, we provide a general method to construct distributions on symmetric spaces. In particular, we define the log-Gaussian distribution as an analogue of the multivariate Gaussian distribution in Euclidean space. With these new kernels on symmetric spaces, we also consider the problem of density estimation. Our proposed approach can use any existing density estimation approach designed for Euclidean spaces and push it forward to the manifold with an easy-to-calculate adjustment. We provide theorems showing that the induced density estimators on the manifold inherit the statistical optimality properties of the parent Euclidean density estimator; this holds for both frequentist and Bayesian nonparametric methods. We illustrate the theory and practical utility of the proposed approach on the space of positive definite matrices

    RF Localization in Indoor Environment

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    In this paper indoor localization system based on the RF power measurements of the Received Signal Strength (RSS) in WLAN environment is presented. Today, the most viable solution for localization is the RSS fingerprinting based approach, where in order to establish a relationship between RSS values and location, different machine learning approaches are used. The advantage of this approach based on WLAN technology is that it does not need new infrastructure (it reuses already and widely deployed equipment), and the RSS measurement is part of the normal operating mode of wireless equipment. We derive the Cramer-Rao Lower Bound (CRLB) of localization accuracy for RSS measurements. In analysis of the bound we give insight in localization performance and deployment issues of a localization system, which could help designing an efficient localization system. To compare different machine learning approaches we developed a localization system based on an artificial neural network, k-nearest neighbors, probabilistic method based on the Gaussian kernel and the histogram method. We tested the developed system in real world WLAN indoor environment, where realistic RSS measurements were collected. Experimental comparison of the results has been investigated and average location estimation error of around 2 meters was obtained

    Time-scale analysis of abrupt changes corrupted by multiplicative noise

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    Multiplicative Abrupt Changes (ACs) have been considered in many applications. These applications include image processing (speckle) and random communication models (fading). Previous authors have shown that the Continuous Wavelet Transform (CWT) has good detection properties for ACs in additive noise. This work applies the CWT to AC detection in multiplicative noise. CWT translation invariance allows to define an AC signature. The problem then becomes signature detection in the time-scale domain. A second-order contrast criterion is defined as a measure of detection performance. This criterion depends upon the first- and second-order moments of the multiplicative process's CWT. An optimal wavelet (maximizing the contrast) is derived for an ideal step in white multiplicative noise. This wavelet is asymptotically optimal for smooth changes and can be approximated for small AC amplitudes by the Haar wavelet. Linear and quadratic suboptimal signature-based detectors are also studied. Closed-form threshold expressions are given as functions of the false alarm probability for three of the detectors. Detection performance is characterized using Receiver Operating Characteristic (ROC) curves computed from Monte-Carlo simulations
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