There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

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Sequential Monte Carlo methods in practice

Thank you for reading principles of optics electromagnetic theory of propagation interference and diffraction of light. As you may know, people have search hundreds times for their favorite novels like this principles of optics electromagnetic theory of propagation interference and diffraction of light, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some infectious bugs inside their computer.

Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Principal component analysis is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas. This paper provides a description of how to understand, use, and interpret principal component analysis. The paper focuses on the use of principal component analysis in typical chemometric areas but the results are generally applicable.

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Principal component analysis

A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.

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Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramer-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha>2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo on separating sources with distribution GG(alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals

Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the Cram&#201;r-Rao Lower Bound

We propose an improved version of algorithm FastICA which is asymptotically efficient, i.e., its accuracy attains the Cramer-Rao lower bound provided that the probability distribution of the signal components belongs to the class of generalized Gaussian distribution. Its computational complexity is only slightly (about three times) higher than that of ordinary symmetric FastICA. Simulation section shows superior performance of the algorithm compared with JADE, and of non-parametric ICA

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Efficient variant of algorithm fastica for independent component analysis attaining the cramer-RAO lower bound

We propose a new low-complexity approximate joint diagonalization (AJD) algorithm, which incorporates nontrivial block-diagonal weight matrices into a weighted least-squares (WLS) AJD criterion. Often in blind source separation (BSS), when the sources are nearly separated, the optimal weight matrix for WLS-based AJD takes a (nearly) block-diagonal form. Based on this observation, we show how the new algorithm can be utilized in an iteratively reweighted separation scheme, thereby giving rise to fast implementation of asymptotically optimal BSS algorithms in various scenarios. In particular, we consider three specific (yet common) scenarios, involving stationary or block-stationary Gaussian sources, for which the optimal weight matrices can be readily estimated from the sample covariance matrices (which are also the target-matrices for the AJD). Comparative simulation results demonstrate the advantages in both speed and accuracy, as well as compliance with the theoretically predicted asymptotic optimality of the resulting BSS algorithms based on the weighted AJD, both on large scale problems with matrices of the size 100times100.

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Fast Approximate Joint Diagonalization Incorporating Weight Matrices

This paper introduces a new underwater acoustic eigenstructure ESPRIT-based algorithm that yields closed-form direction-of-arrival (DOA) estimates using a single vector hydrophone. A vector hydrophone is composed of two or three spatially co-located but orthogonally oriented velocity hydrophones plus another optional co-located pressure hydrophone. This direction finding algorithm may (under most circumstances) resolve up to four uncorrelated monochromatic sources impinging from the near-field or the far-field, but it assumes that all signal frequencies are distinct. It requires no a priori knowledge of the signals' frequencies, suffers no frequency-DOA ambiguity, and pairs automatically the x-axis direction cosines with the y-axis direction cosines. It significantly outperforms an array of spatially displaced pressure hydrophones of comparable array-manifold size and computational load but may involve more complex hardware. This work also derives new Cramer-Rao bounds (CRBs) for various vector hydrophone constructions of arrival angle estimates for the incident uncorrelated sinusoidal signals corrupted by spatio-temporally correlated additive noise.

Petr Tichavsky

Papers

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound

Efficient variant of algorithm fastica for independent component analysis attaining the cramer-RAO lower bound

Fast Approximate Joint Diagonalization Incorporating Weight Matrices

Near-field/far-field azimuth and elevation angle estimation using a single vector hydrophone

Petr Tichavsky

Papers

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the Cram&#201;r-Rao Lower Bound

Efficient variant of algorithm fastica for independent component analysis attaining the cramer-RAO lower bound

Fast Approximate Joint Diagonalization Incorporating Weight Matrices

Near-field/far-field azimuth and elevation angle estimation using a single vector hydrophone

Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound