The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC

Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case

Performance analysis of an improved MUSIC DoA estimator

This paper adresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is proved in the present paper that the traditional MUSIC method also provides DoA consistent estimates having the same asymptotic variances as the G-MUSIC estimates. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that G-MUSIC estimates are still able to consistently separate the sources, while it is no longer the case for the MUSIC ones. The asymptotic variances of G-MUSIC estimates are also evaluated.Comment: Revised versio

A Tutorial on Independent Component Analysis

Independent component analysis (ICA) has become a standard data analysis technique applied to an array of problems in signal processing and machine learning. This tutorial provides an introduction to ICA based on linear algebra formulating an intuition for ICA from first principles. The goal of this tutorial is to provide a solid foundation on this advanced topic so that one might learn the motivation behind ICA, learn why and when to apply this technique and in the process gain an introduction to this exciting field of active research

Dynamic filtering of static dipoles in magnetoencephalography

We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model. In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation

Robust Multiple Signal Classification via Probability Measure Transformation

In this paper, we introduce a new framework for robust multiple signal classification (MUSIC). The proposed framework, called robust measure-transformed (MT) MUSIC, is based on applying a transform to the probability distribution of the received signals, i.e., transformation of the probability measure defined on the observation space. In robust MT-MUSIC, the sample covariance is replaced by the empirical MT-covariance. By judicious choice of the transform we show that: 1) the resulting empirical MT-covariance is B-robust, with bounded influence function that takes negligible values for large norm outliers, and 2) under the assumption of spherically contoured noise distribution, the noise subspace can be determined from the eigendecomposition of the MT-covariance. Furthermore, we derive a new robust measure-transformed minimum description length (MDL) criterion for estimating the number of signals, and extend the MT-MUSIC framework to the case of coherent signals. The proposed approach is illustrated in simulation examples that show its advantages as compared to other robust MUSIC and MDL generalizations

Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrade when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1-D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators

Inverse Modeling for MEG/EEG data

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying source model, and discuss advantages and disadvantages. Finally we describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur

Array signal processing for maximum likelihood direction-of-arrival estimation

Emitter Direction-of-Arrival (DOA) estimation is a fundamental problem in a variety of applications including radar, sonar, and wireless communications. The research has received considerable attention in literature and numerous methods have been proposed. Maximum Likelihood (ML) is a nearly optimal technique producing superior estimates compared to other methods especially in unfavourable conditions, and thus is of significant practical interest. This paper discusses in details the techniques for ML DOA estimation in either white Gaussian noise or unknown noise environment. Their performances are analysed and compared, and evaluated against the theoretical lower bounds