An Eigenvector-Based Test for Local Stationarity Applied to Array Processing

In sonar array processing, a challenging problem is the estimation of the data covariance matrix in the presence of moving targets in the water column, since the time interval of data local stationarity is limited. This work describes an eigenvector-based method for proper data segmentation into intervals that exhibit local stationarity, providing data-driven higher bounds for the number of snapshots available for computation of time-varying sample covariance matrices. Application of the test is illustrated with simulated data in a horizontal array for the detection of a quiet source in the presence of a loud interferer

Direction of arrival estimation of multiple acoustic sources using a maximum likelihood method in the spherical harmonic domain

© 2018 Elsevier Ltd Direction of arrival estimation (DOA) of multiple acoustic sources has been used for a wide range of applications, including room geometry inference, source separation and speech enhancement. The beamformer-based and subspace-based methods are most commonly used for spherical microphone arrays; however, the former suffers from spatial resolution limitations, while the later suffers from performance degradation in noisy environment. This letter proposes a multiple source DOA estimation approach based on the maximum likelihood method in the spherical harmonic domain and implements an efficient sequential iterative search of maxima on the cost function in the spherical harmonic domain. The proposed method avoids the division of the spherical Bessel function, which makes it suitable for both rigid-sphere and open-sphere configurations. Simulation results show that the proposed method has a significant superiority over the commonly used frequency smoothing multiple signal classification method. Experiments in a normal listening room and a reverberation room validate the effectiveness of the proposed method

Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models

This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of available observations is known and comparable in magnitude to the observation dimension. An exact expression as well as an empirical, asymptotically accurate, approximation of the limiting variance is derived. Simulations are performed that corroborate the theoretical claims. A specific application to wireless sensor networks is developed.Comment: 30 p

Almost sure localization of the eigenvalues in a gaussian information plus noise model. Applications to the spiked models

Let $\boldsymbol{\Sigma}_N$ be a $M \times N$ random matrix defined by $\boldsymbol{\Sigma}_N = \mathbf{B}_N + \sigma \mathbf{W}_N$ where $\mathbf{B}_N$ is a uniformly bounded deterministic matrix and where $\mathbf{W}_N$ is an independent identically distributed complex Gaussian matrix with zero mean and variance $\frac{1}{N}$ entries. The purpose of this paper is to study the almost sure location of the eigenvalues $\hat{\lambda}_{1,N} \geq ... \geq \hat{\lambda}_{M,N}$ of the Gram matrix ${\boldsymbol \Sigma}_N {\boldsymbol \Sigma}_N^*$ when $M$ and $N$ converge to $+\infty$ such that the ratio $c_N = \frac{M}{N}$ converges towards a constant $c > 0$. The results are used in order to derive, using an alernative approach, known results concerning the behaviour of the largest eigenvalues of ${\boldsymbol \Sigma}_N {\boldsymbol \Sigma}_N^*$ when the rank of $\mathbf{B}_N$ remains fixed when $M$ and $N$ converge to $+\infty$.Comment: 19 pages, 1 figure, Accepted for publication in Electronic Journal of Probabilit

Multi-Step Knowledge-Aided Iterative ESPRIT for Direction Finding

In this work, we propose a subspace-based algorithm for DOA estimation which iteratively reduces the disturbance factors of the estimated data covariance matrix and incorporates prior knowledge which is gradually obtained on line. An analysis of the MSE of the reshaped data covariance matrix is carried out along with comparisons between computational complexities of the proposed and existing algorithms. Simulations focusing on closely-spaced sources, where they are uncorrelated and correlated, illustrate the improvements achieved.Comment: 7 figures. arXiv admin note: text overlap with arXiv:1703.1052

Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. The conventional multidimensional optimization problem reduces, thanks to this relaxation, to a simple spectral search. Following this principle, we propose estimators based on the Deterministic Maximum Likelihood, Weighted Subspace Fitting and covariance fitting methods. To calculate the pseudo-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that the performance of the proposed estimators is superior to the conventional methods especially in the case of low Signal-to-Noise-Ratio and low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a comparable computational cost as MUSIC.Comment: This work has been submitted to IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

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