102,244 research outputs found
Subspace Leakage Analysis and Improved DOA Estimation with Small Sample Size
Classical methods of DOA estimation such as the MUSIC algorithm are based on
estimating the signal and noise subspaces from the sample covariance matrix.
For a small number of samples, such methods are exposed to performance
breakdown, as the sample covariance matrix can largely deviate from the true
covariance matrix. In this paper, the problem of DOA estimation performance
breakdown is investigated. We consider the structure of the sample covariance
matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown
in the threshold region is associated with the subspace leakage where some
portion of the true signal subspace resides in the estimated noise subspace. In
this paper, the subspace leakage is theoretically derived. We also propose a
two-step method which improves the performance by modifying the sample
covariance matrix such that the amount of the subspace leakage is reduced.
Furthermore, we introduce a phenomenon named as root-swap which occurs in the
root-MUSIC algorithm in the low sample size region and degrades the performance
of the DOA estimation. A new method is then proposed to alleviate this problem.
Numerical examples and simulation results are given for uncorrelated and
correlated sources to illustrate the improvement achieved by the proposed
methods. Moreover, the proposed algorithms are combined with the pseudo-noise
resampling method to further improve the performance.Comment: 37 pages, 10 figures, Submitted to the IEEE Transactions on Signal
Processing in July 201
Estimating the Intrinsic Dimension of Hyperspectral Images Using a Noise-Whitened Eigengap Approach
International audienceLinear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms
Cosmological Covariance of Fast Radio Burst Dispersions
The dispersion of fast radio bursts (FRBs) is a measure of the large-scale
electron distribution. It enables measurements of cosmological parameters,
especially of the expansion rate and the cosmic baryon fraction. The number of
events is expected to increase dramatically over the coming years, and of
particular interest are bursts with identified host galaxy and therefore
redshift information.
In this paper, we explore the covariance matrix of the dispersion measure
(DM) of FRBs induced by the large-scale structure, as bursts from a similar
direction on the sky are correlated by long wavelength modes of the electron
distribution. We derive analytical expressions for the covariance matrix and
examine the impact on parameter estimation from the FRB dispersion measure -
redshift relation. The covariance also contains additional information that is
missed by analysing the events individually. For future samples containing over
FRBs with host identification over the full sky, the covariance needs
to be taken into account for unbiased inference, and the effect increases
dramatically for smaller patches of the sky. Also forecasts must consider these
effects as they would yield too optimistic parameter constraints. Our procedure
can also be applied to the DM of the afterglow of Gamma Ray Bursts.Comment: 8 pages, 5 figures, accepted by MNRAS, matches final submitted
versio
DOA Estimation in Partially Correlated Noise Using Low-Rank/Sparse Matrix Decomposition
We consider the problem of direction-of-arrival (DOA) estimation in unknown
partially correlated noise environments where the noise covariance matrix is
sparse. A sparse noise covariance matrix is a common model for a sparse array
of sensors consisted of several widely separated subarrays. Since interelement
spacing among sensors in a subarray is small, the noise in the subarray is in
general spatially correlated, while, due to large distances between subarrays,
the noise between them is uncorrelated. Consequently, the noise covariance
matrix of such an array has a block diagonal structure which is indeed sparse.
Moreover, in an ordinary nonsparse array, because of small distance between
adjacent sensors, there is noise coupling between neighboring sensors, whereas
one can assume that nonadjacent sensors have spatially uncorrelated noise which
makes again the array noise covariance matrix sparse. Utilizing some recently
available tools in low-rank/sparse matrix decomposition, matrix completion, and
sparse representation, we propose a novel method which can resolve possibly
correlated or even coherent sources in the aforementioned partly correlated
noise. In particular, when the sources are uncorrelated, our approach involves
solving a second-order cone programming (SOCP), and if they are correlated or
coherent, one needs to solve a computationally harder convex program. We
demonstrate the effectiveness of the proposed algorithm by numerical
simulations and comparison to the Cramer-Rao bound (CRB).Comment: in IEEE Sensor Array and Multichannel signal processing workshop
(SAM), 201
Comparison of the estimation of the degree of polarization from four or two intensity images degraded by speckle noise
Active polarimetric imagery is a powerful tool for accessing the information
present in a scene. Indeed, the polarimetric images obtained can reveal
polarizing properties of the objects that are not avalaible using conventional
imaging systems. However, when coherent light is used to illuminate the scene,
the images are degraded by speckle noise. The polarization properties of a
scene are characterized by the degree of polarization. In standard polarimetric
imagery system, four intensity images are needed to estimate this degree . If
we assume the uncorrelation of the measurements, this number can be decreased
to two images using the Orthogonal State Contrast Image (OSCI). However, this
approach appears too restrictive in some cases. We thus propose in this paper a
new statistical parametric method to estimate the degree of polarization
assuming correlated measurements with only two intensity images. The estimators
obtained from four images, from the OSCI and from the proposed method, are
compared using simulated polarimetric data degraded by speckle noise
Performance of internal Covariance Estimators for Cosmic Shear Correlation Functions
Data re-sampling methods such as the delete-one jackknife are a common tool
for estimating the covariance of large scale structure probes. In this paper we
investigate the concepts of internal covariance estimation in the context of
cosmic shear two-point statistics. We demonstrate how to use log-normal
simulations of the convergence field and the corresponding shear field to carry
out realistic tests of internal covariance estimators and find that most
estimators such as jackknife or sub-sample covariance can reach a satisfactory
compromise between bias and variance of the estimated covariance.
In a forecast for the complete, 5-year DES survey we show that internally
estimated covariance matrices can provide a large fraction of the true
uncertainties on cosmological parameters in a 2D cosmic shear analysis. The
volume inside contours of constant likelihood in the -
plane as measured with internally estimated covariance matrices is on average
of the volume derived from the true covariance matrix. The
uncertainty on the parameter combination derived from internally estimated covariances is of
the true uncertainty.Comment: submitted to mnra
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