6,719 research outputs found
Grid-free compressive beamforming
The direction-of-arrival (DOA) estimation problem involves the localization
of a few sources from a limited number of observations on an array of sensors,
thus it can be formulated as a sparse signal reconstruction problem and solved
efficiently with compressive sensing (CS) to achieve high-resolution imaging.
On a discrete angular grid, the CS reconstruction degrades due to basis
mismatch when the DOAs do not coincide with the angular directions on the grid.
To overcome this limitation, a continuous formulation of the DOA problem is
employed and an optimization procedure is introduced, which promotes sparsity
on a continuous optimization variable. The DOA estimation problem with
infinitely many unknowns, i.e., source locations and amplitudes, is solved over
a few optimization variables with semidefinite programming. The grid-free CS
reconstruction provides high-resolution imaging even with non-uniform arrays,
single-snapshot data and under noisy conditions as demonstrated on experimental
towed array data.Comment: 14 pages, 8 figures, journal pape
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
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
Stochastic framework for evaluating the effect of displaced antenna elements on DOA estimation
We establish a statistical framework for investigating the influence of correlated random displacements of antenna elements in a uniform circular antenna array (UCA) on the distribution of direction-of-arrival (DOA) estimates. More specifically, we apply a stochastic collocation method formodeling the sparse UCA root-MUSIC-DOA estimates as polynomial expansions of the random displacements. Compared to Monte-Carlo simulations, this approach yields a speedup of about 40 for the case of a displacement of two antenna elements
On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization
The use of multichannel data in line spectral estimation (or frequency
estimation) is common for improving the estimation accuracy in array
processing, structural health monitoring, wireless communications, and more.
Recently proposed atomic norm methods have attracted considerable attention due
to their provable superiority in accuracy, flexibility and robustness compared
with conventional approaches. In this paper, we analyze atomic norm
minimization for multichannel frequency estimation from noiseless compressive
data, showing that the sample size per channel that ensures exact estimation
decreases with the increase of the number of channels under mild conditions. In
particular, given channels, order samples per channel, selected randomly from
equispaced samples, suffice to ensure with high probability exact
estimation of frequencies that are normalized and mutually separated by at
least . Numerical results are provided corroborating our analysis.Comment: 14 pages, double column, to appear in IEEE Trans. Information Theor
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