Direction-of-Arrival Estimation With ULA: A Spatial Annihilating Filter Reconstruction Perspective

Pan, Yujian; Jin, Huayan; Cao, Wenhui

doi:10.1109/access.2018.2828799

Cited by 9 publications

(15 citation statements)

References 27 publications

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“…Now we need to reconstruct the filter h by solving the optimization problem in (25). Although the first constraint in ( 25) is nonlinear with h and there is another unknown vector variable ν in the optimization problem, ( 25) is able to be perfectly solved by the MMV-STLN approach [30] which is a variation of the classical STLN approach [33]- [35].…”

Section: Filter Reconstruction For Wideband Doa Estimationmentioning

confidence: 99%

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Wideband Direction-of-Arrival Estimation With Arbitrary Array via Coherent Annihilating

et al. 2019

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In this paper, a new wideband DOA estimation method for arbitrary array application is proposed. The arbitrary array manifold is approximately decomposed under the concept of manifold separation technique (MST) and a linear combination of the equal interval sampling complex exponentials (EISCE) can be synthesized. Since the EISCEs at all frequencies contain the same DOA information, they can be annihilated by the same spatial annihilating filter. So, the coherent annihilating scheme is proposed, and all narrowband components are coherently combined to construct an optimization problem under the structural total least squares framework. During the optimization problem construction, the general solution method is proposed to enable the model approximation error in MST to be reduced to a negligible level. Finally, the optimization problem is solved through the multiple measurement vectors structural total least norm (MMV-STLN) approach and the DOAs are estimated from the reconstructed spatial annihilating filter. The new method is free of frequency focusing and is capable of handling both incoherent and coherent signals.The simulation results verify that the proposed method surpasses the existing methods largely in resolution and estimation performance under the low SNR, snapshot deficient, and closely spaced sources scenarios.INDEX TERMS Coherent annihilating, general solution method, low SNR and snapshot deficient scenarios, multiple measurement vectors structural total least norm (MMV-STLN), wideband direction-of-arrival (DOA) estimation.

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Section: Filter Reconstruction For Wideband Doa Estimationmentioning

confidence: 99%

“…3) Start the iteration calculation, and in each iteration solve the stand linear equality constrained LS problem in (27) and update h and ν through (28). 4) Estimate the DOAs using (30) after the convergence of the iteration.…”

Section: Filter Reconstruction For Wideband Doa Estimationmentioning

confidence: 99%

Wideband Direction-of-Arrival Estimation With Arbitrary Array via Coherent Annihilating

et al. 2019

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“…Since x[n] in ( 7) can be seen as the output of the virtual array with Vandermonde manifold, it can be annihilated by a spatial annihilating filter and the DOAs can be obtained from the filter coefficients [21]. Consider filter whose coefficient vector is denoted by…”

Section: Spatial Annihilating For Mst Modelmentioning

confidence: 99%

“…Nevertheless, that method requires the pseudoinverse of the array sampling matrix therein should be a left inverse, which means the array sampling matrix cannot be a fat matrix (more columns than rows) and will limit the order of the Fourier basis, leading to a non-negligible model truncation error. Spatial annihilating filter reconstruction is another DOA estimation method originally designed for ULA and it is equivalent to the deterministic maximum likelihood (DML) estimator of DOA [20], which ensures that it performs well both for coherent sources and under low SNR and limited snapshots scenarios [21]. In this paper, we extend the spatial annihilating filter reconstruction method to the arbitrary array.…”

Section: Introductionmentioning

confidence: 99%

Direction-of-Arrival Estimation for Arbitrary Array: Combining Spatial Annihilating and Manifold Separation

Pan¹,

Zhang²,

Qi³

2019

RADIOENGINEERING

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In this paper, we address the problem of directionof-arrival (DOA) estimation with the arbitrary array. The manifold separation technique (MST) is employed to transform the arbitrary array into a virtual array with Vandermonde manifold on which the spatial annihilating filter reconstruction method can be applied. When building the optimization problem for annihilating filter reconstruction, we propose the general solution modeling which can reduce the truncation error in MST to a negligible level. Finally, the spatial annihilating filter is reconstructed under the structural total least square (STLS) framework with the multiple measurement vectors structural total least norm (MMV-STLN) approach and the DOAs are estimated from the filter coefficients. Numerical simulations have verified the new proposed method adapts well to the low signal-to-noise ratio (SNR), limited snapshots and closely-spaced sources scenarios and can handle the coherent signals.

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“…In structured EIV problems, the regression matrix has a given structure that depends on the problem formulation. Hankel, Toeplitz, or other application-specific matrices appear in problems of metrology Markovsky (2015), system 5 identification Söderström (2007), image restoration Feiz and Rezghi (2017), nuclear magnetic resonance spectroscopy Cai et al (2016), direction-of-arrival estimation Pan et al (2018), and time-of-arrival estimation Jia et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Bias and covariance of the least squares estimate in a structured errors-in-variables problem

Quintana-Carapia

Markovsky

Pintelon

et al. 2020

Computational Statistics & Data Analysis

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A structured errors-in-variables (EIV) problem arising in metrology is studied. The observations of a sensor response are subject to perturbation. The input estimation from the transient response leads to a structured EIV problem. Total least squares (TLS) is a typical estimation method to solve EIV problems. The TLS estimator of an EIV problem is consistent, and can be computed efficiently when the perturbations have zero mean, and are independently and identically distributed (i.i.d). If the perturbation is additionally Gaussian, the TLS solution coincides with maximum-likelihood (ML). However, the computational complexity of structured TLS and total ML prevents their real-time implementation. The least-squares (LS) estimator offers a suboptimal but simple recursive solution to structured EIV problems with correlation, but the statistical properties of the LS estimator are unknown. To know the LS estimate uncertainty in EIV problems, either structured or not, to provide confidence bounds for the estimation uncertainty, and to find the difference from the optimal solutions, the bias and variance of the LS estimates should be quantified.Expressions to predict the bias and variance of LS estimators applied to unstructured and structured EIV problems are derived. The predicted bias and variance quantify the statistical properties of the LS estimate and give an approximation of the uncertainty and the mean squared error for comparison to the Cramér-Rao lower bound of the structured EIV problem.

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Direction-of-Arrival Estimation With ULA: A Spatial Annihilating Filter Reconstruction Perspective

Cited by 9 publications

References 27 publications

Wideband Direction-of-Arrival Estimation With Arbitrary Array via Coherent Annihilating

Wideband Direction-of-Arrival Estimation With Arbitrary Array via Coherent Annihilating

Direction-of-Arrival Estimation for Arbitrary Array: Combining Spatial Annihilating and Manifold Separation

Bias and covariance of the least squares estimate in a structured errors-in-variables problem

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