A novel wideband DOA estimation method using direction-free focusing matrix

Bo, Liankun; Xiong, Jie; Luo, Lai-yuan

doi:10.1109/iccsnt.2013.6967287

Cited by 9 publications

(5 citation statements)

References 12 publications

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“…In CSM, rotational signal subspace (RSS) method is one popular way [2], whose focusing matrices are generated by minimising a Frobenius norm of the array manifold errors

\begin{matrix} right leftthickmathspace.5em \\ \underset{P_{n}}{truemin} ∥ A_{0} (bold-italicθ) - P_{n} A_{n} (bold-italicθ) ∥_{F} \\ normals . normalt . P_{n} P_{n}^{H} = bold-italicI \end{matrix}

where the focusing matrix

{bold-italicP}_{n}

should be an unitary matrix. Then, we have [8]

{bold-italicP}_{n} = {bold-italicU}_{n}^{normalr} false({bold-italicU}_{n}^{normall} false)^{normalH}

where

{bold-italicU}_{n}^{normall}

and

{bold-italicU}_{n}^{normalr}

are the left and right singular vectors of the matrix

Z = {bold-italicA}_{n} false(θ false) {bold-italicA}_{0} false(θ false)^{normalH}

, respectively. Accordingly, the focusing product at the n th frequency is be expressed

{bold-italicY}_{n} = {bold-italicP}_{n} <...>

…”

Section: A Novel Methods For Wideband Doa Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Wideband DOA estimation with deficient snapshots using low rank Toeplitz structure

2019

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In array signal processing, most existing direction-of-arrival (DOA) estimation methods fail to work given deficient snapshots. To solve this problem, this Letter proposes a novel wideband DOA estimation technique by utilising the sparse representation in terms of the low rank Toeplitz structure presented in uniform array geometries, followed by an enhanced MUSIC method. Specifically, each sub-band segment is first focused into the reference frequency band to collect the coherent covariance matrix even in the lack of sufficient samples. Then, the covariance matrix is denoised through a structure-based sparse reconstruction, which exploits the low rank Toeplitz structure. Finally, the DOAs is efficiently estimated via an enhanced MUSIC method. Simulation result confirms the efficacy of the proposed method that works well in MIMO and radar applications.

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“…In CSM, rotational signal subspace (RSS) method is one popular way [2], whose focusing matrices are generated by minimising a Frobenius norm of the array manifold errors

\begin{matrix} right leftthickmathspace.5em \\ \underset{P_{n}}{truemin} ∥ A_{0} (bold-italicθ) - P_{n} A_{n} (bold-italicθ) ∥_{F} \\ normals . normalt . P_{n} P_{n}^{H} = bold-italicI \end{matrix}

where the focusing matrix

{bold-italicP}_{n}

should be an unitary matrix. Then, we have [8]

{bold-italicP}_{n} = {bold-italicU}_{n}^{normalr} false({bold-italicU}_{n}^{normall} false)^{normalH}

where

{bold-italicU}_{n}^{normall}

and

{bold-italicU}_{n}^{normalr}

are the left and right singular vectors of the matrix

Z = {bold-italicA}_{n} false(θ false) {bold-italicA}_{0} false(θ false)^{normalH}

, respectively. Accordingly, the focusing product at the n th frequency is be expressed

{bold-italicY}_{n} = {bold-italicP}_{n} <...>

…”

Section: A Novel Methods For Wideband Doa Estimationmentioning

confidence: 99%

“…Estimation of u :û; 1: Fix the focusing frequency f 0 ; 2: Obtain the focusing matrices (8) and 9; 3: Compute Y n = P n X n ; 4: CalculateR by (15); 5: ComputeR w :R w =R − diag(l W )I;…”

Section: Inputmentioning

confidence: 99%

Wideband DOA estimation with deficient snapshots using low rank Toeplitz structure

2019

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“…It is known that the CSM, which is a classic way of wideband signal processing [ 31 ], can lead to less complexity and better DOA estimation performance. The key point of CSM is to design focusing matrices

, whose purpose are to transform the manifold matrices at frequencies

to that at the pre-selected reference frequency

as follows [ 32 ]

where

denotes the virtual array manifold matrix at the referenced frequency

. Note that rotational signal subspace (RSS) method is a well known way of CSM [ 13 ], whose focusing matrices

are gained through minimizing a Frobenius norm of the obtained virtual array manifold errors

where

should be a unitary matrix, yielding [ 33 ]

…”

Section: Wideband Signal Processing Using Virtual Arraymentioning

confidence: 99%

Underdetermined DOA Estimation for Wideband Signals via Focused Atomic Norm Minimization

Shi

Zhang

Tan

et al. 2020

Entropy

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In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

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“…This method can achieve high accuracy in a high SNR, but in a low SNR, the accuracy of the algorithm may be greatly affected, and this method cannot effectively deal with the problem of coherent sources [ 32 ]. Moreover, another algorithm, known as the coherent signal subspace method (CSSM) [ 33 , 34 , 35 , 36 , 37 ], is often proposed, which focuses the signal subspace at multiple frequencies to the signal subspace at the reference frequency by constructing a focus matrix and summing these focused covariance matrices to construct a single correlation matrix, after which a high-precision narrowband DOA estimation algorithm can be applied to this covariance matrix to obtain the final estimated value. This algorithm achieves great performance in the case of low SNR, and the process of averaging after focusing can reduce the coherence coefficient between signals.…”

Section: Introductionmentioning

confidence: 99%

Direction of Arrival Estimation of Coherent Wideband Sources Using Nested Array

Tang

Deng

et al. 2023

Sensors

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Due to their ability to achieve higher DOA estimation accuracy and larger degrees of freedom (DOF) using a fixed number of antennas, sparse arrays, etc., nested and coprime arrays have attracted a lot of attention in relation to research into direction of arrival (DOA) estimation. However, the usage of the sparse array is based on the assumption that the signals are independent of each other, which is hard to guarantee in practice due to the complex propagation environment. To address the challenge of sparse arrays struggling to handle coherent wideband signals, we propose the following method. Firstly, we exploit the coherent signal subspace method (CSSM) to focus the wideband signals on the reference frequency and assist in the decorrelation process, which can be implemented without any pre-estimations. Then, we virtualize the covariance matrix of sparse array due to the decorrelation operation. Next, an enhanced spatial smoothing algorithm is applied to make full use of the information available in the data covariance matrix, as well as to improve the decorrelation effect, after which stage the multiple signal classification (MUSIC) algorithm is used to obtain DOA estimations. In the simulation, with reference to the root mean square error (RMSE) that varies in tandem with the signal-to-noise ratio (SNR), the algorithm achieves satisfactory results compared to other state-of-the-art algorithms, including sparse arrays using the traditional incoherent signal subspace method (ISSM), the coherent signal subspace method (CSSM), spatial smoothing algorithms, etc. Furthermore, the proposed method is also validated via real data tests, and the error value is only 0.2 degrees in real data tests, which is lower than those of the other methods in real data tests.

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A novel wideband DOA estimation method using direction-free focusing matrix

Cited by 9 publications

References 12 publications

Wideband DOA estimation with deficient snapshots using low rank Toeplitz structure

Wideband DOA estimation with deficient snapshots using low rank Toeplitz structure

Underdetermined DOA Estimation for Wideband Signals via Focused Atomic Norm Minimization

Direction of Arrival Estimation of Coherent Wideband Sources Using Nested Array

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