基于Toeplitz協(xié)方差矩陣重構(gòu)的互質(zhì)陣列DOA估計方法

孫兵; 阮懷林; 吳晨曦; 鐘華

doi:10.11999/JEIT181041

基于Toeplitz協(xié)方差矩陣重構(gòu)的互質(zhì)陣列DOA估計方法

doi: 10.11999/JEIT181041

國防科技大學(xué)電子對抗學(xué)院合肥 230037

基金項目: 國家自然科學(xué)基金(61171170)，安徽省自然科學(xué)基金(1408085QF115)

詳細(xì)信息

作者簡介:
孫兵：男，1991年生，博士生，研究方向為空間信息處理、雷達(dá)及雷達(dá)對抗理論與技術(shù)

阮懷林：男，1964年生，教授，博士生導(dǎo)師，主要研究方向為空間信息處理、雷達(dá)及雷達(dá)對抗理論與技術(shù)、壓縮感知理論

吳晨曦：男，1988年生，講師，博士生，研究方向為陣列信號處理、稀疏重構(gòu)技術(shù)

鐘華：男，1991年生，博士生，研究方向為陣列信號處理

通訊作者:
阮懷林　13721052122@163.com

中圖分類號: TN911.23
計量
- 文章訪問數(shù): 2848
- HTML全文瀏覽量: 1542
- PDF下載量: 156
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2018-11-14
- 修回日期: 2019-03-14
- 網(wǎng)絡(luò)出版日期: 2019-04-13
- 刊出日期: 2019-08-01

Direction of Arrival Estimation with Coprime Array Based on Toeplitz Covariance Matrix Reconstruction

College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China

Funds: The National Natural Science Foundation of China (61171170), The Anhui Province Natural Science Foundation (1408085QF115)

摘要

摘要: 針對基于互質(zhì)陣列的欠定DOA估計方法對于虛擬陣元非連續(xù)部分利用率不高的問題，該文提出一種基于Toeplitz協(xié)方差矩陣重構(gòu)的DOA估計方法。首先，從互質(zhì)陣列差聯(lián)合陣的角度分析虛擬陣元分布特性，結(jié)合其與協(xié)方差矩陣中各元素得到的波程差存在對應(yīng)關(guān)系，將協(xié)方差矩陣進(jìn)行擴(kuò)展得到一個數(shù)據(jù)缺失的高維協(xié)方差矩陣；然后，根據(jù)矩陣填充理論，用跡范數(shù)代替秩范數(shù)進(jìn)行松弛，對缺失元素進(jìn)行填充；最后，利用現(xiàn)有root-MUSIC方法進(jìn)行DOA估計。理論分析和仿真結(jié)果表明，該方法提升了虛擬陣元的利用率，從而增加了虛擬孔徑和可估計信號數(shù)，同時無需對角度域進(jìn)行離散化處理，有效消除了模型失配的影響，并且避免了正則化參數(shù)選取問題，提高了估計精度和分辨率。
- 波達(dá)方向估計 /
- 互質(zhì)陣列 /
- 差聯(lián)合陣列 /
- 矩陣重構(gòu)
Abstract: In order to improve the utilization of non-contiguous virtual array elements in the underdetermined DOA estimation of the coprime array, a DOA estimation method based on Toeplitz covariance matrix reconstruction is proposed. First, the virtual array element distribution characteristics of the matrix are analyzed from the perspective of the difference coarray. Additionally, according to the correspondence between the difference coarray and the wave path difference, the covariance matrix is extended to a Toeplitz array covariance matrix, of which some elements are zero. Then, the Toeplitz matrix is recovered to the full covariance matrix according to the low rank matrix completion theory. Finally, the root-MUSIC method is employed for the DOA estimation. Theoretical analysis and simulation results show that this method can increase the number of the resolvable signals by increasing the number of virtual array elements, eliminate the effect of the off-grid effect without discretization of the angle domain, and avoid regularization parameter selection. Therefore, the estimation accuracy and resolution are improved.
- Direction Of Arrival (DOA) /
- Coprime array /
- Difference coarray /
- Matrix reconstruction

HTML全文

圖 1 互質(zhì)陣列示意圖

下載: 全尺寸圖片幻燈片

圖 2 差聯(lián)合陣示意圖

下載: 全尺寸圖片幻燈片

圖 3 可估計信號數(shù)目比較

下載: 全尺寸圖片幻燈片

圖 4 分辨率比較

下載: 全尺寸圖片幻燈片

圖 5 信噪比對角度均方根誤差影響

下載: 全尺寸圖片幻燈片

圖 6 快拍數(shù)對角度均方根誤差影響

下載: 全尺寸圖片幻燈片

圖 7 運(yùn)算時間隨信號數(shù)變化

下載: 全尺寸圖片幻燈片

參考文獻(xiàn)(21)

VAIDYANATHAN P P and PAL P. Sparse sensing with co-prime samplers and arrays[J]. IEEE Transactions on Signal Processing, 2011, 59(2): 573–586. doi: 10.1109/TSP.2010.2089682

LIU Chunlin and VAIDYANATHAN P P. Remarks on the spatial smoothing step in coarray MUSIC[J]. IEEE Signal Processing Letters, 2015, 22(9): 1438–1442. doi: 10.1109/LSP.2015.2409153

LIU Jing, ZHOU Weidong, HUANG Defeng, et al. Covariance matrix based fast smoothed sparse DOA estimation with partly calibrated array[J]. AEU International Journal of Electronics and Communications, 2018, 84: 8–12. doi: 10.1016/j.aeue.2017.10.026

ALQADAH H F and SCHOLNIK D P. Stable DOA estimation with sparse sensor arrays[C]. 2017 IEEE Radar Conference, Washington, USA, 2017: 803–808.

趙季紅, 馬兆恬, 曲樺, 等. 沖擊噪聲下基于矩陣預(yù)處理的稀疏重構(gòu)DoA估計[J]. 電子與信息學(xué)報, 2018, 40(3): 670–675. doi: 10.11999/JEIT170371

ZHAO Jihong, MA Zhaotian, QU Hua, et al. DoA estimation based on matrix preconditioning through sparse reconstruction in impulsive noise[J]. Journal of Electronics &Information Technology, 2018, 40(3): 670–675. doi: 10.11999/JEIT170371

蔡晶晶, 宗汝, 蔡輝. 基于空域平滑稀疏重構(gòu)的DOA估計算法[J]. 電子與信息學(xué)報, 2016, 38(1): 168–173. doi: 10.11999/JEIT150538

CAI Jingjing, ZONG Ru, and CAI Hui. DOA estimation via sparse representation of the smoothed array covariance matrix[J]. Journal of Electronics &Information Technology, 2016, 38(1): 168–173. doi: 10.11999/JEIT150538

LV Wanghan, WANG Huali, LIU Feng, et al. Wideband DOA estimation based on co-prime arrays with sub-Nyquist sampling[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2016, E99-A(9): 1717–1720. doi: 10.1587/transfun.E99.A.1717

SHEN Qing, CUI Wei, LIU Wei, et al. Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept[J]. Signal Processing, 2017, 130: 299–304. doi: 10.1016/j.sigpro.2016.07.022

CAI Jingjing, LIU Wei, ZONG Ru, et al. Sparse array extension for non-circular signals with subspace and compressive sensing based DOA estimation methods[J]. Signal Processing, 2018, 145: 59–67. doi: 10.1016/j.sigpro.2017.11.012

CHI Yuejie, SCHARF L L, PEZESHKI A, et al. Sensitivity to basis mismatch in compressed sensing[J]. IEEE Transactions on Signal Processing, 2011, 59(5): 2182–2195. doi: 10.1109/TSP.2011.2112650

LI Yuanxin and CHI Yuejie. Compressive parameter estimation with multiple measurement vectors via structured low-rank covariance estimation[C]. 2014 IEEE Workshop on Statistical Signal Processing, Gold Coast, Australia, 2014: 384–387.

RAMIREZ J and KROLIK J. Multiple source localization with moving co-prime arrays[C]. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, Australia, 2015: 2374–2378.

BOUDAHER E, JIA Yong, AHMAD F, et al. Multi-frequency co-prime arrays for high-resolution direction-of-arrival estimation[J]. IEEE Transactions on Signal Processing, 2015, 63(14): 3797–3808. doi: 10.1109/TSP.2015.2432734

BOUDAHER E, AHMAD F, and AMIN M G. Sparsity-based extrapolation for direction-of-arrival estimation using co-prime arrays[C]. Proceedings of SPIE 9857, Compressive Sensing V: from Diverse Modalities to Big Data Analytics, Baltimore, USA, 2016: 98570M.

王洪雁, 房云飛, 裴炳南. 基于矩陣補(bǔ)全的二階統(tǒng)計量重構(gòu)DOA估計方法[J]. 電子與信息學(xué)報, 2018, 40(6): 1383–1389. doi: 10.11999/JEIT170826

WANG Hongyan, FANG Yunfei, and PEI Bingnan. Matrix completion based second order statistic reconstruction DOA estimation method[J]. Journal of Electronics &Information Technology, 2018, 40(6): 1383–1389. doi: 10.11999/JEIT170826

CHEN Caihua, HE Bingsheng, and YUAN Xiaoming. Matrix completion via an alternating direction method[J]. IMA Journal of Numerical Analysis, 2012, 32(1): 227–245. doi: 10.1093/imanum/drq039

MA Shiqian, GOLDFARB D, and CHEN Lifeng. Fixed point and Bregman iterative methods for matrix rank minimization[J]. Mathematical Programming, 2011, 128(1/2): 321–353. doi: 10.1007/s10107-009-0306-5

LI Bo and PETROPULU A. Spectrum sharing between matrix completion based MIMO radars and a MIMO communication system[C]. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, Australia, 2015: 2444–2448.

HU Yao, ZHANG Debing, YE Jieping, et al. Fast and accurate matrix completion via truncated nuclear norm regularization[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(9): 2117–2130. doi: 10.1109/TPAMI.2012.271

WU Xiaohuan, ZHU Weiping, and YAN Jun. A Toeplitz covariance matrix reconstruction approach for direction-of-arrival estimation[J]. IEEE Transactions on Vehicular Technology, 2017, 66(9): 8223–8237. doi: 10.1109/TVT.2017.2695226

LIU Zhangmeng, HUANG Zhitao, and ZHOU Yiyu. Sparsity-inducing direction finding for narrowband and wideband signals based on array covariance vectors[J]. IEEE Transactions on Wireless Communications, 2013, 12(8): 1–12. doi: 10.1109/TWC.2013.071113.121305

相關(guān)文章

施引文獻(xiàn)

資源附件(0)

訪問統(tǒng)計